Vincent Maisonneuve

Dr Mathieu Allix

Dr Michael J Pitcher

me this opportunity in joining the CERAM group and work as a part of the team, also for their supervision and their presence in tough times when I needed their

office of stressed people". Thank you for operating all the TEM measurements, your topnotch experience was really handy in bringing the most information possible to complete the analysis of my different materials especially the amazing STEM-EDS maps you provided for the lanagsite materials project. Thank very much you for your continuous support.

-To Sandra Ory: Thank you for operating all the DSC measurements even in short notice times 🥺. Having nearby offices was a hell of an experience that made my stay at CEMHTI a very memorable one.

-To Weiwei Cao: Or Dr. Cao I should say. I can't thank you enough for all the advices you gave me about how to optimise my synthesis using the ADL given your wide experience.

I wish you all the best in your future career whatever you end up doing.

-To Alessio Zandona: Grazie mille for all the knowledge you brought to the team, and the project we shared together, it was an enjoyable experience working with you. I much liked your human side as you were always there to hear me out.

-To Xue Fang, Renaud Valois, Euan Duncun and Jan Baborak: Thank you for sharing your time with me and reminding me every day how stupid my jokes can be, really appreciate it guys 👍😂. I'm pretty sure you all will be doctors of philosophy in the near future.

I would like to give special thanks to: Yannick Ledemi, Sébastien Chenu, Olivier Hernandez, Alberto José Fernandez-Carrion, Přemysl Beran, Matthew Dyer, Stanislav Savvin, Emmanuelle Suard, Dominique Massiot, Vincent Sarou-Kanian, Franck Fayon and Leire Del-Campo for paying attention to my questions and being part of my research work. Many thanks also to all the other PhD students in the CEMHTI laboratory for the many laughs we had together and the time spent arguing about dumb stuff. I present my sincere gratitude and appreciation to my mother Assia, my father Hassan, my sister Chaymae and my brother Youness for always being by my side and their endless support and never-ending love, even though they are far from me.

To my best mates Yassine Hbiriq (H), Babacar Diallo (babou), Salah Eddine EL Abbadi (momo), Houssine El Barkali, Othmane Noussair (Hit-man). I could not of done this without your tremendous support.

After three years of hard work, dedication, pure passion, sacrifices, my story as a PhD student in the CEMHTI laboratory has reached its final chapter. Many memories are crossing my mind while writing this, obviously there were highs and lows, but I can't express how much I loved the experience and would definitely do it all over again if I had the chance to, with the same energy, conviction and most importantly the same passion.

General introduction

Design and development of new materials is much needed in today's society for various different application types: medical [1]- [6], energy storage and conversion [7]- [10], industrial [11], [12] and security [13]. Recent works have demonstrated the possibility of computationally probing a particular property and then synthesising the material itself [14]- [17]. However, one of the major obstacles relates to the synthesis approach to achieve these materials. At the CEMHTI laboratory, a unique synthesis path of metastable materials is approached: crystallisation from glass or the under-cooled melt. The use of aerodynamic levitation coupled to two CO2 lasers (described in appendices Chapter A.I section A.I.1.1.2) at high temperatures allows samples to be melted at temperatures as high as 3000°C; the setup also affords rapid cooling rates reaching almost 1000°C/s (depending on the material and the carrier gas). This process grants the occurrence of either glass or the direct crystallisation of materials from an under-cooled melt. Additionally, in the case of achieving glass samples, crystallisation can be induced by an appropriate heat treatment at relatively low temperatures. This can produce new materials, for example glass crystallisation allowed the discovery of the first fully crystallised BaAl4O7 transparent ceramic material with two new polymorphs, unattainable by conventional ceramic methods [18].

The context of the present work follows previous PhD student projects in the CEMHTI laboratory who used aerodynamic levitation to develop new polycrystalline transparent ceramic materials in different systems, including aluminates, strontium aluminosilicates, rare earth gallates…etc., where precursor glasses can be formed by the aerodynamic levitation method. This thesis will focus on the synthesis and multi-scale characterisation of two main materials classes:

(i)
Materials for optics: Chapter II and Chapter III.

(ii) Ionic conducting materials for energy application such as solid oxide fuel cells:

Chapter IV and Chapter V.

Chapter I sets the state of the art for the discussed materials in the following chapters. This chapter also describes different alternative synthesis pathways to the conventional ceramic routes to reach for new metastable materials. Several examples of new materials made at the CEMHTI laboratory by crystallisation from glass or an under-cooled melt are given.

Chapter II follows on from Marina Boyer's thesis work (University of Orléans, 2016) on the SrREGa3O7 (RE for rare earth) melilite compounds, during which she discovered a new melilite superstructure crystallising in an orthorhombic supercell for small rare earths RE= [Ho -Yb].

She was also able to synthesise some of these melilite materials as bulk transparent ceramics.

This chapter reports investigations on extending the synthesis limits of this new melilite polymorph but also for the parent tetragonal melilite subcell to small lanthanides, with a detailed structural study of both polymorphs. Additionally, the stability of both melilite structures against temperature is also reported. Finally, the photoluminescence properties are investigated and compared between the glass, parent and superstructured melilites of the same composition.

In Chapter III, a new solid solution Ca3Ga2-2xZnxGe4+xO14 crystallising in the langasite structure family (S.G. P321), which is a melilite related mineral, is investigated by two synthesis processes: glass and melt crystallisation. By refining the synthesis route via a metastable precursor (i.e. glass or melt), the trigonal langasite structure is stabilised all the way to the Ca3ZnGe5O14 (x = 1) compound previously reported to crystallise in a distorted monoclinic C2 cell by single crystal growth methods. The interest of investigating this solid solution is motivated by previous works at the CEMTI laboratory on the Zn1+xGa2-2xGexO4 spinel solid solution, which exhibited interesting long-lasting red luminescence when functionalised by Cr 3+ [19], but also nanoscale phase separation in the parent glass leading to transparent ceramic materials by controlled crystallisation in the Na2O-ZnO-Ga2O3-GeO2

phase system [20]. Moreover, one of the main interests in this work is the characterisation of crystallographic ordering between three isoelectronic cations Zn 2+ , Ga 3+ and Ge 4+ over three different crystallographic sites. To fulfil this task, a combined analysis against SPD, NPD and ss-NMR data was first adopted for the x = 0 and 1 end members. Furthermore, to build a chemically justified model for intermediate compositions such as x = 0.5, an innovative and unique approach was adapted by quantifying the cationic sites occupancies from a full twodimensional signal refinement of acquired atomic resolution STEM-EDS maps for each cation.

Both Chapters IV and V focus on the synthesis of new doped melilite materials with ionic conduction properties for potential SOFC applications. The discovery by J. Fan et al. [21], of the alkali free La2Ga3O7.5 (x = 1) end member which crystallises from an under-cooled melt using the ADL apparatus, and adopts a melilite Ima2 super cell (√2𝑎 × √2𝑏 × 2𝑐), suggested the possibility of increasing the lanthanum doping amounts in the La1+xBa1-xGa3O7+x/2 solid solution, previously set at x = 0.35 attainable by solid state reaction, and motivated the work presented in Chapter IV. Therefore, by crystallising an under-cooled melt of La1+xBa1-xGa3O7+x/2 (0.3 ≤ x < 1) composition, the synthesis of the whole solid solution series is investigated, while setting the x stability limits between the parent tetragonal (P4 ̅ 21m) and orthorhombic (Ima2) melilites. The structural trend is studied by SPD measurement across the whole solid solution compositions, while the cationic and anionic distribution are characterised by NPD measurements at room and high temperatures. To study the electric properties of these materials, AC impedance spectroscopy measurements were used, revealing the high ionic conductivity of these materials, almost equalling the best known melilite conductors [22], [23].

Chapter V on the other hand presents the study of a melilite-like material, Ca5Ga6O14, which possesses the same melilite [GaO4]n infinite 2D framework layers stacked antiparallel with different positioning of the A-sites. In this chapter, the study consists of first defining the most energetically favourable doping aliovalent cation by DFT calculation, then synthesising the doped compound and defining its doping limits by multiple synthesis approaches. The structural characterisation of both doped and parent compounds is reported by coupling SPD, NPD and TEM characterisation techniques. One of the strongest aspects of this work is exploiting the characterisation techniques to their sensitivity limits, as of due to the quite low doping amounts, with only 0.89% of introduced interstitial oxides (to keep a charge balanced composition), makes the determination of their position in the cell particularly hard to resolve with diffraction techniques. Therefore, DFT calculations were used to identify the most energetically favourable position of the interstitial oxide, which helps to interpret the observed results from previous analysis techniques. Ionic conductivity investigations by AC-impedance on SPS-densified pellets of the maximally-doped and parent samples, showed an increase of two orders of magnitude over the parent material. Nevertheless, even by retaining the same melilite framework, the structural constraints imposed by the [GaO4]n sheets stacking and Asites positioning limited the interstitial oxide distribution over the five-fold pentagonal channels, as opposed to the complete disordered P4 ̅ 21m melilite interstitial oxides framework, which inhibits its ionic conductivity and showed much lower values compared the best melilite conductors.

6

Chapter I: State of the Art Introduction.

Materials science is one of the largest research fields ranging from the synthesis, structural determination to properties characterisation of solids, but most importantly the understanding of the link between these three main axes. This is even more important as the demand of novel high performing materials keep on increasing. Materials science therefore includes aspects of engineering, physics and chemistry, related to fulfil these desired aims [1]. Extended inorganic oxides are one of the many materials science subsets and are usually known to be synthesisable by the oldest, simplest and widely used solid state reactions. For instance, this synthesis route has seen its usage in making a large number of high-Tc superconductor materials [1]. Although this method is quite simple to set up, i.e. mixing the starting materials powder and sinter them for long times at high temperatures, in most cases it leads to the thermodynamically stable products. Hence, reaching for metastable new materials can be facilitated by the development of new synthesis routes. In the following chapter, the state of art is described, considering different alternative synthesis approaches to the conventional ceramic routes. Particular attention is given to crystallisation methods from glass or under-cooled molten liquid precursors, as these two synthesis paths are heavily used in this thesis work. Some key material examples obtained by these two methods are also given for optical applications. A small review of new ionic conducting materials is given at the end of the chapter.

Synthesis of metastable inorganic materials.

The conventional ceramic materials synthesis routes by solid-state reaction are widely spread due to their simplicity and effectiveness in making solids react with each other. They usually operate at high temperatures ranging from 900°C to 1600°C with long sintering times and require sometimes multiple heat treatments with intermediate grinding of the powder mixture, leading to the most thermodynamically stable reaction products [2]. Classic manual powder mixing usually leads to precursors grain size at the micron scale, meaning that atoms from the grains core will need high activation energy to diffuse all the way to the interface and react, which can explain the required high temperatures to reach for full precursors reactions in the solid-state. These synthesis procedures have brought to light many key materials with desirable properties, for example thermal, optical and energy properties [3]- [9]. Despite the wide usage of these synthesis paths, the reactions remain limited by the low diffusion rates of the reactants within a solid even at high temperatures. Nonetheless, demands for high-performing novel materials by consumers, industries, and governments continue to increase; for example, nowadays new materials for energy applications and CO2 storage are highly desirable to reduce the negative impact of energy extraction on the environment. Discovery of inorganic materials with new compositions and crystal structures faces two fundamental problems: (i) how to synthesise materials that may be metastable and thus easily missed by conventional ceramic approaches, and (ii) which compositions to target in the first place. The second problem is approachable by prediction of materials properties and crystal structures, shown to be achievable by computational methods narrowing the targeted compositions and facilitating the heavy task of synthesis exploration in the quest of discovering new materials with more efficient or equally performing properties [10]- [18]. Yet, the ultimate challenge lies in synthesising these compounds, which is not always achievable by conventional routes. Formerly, many new materials were discovered with the intention of systems exploration [19]. Soft chemistry is one of the main known approaches to synthesise both stable and metastable materials at low temperatures. This approach involves two alternative pathways: (i) topochemical, which consists of preparing the parent compound by classic routes and then converting it to a descendant phase by cation exchange, hydrolysis or even redox reactions (see Figure Comparison between conventional and soft chemistry synthesis approaches, redrawn and adapted from [2].

The metastable state of matter by definition is a state whose free energy lies at a local minimum and can be converted to the most thermodynamically stable state when energetically disturbed [20], [21] (see Figure I.2). The key points in making new metastable materials are the initial mixture homogeneity and the diffusion distance that atoms will have to travel within the sample mixture to react and form the target compound, as ensuring a good homogeneity of the mixture while reducing the atoms diffusion distance can considerably lower the synthesis temperature. In fact, this allows to reach for energy local minima, thus probing metastable structures. This can be fulfilled by ball milling the mixture, which helps to substantially reduce the grain size to the nanometre scale. Far better procedures can be adopted by making a gel or glass from the initial composition or even melting the mixture (few compound examples are given in section I.3 and section I.4 of this Chapter). These latter approaches strongly depend on the mixture composition, as they can also be phase separated, in which case crystallisation will result in a multi-phase product. Crystallisation from glass: An innovative concept for achieving new metastable materials.

Commonly the word glass has been linked to inorganic oxides which were successfully cooled from their liquid to solid state without crystallising, hence retaining their amorphous structure [22]. Moreover, different definitions have been given to glass materials in order to best describe the glassy state of this category of compounds [23]- [25]; the latest one to date is as follows: "Glass is a nonequilibrium, non-crystalline condensed state of matter that exhibits a glass transition. The structure of glasses is similar to that of their parent supercooled liquids (SCL), and they spontaneously relax toward the SCL state. Their ultimate fate, in the limit of infinite time, is to crystallize" designated by E. D. Zanotto et. al. [22]. Considering this definition, the metastable state of glass is the major motivation behind choosing it as precursor for crystallisation to reach for new metastable materials.

Oxide glasses are usually synthesised by conventional melt quench approaches, which involve melting at high temperatures and then air or water quenching. However, to prevent the emergence of devitrification, i.e. long-range order, during glass synthesis, the melt cooling rate needs to be high enough to "freeze" or suspend atomic movement going from the liquid to solid state of matter. Moreover, the required cooling rates differ from one composition to another, for example borosilicate glasses are very hard to crystallise [25]. Nevertheless, even with sufficient cooling rates, more than one parameter enters the complex equation of accomplishing oxide glass compounds. The crucial parameter in making glass is the starting composition ability to form a covalently bonded network [25], [26]. Glass-making compositions must contain a network former element (e.g. SiO2) which ensures the formation of strongly bonded long atomic chains [25]. Other components can be found in glass composition such as network modifiers (e.g. B, Ca, Ba, Sr…etc) and network intermediaries (e.g. Al, Ga, Ge…etc). The first ones are usually introduced to modify the glass properties, wheras the latter ones role sits in between network formers and modifer, and can play the role of both [25], [26].

The amorphous state of matter represents a long-range non-periodicity in terms of atomic positions, which is usually linked with topological or chemical disorder. The opposite of crystals which show long-range periodicity of atomic positions (but not always chemical ordering). In oxide glasses, even in the absence of long-range order, local order can be discerned on the length scale of several Angstroms, for example SiO4 tetrahedral units taking part of the SiO2 glass network (see Figure I.3). ) Planar projection of quartz network in its both amorphous and crystalline states respectively, drawn from [24]. c) STM image of a partially crystallised SiO2 film. d) coloured STM image (showed in (c)) highlighting the random distribution of [SiO4]n rings in the amorphous SiO2 vs the well-defined [SiO4]6 rings in the crystallised quartz, from [27].

Glass-ceramic materials are usually attained by partial crystallisation of glass compounds, i.e. a significant fraction of the material remains amorphous. The crystallisation task is usually a two-step process: (i) nucleation (homogeneous or heterogeneous), which typically occurs slightly above the glass transition temperature "Tg", (ii) crystal growth at temperatures superior to Tc (Tc > Tg). These steps are illustrated in Figure I.4. Ideally, to control the crystallite growth and size, homogeneous nucleation is highly desired, as it induces volume crystallisation.

However, this phenomenon is rarely observed in glass-ceramic materials and heterogeneous nucleation is the dominant process, being thermodynamically favoured, i.e. surface crystallisation [25]. Surface or bulk crystallisation mechanisms are highly relevant when it comes to the materials related properties, as they both can lead to different performance of the same material. For a controlled nucleation, the addition of nucleating agents (like TiO2, ZrO2, …etc) have shown to help achieving a volume crystallisation instead of the expected surface crystallisation [28], [29]. This discovery marked a milestone and the start of the glass-ceramic era, as soon after commercial glass-ceramics starting emerging with managed crystallite numbers and sizes. Illustration of the crystallisation process evidencing the temperature depending phenomena of nucleation and crystals growth using a DSC curve. The insert SEM images were taken from [30].

Direct crystallisation from under-cooled melts.

Glass synthesis is not always a successful process, as for some compositions crystallisation might occur on the cooling. Taking advantage of a melt homogeneity in its liquid state and metastable aspect, it is possible to reach for new materials by operating a direct crystallisation from the under-cooled melt. In different words, it means that crystallisation of the melt occurs at temperatures far below the liquidus point on the phase diagram. In this aspect, this procedure can be perceived as an alternative synthesis process to the previously described glass crystallisation process in the hunt for new out of equilibrium materials. Direct crystallisation from the under-cooled liquid operates by heating a sample until reaching its liquid state, then cooling to room temperature using an appropriate (rapid) cooling rate to secure a crystalline compound directly. Moreover, using the ADL apparatus offer the possibility to control the melt's cooling rates, by controlling the lasers power. This was demonstrated in several works as a promising strategy to reach for new metastable crystalline compounds, with new and interesting properties (discussed in the next sections). It is feasible by this approach to synthesise millimetre sized single crystalline domains in certain cases [31]. Nevertheless, it is rather different to conventional single crystal synthesis approaches from the melt (i.e. crystal pulling, directional solidification floating zone, Verneuil technique) [32] in the sense that the crystallisation occurs under conditions that are far from equilibrium.

New materials for optical ceramics.

New materials with optical properties, especially new transparent ceramics, are one of the major research axes of the CERAM group at the CEMHTI laboratory. The aerodynamic levitation coupled to two CO2 lasers offers the possibility to melt samples with melting temperatures as high as 3000°C while levitated by a carrier gas of choice (argon, oxygen, …)

in a contactless process. This procedure allows to reach very high cooling rates (1000°C/s in some cases), but most importantly it prevents impurity contamination that may come from the sample holder, or the formation of crystal nucleation centres from contact points between the sample and the sample holder leading to heterogeneous crystallisation, which permits the family of glass-forming compositions to be enlarged. Operating crystallisation from glass or melt precursors offers a certain degree of control of the crystallised sample microstructure, which is essential in seeking for new transparent ceramic materials as light scattering needs to be minimized. Regarding this aspect, many glass and melt crystallised materials have been reported as transparent ceramics, and even functionalised by rare earth doping, which unveiled interesting emission, scintillation and luminescence properties.

In the BaO-Al2O3 binary system, the BaAl4O7 compound was found to be non-synthesisable by conventional solid state routes [33]. Glass of BaAl4O7 composition was successfully synthesised using aerodynamic levitation coupled to two CO2 lasers. Interestingly, by adopting the right heat treatment it is possible to crystallise this glass sample under two new phase pure α or β orthorhombic polymorphs [33]. Moreover, this composition was also reported as the first highly transparent polycrystalline ceramic (see Figure I.5), achieved by full and congruent crystallisation from a bulk glass [33], with potential optical applications (scintillators, optical lenses, high energy lasers, …). Since this finding, many works have been conducted on polycrystalline ceramic materials crystallised from glass for potential use in optics, photonic or energy fields. Additionally, by substituting Al2O3 for Ga2O3 in the initial mixture, the BaGa4O7 material was reported to be uniquely attainable by a direct crystallisation from the melt route.

This previously unreported compound was described in a monoclinic structure (S.G. I2/m), and displayed strong luminescence in the orange-red region when doped with Eu 3+ and excited under a 393 nm wavelength [34]. All from [33].

Other interesting systems could be the strontium aluminate system, where the glass crystallised Sr3Al2O6 compound exhibits high transparency in the visible range, thanks to its cubic symmetry (S.G. Pa3 ̅ ), no birefringence effects were found (optical isotropy). Moreover, scintillation and emission properties in the visible and infrared ranges were observed when doped with Ce 3+ , Er 3+ and Er 3+ +Ho 3+ respectively [35]. Furthermore, studied solid solutions of strontium alumino-silicates Sr1-x/2Al2-xSixO4 and Sr1+x/2Al2+xSi2-xO8, reported large scale fully transparent bulk ceramics (Figure I.6a and Figure I.6b) with tunable luminescent properties controlled by the related chemical disorder of their crystal structures [36], [37]. The Bi0.8Nb0.8Te2.4O8 compound was successfully crystallised in a large-scale (discs of 60 mm diameter) transparent ceramic by full and congruent crystallisation from a 75TeO2-12.5Nb2O5-12.5Bi2O3 parent glass precursor composition (see Figure I.6c). The same study of this compound has revealed its crystallisation in a new cubic cell (S.G. Fm3 ̅ m) with a transparency in a wider range (3-7 μm) compared to that from the earlier described alumino-silicates solid solutions (4.2 µm) [38]. (60 mm in diameter). The insert inside the disc shows an EBSD-SEM map of the material evidencing crystalline domains sizes. The insert at the bottom right shows a ceramic fibre of the same composition. These figures were taken from [37] and [38].

More recently, in the CEMHTI laboratory, Weiwei Cao former PhD student has operated direct and full crystallisation from the under-cooled liquid as an approach to synthesise highly non-stoichiometric YAG (yttrium aluminium garnet) materials. In the literature the Y3+xAl5-xO12 solid solution was reported with a maximum value of x = 0.03, synthesisable by solid-state reaction [39]. Moreover, this amount was extended to the value of x = 0.40 by W. Cao in her thesis work [40]. The increase of non-stoichiometry in this compound induced a significant population of Y 3+ (< 20 %) on the 6-coordinated 16a sites of the garnet structure (S.G. Ia3 ̅ d) which usually host Al 3+ exclusively. This was detected directly by crystallography rather than the previous indirect analyses of the cell parameters trend and energy calculations [39]- [41]. Interestingly, when non-stoichiometry is introduced, the luminescence properties can be strongly modified compared to the stoichiometric YAG garnet, depending on the coordination preference of the rare earth dopant ions [40].

The melilite compounds have also been studied as potential transparent ceramics by aerodynamic levitation methods. They have a general formula of A2B'(B2O7) which actually groups the åkermanite, Gehlénite, Okayamalite, Hardystonite and Gugiaïteare minerals that crystallise under the same structure family, adopting a tetragonal cell with a symmetry following the P4 ̅ 2 1 m space group (n°113) (Figure I.7). Their structure can be described as stacked sheets along the c-axis, which are formed by corner sharing (B',B)O4 tetrahedra, creating edge-sharing [(B',B)O4]5 pentagonal channels where the A-site cations are held in the centre and in between the structure layers. Since their discovery, the melilite compounds attracted a lot of researchers interest due to their remarkable underlaying B'(B2O7) framework ability to distort, which led to the development of new synthetic melilite compositions, hence enlarging the field of compositions that takes part of this family. In the last century, newly developed melilite compounds showed different phase transitions from their parent tetragonal P4 ̅ 2 1 m structure, with both modulations and supercells [42]- [48]. One of the leading motivations behind developing new melilite compound (especially the ABC3O7 compositions) is because of their impressive properties, with potential applications in the optical, piezoelectric and energy fields [49]- [52]. The (AE,RE)C3O7 melilite compositions where AE is an alkaline earth and RE a rare earth, were reported to manifest interesting transparency in the NIR range.

Moreover, Marina Boyer a former PhD student in the CEMHTI laboratory, reported for the first time the stabilisation of a SrREGa3O7 melilite series with RE= [Eu -Yb] as fully transparent bulk ceramics (Figure I.7c) achieved by congruent crystallisation from glass [53], [54].

However, one of the major limiting transparency factors of these materials is the sample colouration arising from the RE nature. Nevertheless, both SrGdGa3O7 and SrYGa3O7 compositions were also obtained as colourless bulk ceramic samples, showing very high transparency reaching a transmittance of 80% in the NIR region at ⁓ 2700 nm (Figure I.7d) [53], [54]. These (AE,RE)C3O7 composition-type, single-crystal materials, were also reported with promising piezoelectric and elastic properties at high temperatures [51]. and d) panels were taken from [53].

Highly transparent glass-ceramic materials were also obtained by a controlled crystallisation from Na2O-ZnO-Ga2O3-GeO2 systems, where ZnGa2O4 spinel nano-crystals can be found embedded in a GeO2-rich glassy matrix [55]. In this system, the size of nano-crystals is fairly controlled by tuning the amount of Na2O, which is found to not interfere in the crystals compositions but remains in the amorphous matrix. These materials can be easily functionalised by Cr 3+ doping as demonstrated for Zn1+xGa2-2x(Ge/Sn)xO4:Cr 3+ (0 ≤ x ≤ 0.5) solid solution in [56], leading to a considerable improvements of their long-lasting luminescence properties.

Therefore, the occurrence of a high symmetry phase in the same system to potentially play the role of ZnGa2O4 spinels are of interest to investigate for new optically active materials.

Attempts to expand this study and develop new glass-ceramic compounds at nearby compositions has revealed the crystallisation of new langasite-type materials [57]. The A3BC3D2O14 langasite materials family which counts more than 250 members, is a melilite-related mineral. This structure family crystallises in a trigonal P321 cell, where A is an ). These structures were first reported in the CaCO3-Ga2O3-GeO2 ternary system, with the discovery of the Ca3Ga2Ge4O14 compound in 1980 [58], which can be readily produced as transparent materials by single crystals growth methods [59], [60]. Moreover, a few langasite compositions crystallise under a monoclinic C2 polymorph, or undergo a phase transition at high pressure/temperature (P321 → C2) [61]- [63]. Furthermore, langasite compounds have also been reported with compelling luminescence properties, as in the Eu 3+ doped La3Ga5MO14 M= [Zr, Hf, Sn] compound, assumingly promising red-emitting LED phosphors due to their high colour purity and thermal stability [64]. New oxide ion conductor materials.

Research for new renewable energy sources as clean technologies is driven by the motivation of future decarbonisation and limiting planet pollution. In this aspect fuel cells are of interest [START_REF] Irvine | Solid Oxide Fuels Cells: Facts and Figures: Past Present and Future Perspectives for SOFC Technologies[END_REF]. Among the existing fuel cells types (e.g. alkaline fuel cells "AFC", molten carbonate fuel cells "MCFC", …) [START_REF] Larminie | Fuel cell systems explained[END_REF], here we focus on solid oxide fuel cells (SOFCs). In SOFCs, the electrolyte is a dense ceramic material with O 2-anions taking the role of mobile charge carriers.

SOFCs usually operate at temperatures around 1000°C due to the slow oxide ion migration at intermediate temperatures (500°C -750°C). However, at these temperatures their functioning cost is high [START_REF] Wachsman | [END_REF]. Developing new better performing oxide ion conductor materials (i.e. fast ion conduction) at intermediate temperatures will strongly benefit SOFCs in reducing their working temperature, and consequently lowering their functioning cost [START_REF] Wachsman | [END_REF], [68].

SOFCs are composed of a dense solid electrolyte (ceramic), sandwiched between the cathode and the anode, as illustrated in Figure I.9. Oxygen from the atmosphere is reduced at the cathode surface (Equation I.1), and diffuses through the cathode and electrolyte until it reaches the anode, where it is oxidised to H2O (Equation I.2). For all three components the materials choice is crucial for an operating SOFC [69]- [START_REF] Taroco | Ceramic Materials for Solid Oxide Fuel Cells[END_REF]. SOFCs can also operate by proton or dual oxideproton conduction [START_REF] Lu | [END_REF]- [76]; these will not be further discussed, as only oxide ion conductors will be addressed in this thesis. showing its different components, from [START_REF] Taroco | Ceramic Materials for Solid Oxide Fuel Cells[END_REF].

Electrolyte materials.

Development of new oxide electrolyte materials operating at intermediate temperature has tremendously increased in the last century. It has been proven that introducing oxygen defects while leaving the crystal structure as undisturbed as possible is highly preferable in making 20 good oxide ion conductors electrolytes [77]. In the following, a few important oxide-conductors structure-types will be addressed.

Fluorite structured oxides: Since early works of W. Nerst (1900s) on the fluorite structured oxide materials, many studies have been reported on these structure-type materials as potential candidates for oxide ion conductor electrolytes [77], [START_REF] Huang | Solid Oxide Fuel Cell Technology: Principles, Performance and Operations[END_REF]. AO2 fluorite-type oxides crystallise in a cubic motif with the highest symmetry space group (Fm3 ̅ m) where the cations sit in a 4a site and are 8-coordinated, whereas the oxygens are held in the centre of an OA4 tetrahedron (8c site) (see Figure I.10). These materials are usually doped with rare earth or alkaline cations substituting the host A cation, which introduce vacancies into the oxide sublattice, allowing the oxygen to migrate to adjacent (vacant) sites, thus enhancing the ionic conduction mechanism.

Ytrria-stabilized zirconia Zr1-xYxO2-δ (YSZ) are among the best oxygen ion conductors [START_REF] Huang | Solid Oxide Fuel Cell Technology: Principles, Performance and Operations[END_REF] at elevated temperatures, besides the δ-Bi2O3 (i.e. Bi0.75Y0.25O1.5) which exhibits an oxide ion conductivity of ~ 1 S cm -1 at 750°C [START_REF] Takahashi | [END_REF] but is only stable in the temperature range 730°C -824°C [80]. Moreover, Ce1-xMxO2δ M= [Gd, Sm] (GDC and SDC) are strong candidates for use at temperatures as low as 550°C [77] (see Figure I.12).

Perovskite oxides: Perovskite oxides are of interest materials, thanks to their ABO3 structure-type which offers two distinct cation sites that can be both substituted with lower valence cations, thus leading to a wide range of possible perovskite-based oxide ion conducting materials [77] (excluding interstitial oxide containing perovskites). The typical perovskite crystal structure consists on a simple small cubic lattice where the A-and B-sites are 12-and 6-coordinated respectively (see Figure I.10). However, only few oxides crystallise under this cell-type and other distorted perovskite variants are often observed [START_REF] Tatsumi | Perovskite Oxide for Solid Oxide Fuel Cells[END_REF]. Ishihara et al [START_REF] Ishihara | [END_REF] first reported fast oxide-ion conduction in the La1-xSrxGa1-yMgyO3-δ (LSGM) which crystallise in a perovskite cell and reach impressive conductivity values of 8.10 -2 S.cm -1 at 600°C for x = 0.2 (see Figure I.12).

BiMeVOx: The Bi4V2O11 is the parent compound of this solid solution family and represent two reversable structural phase transitions α ↔ β and β ↔ γ, with an ionic conductivity of 0.1 S.cm -1 at T > 550°C attained under the γ polymorph [77], [83]. The γ-Bi4V2O11 structure can be described as an alternated stacking between an A layer, i.e. [Bi2O2] 2+ , and a B layer, i.e.

[VO3.5⧠0.5] 2-, with ⧠ representing oxide ion vacancies (see Figure I.10d). As in the fluoritebased and perovskite-based conductors, oxide vacancies provide fast charge transport at high temperature. To stabilise the γ polymorph at room temperature, usually vanadium substitution is considered by lower valence cations to introduce oxygen vacancies, hence increase the material conductivity at low temperature. For example, the Bi2V1.9Cu0.1O5. 35 (BICUVOX.10) compound is stabilised at room temperature under an incommensurate supercell of the disordered tetragonal γ polymorph, noted γ'. It is only at higher temperatures (⁓ T > 400°C)

that the γ'↔γ phase transition occurs [84]- [86]. The BICUVOX.10 compound showed a considerable increase of its ionic conductivity by almost three orders of magnitude at low temperatures over the Bi4V2O11 parent compound, i.e. 0.5×10 -2 S.cm -1 vs 10 -5 S.cm -1 respectively at 300°C [83].

Apatites:

The A(1)2A( 2

Melilite and melilite-related oxides:

The melilite layered structure was already described in section I. 3. The ionic conductivity in these compounds family is enhanced by the introduction of interstitial oxides (Oint), which is usually fulfilled by aliovalent atoms substitution; for example, in the RE1+xAE1-xGa3O7+x/2 melilite solid solution the alkali earth metal (AE 2+ ) is exchanged by a rare earth cation (RE 3+ ); therefore, interstitial oxides are introduced to the knock-on process between nearby charge carrier oxides [89], [90]. Previous studies have reported ionic conductivity of the La1.54Sr0.46Ga3O7.27 and La1.64Ca0.36Ga3O7.32 melilites revealing a value of 0.1 S.cm -1 at 800°C [49], [91], [92], which is still the best observed conductivity of a melilite compound to date (see Figure I.12). The barium analogue of these melilite solid solutions was also reported, but with a far smaller limit of Oint, i.e.

La1.35Ba0.65Ga3O7.175, hence its conductivity is one order of magnitude lower 1.6×10 -3 S.cm -1 at 600°C than the best-performing Ca and Sr melilites . Moreover, an alkali earth-free La2Ga3O7.5

melilite with the highest concentration of interstitial oxides was successfully synthesised by J.

Fan et. al. [42] using direct crystallisation from the under-cooled melt as a synthesis route, as it is unreachable by conventional solid state reactions. The high concentration of interstitial oxides leads to their ordering in a one-dimensional chain-like arrangement (see Figure I.11b), hence an Ima2 orthorhombic melilite superstructure is stabilised instead of the tetragonal P4 ̅ 21m structure. The interstitial oxides ordering is driven by their local environment relaxation, as in order minimise repulsion between two close oxides the Ga-O-Ga angles are distorted pushing these oxides outside the five-membered rings. In fact, this relaxation causes even more constraints on the surrounding edge-sharing pentagons which are better suited being interstitial oxide free. The ordering of these oxides has a limiting effect on the ionic conduction of this compound, as even with such high interstitial oxides concentration, the sample reaches 0.01 S.cm -1 at 800°C, which is one order of magnitude less than the previously described Sr-based and Ca-based melilites. The langasite structure as described above (section I.3), can be described as a melilite related mineral, due to the similarities between their structures. In previous works langasite oxide ion conductors were reported with quite high interstitial oxide concentration, as in La3Ga5-xGe1+xO14+x/2 (0 < x ≤ 1.5) [93]. This solid solution was reported with x = 0.3 as a Ga substitution limit when synthesised by solid-state reactions. Nevertheless, the maximum x amount was substantially extended to x = 1.5 when a sol-gel synthesis approach was adopted [93]. In contrast with the melilite structures which host the interstitial oxide in the framework five-membered rings centre, the langasites accommodate these additional oxides by forming framework bridging (Ga,Ge)2O8 units, allowed by (Ga,Ge)-O-(Ga,Ge) angles distortion. The La3Ga5-xGe1+xO14+x/2 solid solution conductivity was also studied and indicated a maximum value of 0.01 S.cm -1 at 800°C for x = 0.5 composition. Hence, these two families in general are of interest in synthesising new electrolyte materials due to their capacity to host high interstitial oxides concentration and their fast charge transport mechanism. 5) Ba2In2O5 (Brownmillerite), ( 6) Bi4Cu0.15Ti0.15V1.7O11-δ (BICUTIVOX), ( 7) La9.75Sr0.25(SiO4)6O2.895 (Si-apatite), ( 8) La9.5(Ge5.5Al0.5O24)O2 (Geapatite), ( 9) La1.54Sr0.46Ga3O7.27 (Sr-melilite) and ( 10) La1.64Ca0.36Ga3O7.32 (Ca-melilite). Solid and dashed lines correspond to vacancies and interstitial conductor materials. This figure was taken from [START_REF] Diaz-Lopez | A Study of Novel Electrolyte Materials with Interstitial Oxides as Mobile Species[END_REF].

Chapter II: Cationic Ordering and Transparent ceramics are usually obtained by powder sintering processes at high temperatures and high pressures routes [1]- [3]. However, full and congruent crystallisation from a bulk glass was shown to be an alternative path to achieve crack-less, dense transparent ceramics without porosity when both the amorphous and crystalline phases have similar densities [4]- [12]. Crystallisation from glass precursors was also demonstrated as a way to synthesise new metastable structures, as demonstrated in the BaO-Al2O3 [4], Bi2O3-Nb2O5-TeO [13] and SrO-SiO2-Al2O3 [5], [14], [15] systems.

The melilite compositions were shown to yield transparent ceramic materials when synthesised by glass crystallisation [10], [12]. The ABC3O7 melilites crystallise in a tetragonal (S.G. P4 ̅ 21m) cell and adopt a layered structure stacked along the c-axis, and formed by 3-and 4-vertex linked MO4 tetrahedra, creating pentagonal channels accommodating different sized A-site cations sandwiched between the MO4 layers, thanks to their network strong flexibility (Figure II.1a) [16]. These compounds are of interest due to their well-known piezoelectric, optical and ionic conductivity properties [12], [17]- [26]. The melilite structures with general formula (AE,RE)C3O7 where AE and RE represents an alkali earth and rare earth elements and C = [Al, Ga], have been reported for RE = [La -Er, Y] to be synthesisable by ceramic routes, whereas for the smallest rare earth cations RE = [Tm, Yb, Lu] their synthesis by classic solid-state reaction was shown to be unsuccessful [16]. In some cases, the melilite compounds do not only crystallise in the parent tetragonal structure, but exhibit different modulations or supercells due to the MO4 layered framework distortion, which are usually linked to an ordering of the A/B-site cations or intercalation of interstitial oxides. Such behaviour can be noticed in the CaREGa3O7 RE= [La, Nd] melilites [27], [28] or the Ca2MC2O7 M = [Mg 2+ , Co 2+ , Zn 2+ ] C = [Si 4+ , Ge 4+ ] ackermanites [29]- [32] crystallising in 5D modulated incommensurate structures, or exhibiting fully commensurate superstructure cell as seen for Bi2ZnB2O7 [33] and La2Ga3O7.5 [34]. During Marina Boyer's PhD [35], she reported for the first time the synthesis of SrREGa3O7 RE = [Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb and Y] melilites by full and congruent crystallisation from bulk glass precursors; hence, achieving the stabilisation of the melilite structure with small rare earths [12]. However, from her study the Ho, Er, Tm and Yb compositions exhibit more Bragg diffraction peaks by PXRD, compared to the larger rare earth compositions [12], [35].

By using selected area electron diffraction (SAED), the patterns were indexed in a P2 1 2 1 2

(3*a, b, c) supercell of the original P4 ̅ 21m structure. From structure solution using the charge flipping method implemented in JANA2006 [36], the a parameter tripling was assigned to an ordering of the A-site cations, with 3 distinct crystallographic A-sites: 1 fully occupied by RE, 1 fully occupied by Sr and one 50%/50% mixed RE/Sr [35], [37] The current chapter will address the following points: (i) exploration of stabilising this new ordered melilite polymorph to other rare earths, with a fine structural study of these compounds, (ii) explore the possibility of isolating the parent disordered melilite structure for the compositions crystallising under the ordered polymorph, studying the thermal stability of these structures and their phase transitions, (iii) explain the ordering origin and why different ordering types are disfavoured, (iv) the ordering effect on these compounds optical properties.

Synthesis by full and congruent glass crystallisation.

First, stoichiometric amounts of SrCO3, Ga2O3 and RE2O3 RE = [Dy, Ho, Er, Tm, Yb, Lu

and Y] (all from Strem Chemicals, purity > 99.9 %) were weighed according to the nominal chemical formula SrREGa3O7 and mixed together in an agate mortar using ethanol to ensure a better homogeneity of the sample. The resulting powder mixtures were left to dry on the bench for a couple of minutes and pressed to pellets, then broken into small pieces of ~ 60mg each.

The pellet chunks were levitated (using argon gas) and melted individually using the aerodynamic levitation coupled to two CO2 lasers apparatus (as described in the appendices Chapter A.I section A.I. In order to determine the glass precursors transition and crystallisation temperatures (i.e.

"Tg" and "Tc" respectively), DSC measurements were performed from room temperature to 920°C, upon heating and cooling using 10°C/min rates. In Following this, a longer scan (in the 5°-50° (2) range using a 0.015° step and 5s/step as a measuring time) was performed to improve the signal to noise ratio (see Figure A. 9), evidencing the low angle small intensity supercell melilite peaks. This sets the synthesisability As for the Lu melilite, its synthesis as a phase pure sample was more difficult to achieve due to the crystallisation of the Lu3Ga5O12 garnet as a secondary phase. In this perspective, the crystallisation temperature was reduced to 805°C for 2h then the sample was quenched by placing the Pt crucible into a dish of water, which produced only the ordered melilite.

To map the thermal stability and bring a full picture of all the studied compositions, data from DSC and VT-PXRD were combined with previous results from [16] and drawn in phase Synchrotron powder diffraction analysis.

To explore the cationic ordering over the compositions with different RE, synchrotron powder diffraction (SPD) and laboratory PXRD measurements were acquired on SrREGa3O7 ordered and disordered samples (see Table II.1 for the measurement conditions of each rare earth). Rietveld refinements were carried out using Topas academic (V6) software [39], with the following constraints and conditions:

• Each of the three A-sites to be fully occupied:

OccRE1 * + OccSr1 = 1, OccRE2 + OccSr2 = 1, OccRE3 + OccSr3 = 1.
For the P21212 melilite only.

• Constrained A-site 3 partial occupancies to A-site 1 and A-site 2 as follow: OccRE3=

1.5 -OccRE1 -OccRE2. For the P21212 melilite only.

• An overall composition constrained to the nominal: Rietveld refinement of this composition was run with fixed A-sites occupancies to 0.5/0.5

(Occ𝑅𝐸1+Occ𝑅𝐸2+Occ𝑅𝐸3)×4 Z = 1, (OccSr1+OccSr2+OccSr3)
Yb1/Sr1, 1/0 Yb2/Sr2, 0/1 Yb3/Sr3, which did not affect the reliability factors. These occupation constraints were applied to the Tm sample as its refined occupancies were close to the ideal ordered model (as in the Yb compound). Moreover, the refined partial occupancies of the other RE ordered melilites were quite far from the ideal model (A-sites disorder > 7%), hence the Sr/RE occupancies were not fixed as in the Yb and Tm compounds (see Table II.3).

The SrLuGa3O7 composition diffraction pattern had the broadest peak profile of all compositions and was found to be the most difficult to refine, as some hkl-independent peak broadening was observed and the refined structure was shown to be physically non-meaningful with oxygens moving far from their initial positions, breaking the GaO4 infinite framework. To solve the problem of oxygen atoms moving too far away from their initial position, soft restraints were added to the Lu refinement, by setting dummy oxygen atoms (site occupation = 0) positioned from the SrYbGa3O7 refined model, and constraining the oxygens to not move too far from these dummy atoms while the refinement runs. The allowance degree of the constraint was adjusted until a stable refinement was reached. Moreover, a large Biso value was noticed for the mixed site Lu3/Sr3 site, doubling the value of the other two A-sites (Lu3/Sr3 as a function of the rare earth, as a matter of fact the contrast between aordered/3 and adisordered gets narrower toward bigger sized REs, evidencing the tendency to stabilise the parent polymorph at the expense of the ordered melilite, also compatible with the observed slope change in the bordered trend. Furthermore, the ordering trend shows to be slightly deviated from the perfect Yb model as the rare earths size increases (from Er to Dy compositions), where both strontium and rare earth cations can be found in small amounts on each other's dedicated cationic site. This can be best seen in the SrErGa3O7 compound, as it shows the most disorder over its three cationic A-sites observed in the synthesised RE's series, where their refined occupancies deviate from: 0.5/0.5 for RE1/Sr1 site 1, 1/0 for RE2/Sr2 site 2 and 1/0 for Sr3/RE3 site 3, to: 0.504(3)/0.496(3) for Er1/Sr1 site 1, 0.863(3)/0.137(3) for Er2/Sr2 site 2 and 0.868(4)/0.132(4) for Sr3/Er3 site 3. Even though these rare-earths (Dy-Er) keep a strong ordering tendency, the refined partial disorder is coherent with the weakening stability of the P21212 melilite supercell as the rare earth size increases, as seen in the ordering temperatures provided by differential scanning calorimetry indicating a decrease with the increase of the RE size to the point where the delivered thermal energy is no longer sufficient to induce A-site ordering (case of Tb). In studies reported by Wei et. al. [27], [28] on the CaREGa3O7 RE = [La, Nd] tetragonal melilites, they revealed a five-dimensional structural modulation of these structures, and also mapped the 5D modulated parent melilite region by relating it to the A/B cations radius ratio. Atomic scale observation of the super structured melilite.

To provide an accurate picture of the local structure and the arrangement (distribution) between strontium and rare earth cations at the nanometre scale, not obtainable from the Rietveld refinement as the structure is averaged across the whole measured sample, atomicscale STEM-EDS measurements were conducted on the SrYbGa3O7 compound. First a glass bead of SrYbGa3O7 composition was annealed at 815°C for 2h in an open atmosphere furnace, and cooled inside the furnace to room temperature (ordered melilite synthesis procedure as described in section II.3). The bead was optically polished to a disk of 50µm, a thin foil of this Considering the hexagonal tiling appearance of the underlying melilite structure in "Cairo pentagonal tiling" or "MacMahon's net" [40] way to distort the GaO4 framework, as the CaLaGa3O7 and CaNdGa3O7 structures were described as incommensurate, displaying a pair of modulation vectors parallel to the ab plane [27], [28]. While these compounds still show cationic disorder over the A-sites, Ca shows a slight preference for the smallest 6-coordinated sites, where 54% of that site is occupied by Ca atoms in CaLaGa3O7, and slightly above 60% in CaNdGa3O7. However, the low contrast in ionic radii between Ca/La and Ca/Nd, 0.97 and 1.01 respectively, does not supply adequate driving force for full long range cationic ordering to take place. In our synthesised SrREGa3O7 compounds, both conditions of (i) size contrast between Sr and RE, and (ii) small enough rare earth cations to be stable in 6 coordinated sites, are gathered, finding the sweet spot for stabilisation of the P21212 ordered melilite. The parent structure and 5D-modulated structure regions have been compiled from the literature [16], [27], [28]. Note that the parent structure region for AE = Ca is marked with an asterisk, as it was reported prior to the discovery of structural modulation in CaLaGa3O7 and CaNdGa3O7.

Optical properties of the SrErGa3O7 compound.

It is well known from the literature that RE-doped glass-ceramics exhibit interesting optical photoluminescence properties [41]- [44]. In this section, the optical properties (luminescence / photoluminescence) of the ordered melilite were measured on the SrErGa3O7 composition, as the Er 3+ spectroscopy is well known and has been exploited in numerous applications [45], [46].

Another point is that this study will allow to probe the effect on the properties of local ordering of the A-sites in glass, disordered and ordered melilites.

To visualise the ordering impact on the optical properties of the crystallised melilite ceramics, photoluminescence spectra were recorded by Yannick Ledemi at Université Laval (Quebec, Canada), on both bulk and powder samples at room temperature in the 1400 -1650 nm region under excitation at 520 nm using a Xe lamp source. Full attention was given to collect data of ceramic and glass compounds under the exact same experimental conditions to pursue an accurate comparison. In Figure II.18a showing the bulk emission spectrum collected on both glass and ordered melilites of the SrErGa3O7 composition, a clear peak restructuration and strong emission intensity increase can be noticed for the ceramic material compared to its glass analogue. The peaks structuration (narrower and more well defined) on the ceramic sample can be related to the long range structural order of the crystals in ceramic samples vs the amorphous state (short range structural order) of the glass, similarly seen in single crystal materials [41], [44], [47]. The strong increase of the main peak intensity on the other hand is the signature of the local ordering and the designation of the RE-only site which is fully occupied by Er 3+ cations (in this case), favouring a more efficient energy transfer between the RE ions of the crystalline phase. One can also notice that the intensity difference of the main Er 3+ emission band is not as significant on powder samples as it is observed on polished beads bulk samples, which is mainly due to light scattering phenomena induced by grain boundaries (more present in powder samples vs bulk) (Figure II.18b). On the other hand, the parent melilite Er 3+ emission bands show a very similar intensity to the glass compound, which is consistent with the local cationic disorder of the RE that can be comparable in both these compounds. Comparing the parent disordered to the ordered melilite Er 3+ ion emission band, the intensity is almost doubled in the ordered compound, which as indicated above is arising from the local ordering of the A-sites.

Conclusion and perspectives.

In this chapter, the synthesis of the newly reported SrREGa3O7 P21212 ordered melilite was investigated, revealing the possibility of synthesising this new structure for Lu and Dy rare earths as the REs stability limit of this superstructure, with a precise and controlled heating/cooling protocol of glass precursors. Furthermore, the synthesis of the SrREGa3O7 disordered P4 ̅ 21m melilite with small rare-earths was also studied by glass crystallisation, demonstrating the attainability of the parent tetragonal melilite structure for the whole RE series except Lu. Hence, the P4 ̅ 21m SrYbGa3O7 compound is reporting here for the first time. The stability and occurrence of both melilite polymorphs vs temperature was studied using both in situ VT-PXRD and DSC techniques. This combined approach unfolded the existence of three distinct SrREGa3O7 compositions categories with different ordering/disordering mechanisms.

First the RE = [Yb, Lu] compositions which crystallise in and retain the ordered melilite until they decompose (from VT-PXRD); however, DSC has shown with fast enough heating rates, the disordered ytterbium polymorph also exists, which was successfully stabilised phase pure at room temperature and its crystal structure refined. Second, RE = [Er, Tm] both crystallise in the disordered melilite structure and undergo ordering while cooling. The last category contains the Dy and Ho rare earths, as they crystallise in the disordered polymorph and do not order on cooling in a furnace; however, the controlled synthesis parameters in the DSC offer the possibility to stabilise the P21212 ordered melilite for these compositions also. The competition between both melilite structures was assigned here to two crucial parameters: (i) the size mismatch between strontium and rare earth atoms, (ii) the ionic radii of the rare earth on its own, as the eventuality of the ordered melilite was assigned to a combination of both these parameters. Namely, the Lu compound could not be crystallised in the tetragonal melilite due to the its big size difference with Sr atoms and its low decomposition temperature, while on the other extreme of the superstructure limits, Tb could not be achieved in the P21212 ordered cell as it is too big to be held in a [6+1] coordination type. The discovery of this new ordered melilite also comes with interesting optical properties compared to their disordered image and corresponding glasses. As described in section II.6, the superstructured melilite photoluminescence spectrum shows a clear band restructuration and significant increase of the RE main emission band intensity compared to its glass and tetragonal melilite analogues in the near infrared, which makes it a potential candidate for the development of compact sources for remote sensing, environment, surgery and security and defence [48]- [52].

This family of compounds still shows a wide variety of compositions to be studied especially In the general introduction and Chapter I, the interests in researching systems with potential nano-crystallised products from glass precursors for new transparent functionalisable ceramic materials was described. In this context, the existence of stable phases in the CaO-ZnO-Ga2O3-GeO2 system such as Ca3Ga2Ge4O14 and Ca3ZnGe5O14 crystallising in the lanagasite [1] and taikanite [2] structures respectively, and capable of hosting multiple cations is of interest to study [3].

The langasite structures family with a general formula A3BC3D2O14 are much of interest materials due to their piezoelectric [4], wide transparency up to 7 𝜇m and high laser damage threshold (LDT) [5], [6], low temperature multiferroic 3d cations behaviour [7], [8] and ionic conductivity properties [9]. Their structure can be described as a melilite-related family compound, their layered framework thus offers four different crystallographic sites, where A is The Ca3Ga2Ge4O14 compound was first discovered and reported by E. L. Belokoneva et al [1] in 1980, and was identified as the first member of the langasite family. Its structure was proposed to crystallise in a trigonal cell with the P3 space group symmetry, but this was soon after revised to the P321 space group [10]. Its crystal structure is as described above, where the A-sites host the Ca atoms, B-and C-sites accommodate Ga and Ge in a disordered scheme, while the D-site remains fully occupied by Ge atoms [9], [10]. The cationic disorder between Ga and Ge over the B-C-and D-sites in the Ca3Ga2Ge4O14 compound, was characterised by single crystal X-ray diffraction, and their occupancies were assigned according to the cationoxide first neighbours distance analysis [11]. Moreover, recent work characterised the cationic disorder by anomalous diffraction indicating dominant population of the 1a site by Ge atoms (0.2Ga/0.8Ge) [12], [13]; however results were far from the previously reported ones in [11] which declared an almost equal distribution between Ga and Ga over the 1a site (0.4Ga/0.6Ge).

The Ca3ZnGe5O14 phase was reported to be a theoretical phase which can't be synthesised by conventional single crystal growth methods [14]. Nevertheless, it was recently obtained as a by-product from sintering attempts of a phase pure CaCu0.95Zn0.05Ge2O6 compound in an open platinum tube [2], as single crystal form. Its structure was related to the taikanite family [15], , with a completely ordered langasite framework, where Zn 2+ fully occupies the octahedral sites, while the tetrahedral framework sites are entirely formed by Ge 4+ atoms. In this case, the cationic distribution between Zn 2+ and Ge 4+ was also investigated only based on single crystal X-ray diffraction via a bond valence sum analysis. Several works demonstrated that the langasite family can also adopt a monoclinic cell, going through a high pressure phase transition (P321→C2) (e.g. La3Nb0.5Ga5.5O14) [16], [17], or a reversed phase transition at high temperatures (C2→P321) (e.g. La3SbZn3Si2O14) [17], [18], which would suggest the possibility to synthesise the trigonal polymorph of the Ca3ZnGe5O14 phase.

Characterisation of the atomic disorder in complex systems containing neighbouring elements from the periodic table, can be a tough task to answer because of the close X-ray scattering factors and multiple possible solutions when a crystallographic site hosts more than two cations. However, it is sometimes important to resolve the element distributions in the cell, especially where cation ordering controls structural polarity [19], suppresses thermal conductivity [20], or influences lithium battery cyclability [21]. In this chapter the possibility to synthesise the Ca3Ga2-2xZnxGe4+xO14 solid solution from x = 0 all the way to x = 1 is investigated by full and congruent crystallisation from glass or molten liquid, while retaining the trigonal polymorph across the whole solid solution series, thus successfully achieving the stabilisation of the first trigonal P321 Ca3ZnGe5O14 phase. Characterisation of their structure and related cationic distribution between three successive elements from the periodic table was challenging, due to the absence of X-ray scattering contrast, or close neutron scattering lengths and the possibility of more than two cation types sharing a single crystallographic site. Using a combined approach between SPD and NPD data, the ordering between Ge/Ga and Ge/Zn for x = 0 and x = 1 compositions was determined. As for intermediate compositions, combination between SPD, NPD and quantitative analysis of atomic scale STEM-EDS maps, by a new twodimensional fitting approach, brings insight to the changes in cation arrangement in the layered framework across the solid solution series.

Ca3Ga2-2xZnxGe4+xO14 (0≤x≤1) solid solution synthesis investigations.

Solid-state reaction.

First, a mixture with stoichiometric amounts of high purity precursors CaCO3 99.95%, Ga2O3 99.998%, ZnO 99.999%, GeO2 99.9% (all from Strem Chemicals) were weighed according to the nominal composition for 0≤x≤1, then ground together for several minutes in an agate mortar in presence of ethanol for a better homogeneity of the sample. The resulting powder was then dried at 100°C for 20 minutes to evaporate the remaining ethanol, and pressed into pellets of 16 mm each.

In order to investigate the synthesis of the Ca3Ga2-2xZnxGe4+xO14 (0≤x≤1) solid solution compounds, initial attempts were conducted by solid-state reactions, starting from the prepared mixture described above. In situ VT-PXRD measurements were conducted from room temperature (RT) to 50°C in one heating step, and then to 1200°C (50°C/step) in an angular range of 10°-50° (2) using a step of 0.016° and a measuring time of 0.7 s/step, on the Ca3Ga2Ge4O14 (x =0) parent compound. In Figure III.2, it is visible that the main Ca3Ga2Ge4O14 (x =0) langasite starts forming at 950°C along with the CaGeO3 perovskite. At 1200°C both phases are still present with unreacted Ga2O3, which indicates that either higher temperatures are required or a longer reaction time is needed to achieve a full reaction of the mixture and obtain a langasite phase pure sample. However, the sample mixture melts around 1250°C, which excludes the possibility of raising the ceramic synthesis temperature to higher values.

Following this, the initial mixture was left to react for 48 hours at 1200°C with intermediate grinding each 12h, which resulted still in a mixed sample between Ca3Ga2Ge4O14 (x =0) langasite, CaGeO3 perovskite and Ga2O3. Different synthesis routes were then considered. Crystallisation from glass and under-cooled melt.

In order to achieve a phase pure sample, crystallisation from glass or under-cooled melt was considered as an alternate synthesis route. The initial mixture pellets of compositions Ca3Ga2-2xZnxGe4+xO14 (0≤x≤1) (described in section III.2.1) were broken into small fragments of ~ 35 mg each, then melted individually using the ADL apparatus coupled to two CO2 lasers [22], [23]. These samples reached liquid state between 1250°C -1350°C (depending on the composition), and were further heated up to 1500°C to ensure their homogeneity, then subsequently quenched by turning the lasers off, reaching high cooling rates (estimated around 300°C/s) in order to achieve vitrification [24], and leading to glass precursors in the form of spherical beads. The synthesised glass beads were checked by laboratory PXRD. As shown in compositions favoured multi-phase samples between the main langasite and melilite impurity.

Crystallisation of the melt was achieved by adjusting the carrier gas flow (argon in this case) so that the levitating molten bead touches the nozzle while cooling. The contact surface thus acts as a nucleation centre for crystallisation of the entire bead when the lasers are turned off. To summarise the final synthesis conditions of the Ca3Ga2-2xZnxGe4+xO14 (0 ≤ x ≤ 1) solid solution compounds, crystallisation from the melt was used to achieve a phase pure and highly crystalline Ca3Ga2Ge4O14 (x = 0) langasite. Crystallisation from bulk glass samples on the other hand was used to synthesise a single phase langasite for Ca3Ga2-2xZnxGe4+xO14 (x = 0.25, 0.5, [11] a : constrained to refine to the same Biso values. Metastable structures achieved by glass crystallisation can show a high temperature phase transition to the more thermodynamically stable polymorph. For example, in the Al2O3-SrO-SiO2 ternary diagram, the glass Sr1+x/2Al2+xSi2-xO8 (x = 0) composition was shown to crystallise first in an intermediate metastable hexagonal P63/mcm polymorph, and then goes through a phase transition to a more thermodynamically stable monoclinic I2/m structure [28], [29].

Similar behaviour was noticed by solid state reaction where only the monoclinic polymorph could be stabilised as phase pure [30], [31]. In the langasite structures family, some compositions (e.g. La3Nb0.5Ga5.5O14 [17]) also show phase transition going from the trigonal P321 to a monoclinic C2 structure under high pressure/temperature. This phase transition was determined by an abrupt slope change in the trigonal cell parameters trend vs T(°C) or vs P(GPa). In our glass crystallised Ca3ZnGe5O14 (x = 1) compound, to test the stability of the Cationic order/disorder characterisation for Ca3Ga2Ge4O14 (x = 0) and Ca3ZnGe5O14 (x = 1) end members by solid state nuclear magnetic resonance (ss-NMR) and neutron powder diffraction (NPD). 71 Ga and 67 Zn SS-NMR. 71 Ga solid-state NMR (ss-NMR) is a powerful tool to probe the local structure in terms of coordination and also to provide a quantification of its different environments [32], [33]. 71 Ga solid state NMR spectroscopy was performed on the x = 0 member only (Ca3Ga2Ge4O14) at 20 T with a Bruker Avance Neo spectrometer equipped with a 0.7 mm magic angle spinning (MAS) double resonance Bruker probehead. The powder sample was spun at a MAS frequency of 100 kHz. Given the wide spectral broadening of the 71 Ga NMR environments, a radiofrequency field of 125 kHz was used, which corresponds to 90° and 180° central-transition selective pulses of 1 µs and 2 µs, respectively. A spin echo experiment was recorded using a full echo acquisition (interpulse delay of 150 µs), a recycling delay of 2 s, and with 26000 scans.

P321
Furthermore, a two-dimensional QPASS (Quadrupolar Phase-Adjusted Spinning Sidebands) [34] experiment was performed in order to improve the spectral resolution of the Ga environments by separating the overlapping spinning sidebands. Eight sets of timings (constant full duration of seven rotor periods) were needed for a proper separation, with a recycling delay of 2 s, and 8000 scans per set of timings. The spectra were referenced to a 1 M gallium nitrate solution.

As shown in Figure III.14, the spectrum obtained from the spin echo experiment lacks of resolution because of overlapping spinning sidebands, even at ultra-high MAS frequency (100 kHz). Moreover, one can hardly distinguish two Ga environments indicated by the intense peak at 0 ppm and the shouldering at the left side of this peak. Attempts to quantify these two environments by fitting the signal using the Dmfit software [35] and defining two contributions revealed unsuccessful, as the spinning side bands intensity could not be fitted.

The "spinning sidebands-free" QPASS spectrum allows to achieve ultimate spectral resolution, and clearly identifies these two contributions located at ca. 0 ppm and 100 ppm corresponding to 6-coordinated and 4-coordinated Ga respectively. However, the complexity of the QPASS experiment does not allow a precise quantification the two Ga environments.

The observed 71 Ga lineshapes have smoothed profiles as opposed to singularities of the quadripolar signal expected for fully ordered crystalline phases [36], indicative of geometrical and chemical disorder of both Ga environments in the second coordination sphere [37]. 71 Ga NMR spectra acquired on a sample of composition Ca3Ga2Ge4O14 (x = 0) by a MAS spinecho (green) and a QPASS (blue) experiments, showing the two coordination types of Ga in the sample. 67 Zn ss-NMR remains a challenging task to accomplish due the nucleus low natural abundance (4.1%), weak gyromagnetic ratio (2.667 MHz/T) and potentially large quadrupolar effects (nuclear spin = 5/2). To elucidate the Zn 2+ cations ordering type in the Ca3ZnGe5O14 (x = 1) compound, 67 Zn ss-NMR spectrum was recorded at a high magnetic field of 17.6 T ( 67 Zn Larmor frequency of 46.9 MHz) using a 4 mm magic angle spinning (MAS) probehead.

Moreover, a CPMG echo-train acquisition was used to improve the measurement sensitivity [38]- [42]. Furthermore, a radio frequency field of ⁓15 kHz, selective of the 67 Zn central transition, was adopted (corresponding 90° and 180° selective-pulse durations of 5.6 and 11.2 µs) and a spinning frequency st at 14 kHz. 128 rotor-synchronized echoes spaced by 1 ms (corresponding to 14 rotor periods) have been recorded and 25,600 transients were co-added with a recycle delay of 3 s, which led to 21 hours of total experiment time.

A 67 Zn spikelet spectrum was obtained by applying a direct Fourier transform to the whole acquired echo train, and is shown in Figure III.15a. This spectrum discretisation processing distributes the whole spectrum intensity in a limited number of narrow spikes that reproduce the spectral envelope, thus allowing the improvement of the signal to noise ratio [41], [42]. The signal obtained from 67 Zn central-transition shows to extends over a large chemical shift range (900 ppm), and exhibits a maximum intensity in the +50 to -50 ppm region. The signal shape suggests a partial overlapping of two resonance with asymmetric line shapes, characteristic of a distribution of the quadripolar interactions, indicative of local disorder between Zn 2+ and Ge 4+ cations. Accordingly, attempt to reconstruct the 67 Zn spectrum with a single contribution affected by second-order quadripolar effects were unsuccessful. Moreover, two contributions with distribution of the quadrupolar coupling (Czjezk Gaussian Isotropic Model [43], [44])

were deployed at 60 ppm and 360 ppm isotropic chemical shifts and average quadripolar coupling constants of 7.3 MHz and 9.3 MHz (see Figure III.15b). From the 67 Zn NMR reported literature, these contributions placed at 60 ppm and 360 ppm can be assigned to 4-and 6coordinated Zn atoms [45]- [47] in the Ca3ZnGe5O14 (x = 1) compound. However, direct quantification of these two Zn coordination types could not be possible from this CPMG spectrum with low signal to noise ratio.

Despite the down sides of unquantified 71 Ca3Ga2Ge4O14 (x = 0) and Ca3ZnGe5O14 (x = 1) NPD refinement.

Due to the close atomic number between Ga, Zn and Ge (same Z number), it is not possible to characterise the chemical disorder between these cations over the 1a, 3f, 2d sites using only PXRD. However, from 71 Ga and 67 Zn ss-NMR, these two elements were found to be present in both four and six coordination types offered by the cell. The end member compositions Ca3Ga2- Zn respectively) [48], allowing the use of NPD to refine the Ga/Ge and Zn/Ge ratios directly.

Large sample batches ⁓3.5 g of Ca3Ga2-2xZnxGe4+xO14 (x = 0, 0. * Note that OccXn notation means the occupancy of the atom X in the site n For both end member compositions (x = 0 and 1) the cationic distribution was shown to occur only among the 1a and 3f sites, while the 2d sites remains fully occupied by Ge atoms (as previously reported for Ca3Ga2Ge4O14 single crystals synthesised by the Czochralski method in [10], [11]). The refined occupancies for x = 0 composition led to a distribution of 0.51(8)Ga/0.49 (8)Ge on the 1a site and 0.50(3)Ga/0.50(3)Ge on the 3f site, which displays a complete disorder over the two crystallographic sites, consistent with the 71 Ga MAS and QPASS NMR collected spectrum showing signal arising from the two coordination types of the structural gallium. Taking into account each site multiplicity only 25(4)% of the total Ga amount is held in the 6-coordinated B-sites(1a), whereas the remaining 75(4)% goes to the 4coordinated C-sites(3f). However, in the latest structural study of the Ca3Ga2Ge4O14 compound reported by A. Dudka et. al. [12] our results are far different from theirs. In [12], the structural disorder was characterised by anomalous scattering on single crystals grown by the Czochralski method [12], [13]. They showed that only 10% of the Ga 3+ cations are held in the 1a sites with the remainder present in the 3f sites (see Table III.5). In both materials, our melt crystallised and the single crystals reported in [12], even though the cationic distribution is different between the 1a and the 3f sites, the tetrahedral 2d sites are exclusively occupied by Ge 4+ . This suggests that the synthesis route can influence the extent of Ga 3+ /Ge 4+ ordering in these structures, with melt-crystallisation favouring a higher degree of disorder in this case, compared to the single crystals reported in [12]. The strontium and barium analogues (Sr3Ga2Ge4O14 and Ba3Ga2Ge4O14) were also reported [11], [14], [49] to crystallise isostructural to the parent Ca3Ga2Ge4O14 langasite, synthesised by Czochralski and flux-growth single crystal routes. In the Ba compound the Ga was assigned to only the tetrahedral sites, occupying ⅔ of the 3f site [14]. Moreover, in other studies, it was pointed out that Ga was only held in the 2d site [49] with a different synthesis approach as mentioned above. In both these studies, analyses were based on single crystal laboratory X-ray diffraction data, with cation-oxide distance analysis to quantify each site disorder. Which is another example of different synthesis routes leading to different cationic ordering.

On the other extreme of the solid solution Ca3ZnGe5O14 (x = 1), Rietveld refined NPD data also confirmed that the cationic disorder occurs only between the 1a and 3f sites, with the 2d sites remaining fully occupied by Ge atoms. The refined occupancies over the mixed sites, 0.52(4)Zn/0.48(4)Ge on the 1a and 0.16(1)Zn/0.84(1)Ge on the 3f, show that the total amount of Zn is almost equally dispersed over the two coordination types, 52(4)% on the 1a 6coordinated site and 48(1)% on the 3f 4-coordinated site. Moreover, the B-and C-site cationoxide bonds show notable differences going from the Ca3Ga2Ge4O14 langasite to the full Ga substituted compound Ca3ZnGe5O14 (Table III.6 and Table III.7), which also could be interpreted as a difference in the average site cation radii due to the different ordering type between the x = 0 and 1 compounds. 4) with a mean Ge3-O distance of 1.758(4)Å and 1.759(3)Å for both x = 0 and x = 1 compounds respectively. As for the 1a and 3f sites, refined occupancies indicated that full ordering is disfavoured, as both sites had mixed occupancies between Ga/Ge (x = 0) and Zn/Ge (x = 1). This is better seen in the calculated BVS values indicating that all three cations "Zn, Ge, Ga" are either underor over-bonded in the two different coordination types (B-C-and Dsites). The differences between the reported single-crystal Ca3ZnGe5O14 monoclinic C2 [2] and the glass crystallised Ca3ZnGe5O14 (x = 1) trigonal P321 structures was described in section III.3.

In Table III.8 a comparaison between the octahedral (1a), tetrahedral (3f and 2d) M-O bond distances between the reported C2 against the NPD refined x = 1 P321 structures is illustated.

For the 1a site (notted Zn1 octa site in Characterisation of the cationic distribution in compounds containing multiple elements with close atomic and neutron scattering factors is a problem that is usually addressed by coupling multiple techniques. In the Zn1+xGa2-2xGexO4 (0 ≤ x ≤ 0.5) solid solution, the cationic disorder was characterised by coupling NPD and 71 Ga NMR [3]. In a different recent study of a more complex oxide system, the high entropy oxide "HEO" material of composition (Cr0.2Mn0.2Fe0.2Co0.2Ni0.2)3O4 crystallises in a spinel structure, and contains several successive first row transition metal cations. The cationic disorder characterisation between Cr, Mn, Fe, Co and Ni over the two possible crystallographic sites offered by the spinel structures, was achieved by coupling X-ray absorption near edge spectroscopy (XANES), soft X-ray magnetic circular dichroism (XMCD) and 57 Fe Mössbauer spectroscopy (both in presence and absence of an external magnetic field), complemented with SPD, NPD and TEM techniques [50].

For the Ca3GaZn0.5Ge4.5O14 (x = 0.5) intermediate composition, where Ga 3+ , Ge 4+ and Zn 2+ cation compete for the langasite's layered framework sites (B-C-and D-sites with their 1a, 3f and 2d respective Wykoff positions), characterisation of this simultaneous disorder of three cations is an impossible task to resolve relying only on neutron diffraction. Hence, to construct a suitable Rietveld model for the Ca3GaZn0.5Ge4.5O14 (x = 0.5) sample NPD refinement, another characterisation technique is needed. From x = 0 and 1 samples we know that 71 Ga and 67 Zn ss-NMR is not an option due to the high disorder present in the material and how challenging it is to extract quantitative information in this solid solution study.

P. Lu et al [51], [52] has demonstrated the use of two-dimensionally fitted STEM-EDS maps to extract direct information from SrTiO3 films, thus quantifying the chemical distribution of the different elements present in the measured sample. In this section, the possibility of quantifying the cationic disorder between three isoelectronic (Zn 2+ , Ga 3+ , Ge 4+ ) cations is investigated by a one-dimensional "1D" STEM-EDS profile elements refinement approach, and for the first time, a two-dimensional "2D" STEM-EDS maps fitting on powder measured samples. to the column's mean atomic number (𝑍 ̅ ). Hence, the darkest and brightest spots will represent the lightest "Ca" and heaviest "Ge, Ga, Zn" elements respectively. EDS maps, Ca can clearly be seen occupying only the A-sites (3e). Ge on the other hand is the only cation observed at all three sites (1a, 3f and 2d), consistent with structural distribution noticed in the x = 0 and x = 1 end member compounds from the Ca3Ga2-2xZnxGe4+xO14 solid solution. For Ga and Zn STEM-EDS maps, the data were noisier due to their relatively low abundance and concentration, so in order to highlight their atomic positions a Wiener filter [55], [56] was applied to enhance the signal to noise ratio. The Ga signal shows individual triangular forms, leading to think that it is present in both coordination types (6-coordinated 1a and 4coordinated 3f). The Zn cations appear to be only present on the central 1a sites, however due to its very low concentration in the cell (2.22%), and its broad circularly shaped signal on the EDS map diffused over both neighbouring site types, it is hard to say if it is only held on the 1a site or on both 1a and 3f sites.

III.5.1.1. One-dimensional fitting approach (1D).

From STEM-EDS maps we know that the A-sites (3e) are only occupied by Ca atoms, the D-sites(2d) sites also shows to be completely inhabited by Ge atoms. Therefore, the sites of interest here are the central B-site(1a) and the neighbouring C-sites(3f). In ). The Zn profile was initially fitted using one Gaussian at the 3f position (see Figure I22c), however a subtle asymmetric profile shape could still be noticed. Hence, a second Gaussian contribution was added at the 3f which improved the overall fit of the profile, indicating a small amount of Zn present also on that site. Assuming that the refined Gaussian area is proportional to the element content on the site, partial occupancies were calculated using the following two equations:

(i)

OccGe 1a
OccGe 3f = Ge fitted area on the 1a

Ge fitted area on the 3f

, same equation for Zn and Ge.

(ii) OccGe1a+3*OccGe3f+2*OccGe2d = 4.5, OccGa1a+3*OccGa3f = 1, OccZn1a+3*OccZn3f = 0.5.

Results from the 1D refinement were as follow:

OccGe 1a
OccGe 3f = 0.9,

OccGa 1a

OccGa 3f = 1.17 and

OccZn 1a

OccZn 3f =2.6, which leads to the following occupancies 0.23 (10)Zn/0.57(5)Ge / 0.28(8)Ga and 0.09(4)Zn/0.64(2)Ge/0.24(3)Ga on the 1a and 3f respectively. Despite the possibility of quantifying the cationic disorder by one-dimensionally fitting the extracted intensity profile from the STEM-EDS maps. This method has certain limitations that can induce biases to the targeted information.

• The use of a Wiener filter affects not only the noise but the actual signal also.

• Parasitic signal coming from neighbouring sites when the interatomic distances are very small.

• Not taking advantage of the whole measured signal.

III.5.1.2. Two-dimensional fitting approach (2d).

As stated above in section III.5, P. Lu et al [51], [52] demonstrated the use of the two-dimensional aspect of the EDS maps to reduce the 1D refinement approach related issues.

However, only nicely crystallised and well oriented thin specimens of SrTiO3 were used in the previously reported studies [51], [52] as examples, and has never been done for powder samples, where recording STEM data is even harder due to the sample thickness inhomogeneities, size limitation of the grains and orientation problems. This approach has the advantage of considering the actual 2D nature of the signal, offering the possibility to reduce the associated errors of the: (i) 1D signal integration, (ii) side signal from the integrated area boundaries, especially when the sites of interest does not line on a straight column. Our approach here was to analyse two different zones from the central part of the 2D elemental images to minimize possible errors or deformation at the borders (see Figure III.22). These regions contain one central 1a site, three and six first neighbours 3f and 2d sites respectively.

The refinements were carried out using the simplest model possible, composed of: (i) background offset (ii) sum of two-dimensional Gaussian lines for each site, where each Gaussian is characterised by its x and y position components. The three 3f sites surrounding the 1a, were constrained to have the same peak width for each cation and each of the two zones independently. Germanium data (with the best signal to noise ratio due to its high concentration on the cell) were refined first to extract the 1a and 3f peaks positions, width and amplitudes. Ga First, a mean value of the Gaussian areas under the three 3f sites was calculated (for each cation), then the same occupancy calculation logic employed in the 1D approach was used here for the 2D approach, with normalisation so that each site maximum content equals 1.

Nevertheless, the obtained results were very close to the 1D fitting procedure (see Figure III.12). Here, the Zn signal is demonstrated to not only arise from the 1a sites but also from the neighbouring 3f, as the fit could not converge with the given constraints (fixed 1a position and peak width). The final refined occupancies from both zones are represented in Table III.10. Knowing from STEM-EDS quantitative analysis that the 2d sites remain occupied solely by Ge atoms, and that Ga and Zn are distributed in a similar way to their related parent compounds (Ga atoms almost dispersed in a 1:1 disposal between the 1a and 3f, and Zn in 1:3 disposal), the starting occupancies were fixed as follow:

• 1a site: 0.25Ga/0.25Zn/0.5Ge

• 3f site: 0.25Ga/0.083Zn/0.667Ge

• 2d site: 1Ge

Rietveld refinements were then carried out using the described starting model, with the constraints of keeping each site full, and an overall composition matching the nominal one. The gallium occupancies were also fixed for the first runs to maximise the neutron scattering difference between our cations. Hence, only the Ge occupancy on the 1a site was freely refined, while the Zn one was deduced by the deployed constraints. After convergence was reached, Ga III.10 for zone1 and zone2 individual refined occupancies.

As demonstrated in Table III.12, the Rietveld refined model (constructed from the 2D quantitative analysis of STEM-EDS maps) against NPD data shows little variation from the initial given occupancy values of the different cations and produces a good fit to the acquired data. This illustrates the complementary of the two techniques in this study. The characterised disorder in the Ca3GaZn0.5Ge4.5O14 (x = 0.5) compound follows the same trend found in the x = 0 and 1 end members, where gallium atoms do not show a preference between the two coordination types and the 1:1 ratio is respected in the x = 0.5 compound, as seen for x = 0. Zinc on the other hand appears to be out-competed by germanium for the tetrahedral sites, consistent with the x = 1 compound refined structure. Moreover, this behaviour is also observed in the Zn1+xGa2-2xGexO4 spinel solid-solutions, where Zn atoms are out-competed by Ga and Ge atoms in the 6-coordinated sites. The disorder trend of the Ca3Ga2-2xZnxGe4+xO14 solidsolution can also be noticed in the polyhedral volume change at the 1a and 3f sites. As illustrated in Figure III.26, the Rietveld refined M-O distances at the 1a (octahedral), 3f (tetrahedral) framework sites, as Zn 2+ is substituted into the structure, illustrate a marked increase of the MO6 octahedra volume, which goes against the overall decreasing trend observed in unit cell volume, indicating that the 1a site is becoming preferentially populated by larger cations. As the solid solution is traversed, the oxygens thermal parameters show a notable increase, going from Biso= 1.18(4) Å 2 (x = 0), 1.66(5) Å 2 (x = 0.5) to 2.17(7) Å 2 (x = 1), consistent with the increase of the cationic size mismatch due to the Ga substitution by Zn and Ge inducing local static disorder of their coordinating oxides.

Figure III.26. a), b) Comparison between SPD (hollow circle) and NPD (full box) refined bond distances "B-O3 in black, C-O2 in blue and C-O3 in red" and mixed sites volumes "B-site (1a) in orange, C-site (3f) in

green" respectively for x = 0, 0.25, 0.5, 0.75, 1 compositions.

Conclusion and perspectives.

In this chapter the synthesis of the new Ca3Ga2-2xZnxGe4+xO14 (0 ≤ x ≤ 1) solid solution was investigated for the first time by crystallisation from glass or under-cooled melt. The (x = 0) sample showed to reach higher crystallinity rates when crystallised directly from the melt, while the (0.25 ≤ x ≤ 1) compositions were achieved phase pure by congruent crystallisation from glass. The related structures and cationic disorder were fully characterised by combining SPD, NPD and atomic-resolution STEM-EDS. Across the solid solution, all samples retained the same P321 trigonal structure; hence, the Ca3ZnGe5O14 langasite is reported for the first time to crystallise in the trigonal P321 structure, in contrast to the previous report of a fully ordered monoclinic C2 structure. For compositions x = 0 and x = 1, the presence of only two cations allowed the use of neutron diffraction to quantify the cationic distribution over the layered framework (B, C and D) sites. As for the intermediate x = 0.5 composition, the presence of three cations with close atomic numbers and neutron scattering lengths, a 1D and 2D fitting approach of atomic scale STEM-EDS maps allowed to quantify its related cationic disorder and construct a chemically justified starting structural model for NPD data Rietveld refinement.

Furthermore, the cationic disorder between Ge 4+ /Ga 3+ (x = 0) and Ge 4+ /Zn 2+ (x = 1) was found to occur only at the 1a and 3f sites (B-and C-sites respectively), while the 2d "D-sites" showed a full domination by germanium atoms. Consistent with previous studies of the Ca3Ga2Ge4O14 (x = 0) single crystals showing a different cationic distribution of Ga within the same 1a and 3f sites. On the other hand, our results for the Ca3ZnGe5O14 (x = 1) showing a partial occupancy of Zn atoms in both coordination types, are far from the reported fully ordered Ca3ZnGe5O14

where Zn is only held in the 1a 6-coordinated site. The difference in the ordering between Ge 4+ , Ga 3+ and Zn 2+ compared to the literature could be assigned to the different synthesis routes employed here, favouring metastable structures. The study of the x = 0.5 composition for the first time, revealed the same ordering trend for Ga and Zn as the x = 0 and 1 compounds respectively, while Ge retained its full occupancy of the 2d sites. The approach to fully characterise this complex composition, was to first quantify the disorder using quantitative fits to 2D atomic-scale STEM-EDS maps to build a structural model for NPD refinements using chemically justified constraints. In principle, this 2D EDS maps refinements procedure can be applied for a wide range of materials, containing multiple elements with close atomic numbers (poor scattering contrast), distributed over different crystallographic sites.

The langasite structure's layered framework can be attractive for different types of studies.

For example, its kagomé lattice formed by the B-sites, is usually linked with magnetic frustration and spin liquid focused properties. In this context iron-doped Ca3Ga2-xFexGe4O14 compositions can be of much interest to investigate. The A3TeZn2Ge3O14 (A = Sr, Ba, and Pb) compositions adopting also the langasite structure [54], where only the C-sites are mixed between Zn and Ge, while the B-and D-sites are fully occupied by Te and Ge atoms respectively, showed a great SHG "second harmonic generation" response (13×KDP for 97

b) Arrhenius plots of the La1+xAE1-xGa3O7+x/2 melilites bulk conductivities at different x values with AE= Ca, Sr and

Ba. (a) panel was adapted from [10], (b) panel was adapted from [3], [5], [6].

In the CEMHTI laboratory, an alkali earth free melilite (i.e. La2Ga3O7. ). This means that its oxide ion conductivity also has 1D character, as indicated by molecular dynamic calculations in [12], and is ~10x lower at 800°C than that of near-optimal compositions such as La1.54Sr0.46Ga3O7.27 and La1.64Ca0.36Ga3O7.32, but still ~ 10 3 × greater than its opposing (x = 0) end member LaAEGa3O7 AE= Ca, Sr [2]. The retention of the melilite structure by La2Ga3O7.5 implies the existence of a new range of La1+xAE1-xGa3O7+x/2 compositions between the previously defined limits (x = 0.64, 0.54 and 0.35 for AE= Ca, Sr and Ba respectively), which have not yet been explored. In this chapter, the melilite Ba-containing series La1+xBa1-xGa3O7+x/2 solid solution synthesis is investigated by direct crystallisation of the under-cooled melt, as it has the broadest range of unknown super-excess compositions, and an unknown structural transition point. A structural study is also conducted, characterising the tetragonal melilite stability and its transition to the Oint ordered orthorhombic melilite as a function of the Ba substituted amount. The related cationic and anionic disorder is also mapped by combining SPD and NPD measurements.

Finally, the ionic conductivity of these solid solution samples is determined by AC impedance spectroscopy. The main interest here is to look for the highest Oint concentration containing La1+xBa1-xGa3O7+x/2 tetragonal melilite compound, and compare its conductivity to the Ca and Sr analogues.

Synthesis by direct crystallisation from the melt.

To extend the dopant limits and increase the Oint concentration in the La1+xBa1-xGa3O7+x/2 solid solution, direct crystallisation from the melt was performed using the ADL apparatus using a similar protocol to that reported for La2Ga3O7.5 [11]. Regardless of the barium amount all compositions were prepared following the same protocol. First, stoichiometric amounts of BaCO3 (STREM chemicals, 99.999% purity), La2O3 (STREM chemicals, 99.9% purity) and Ga2O3 (STREM chemicals, 99.998% purity) were weighed and ground together in an agate mortar, with ethanol to improve the homogenisation of the mixture. The resulting powder was dried at 100°C in a conventional laboratory oven for 10 min. The obtained dry sample was pressed into pellets of 13 mm each and broken into small fragments of ⁓50 mg each. Pellet chunks were levitated and melted using the ADL apparatus (described in the appendices Chapter A.I section A.I.1.1.2). The beads melted between 1800°C and 1850°C and were further heated to 1950°C for few seconds, then subsequently quenched by turning the lasers off. This procedure resulted in a direct crystallisation from the melt of the beads as indicated by a flash occurring on the cooling. The samples were obtained in the form of small beads (diameter of ⁓3mm) that appeared to be highly transparent, as reported for the La2Ga3O7.5 superstructured melilite bead samples [11].

The synthesised La1+xBa1-xGa3O7+x/2 (0.3 ≤ x ≤ 0.9) beads were first checked by laboratory PXRD, to detect the dopant limit for which the tetragonal 𝑃4 ̅ 2 1 𝑚 melilite is no longer stable.

To do so, a bead of each composition was crushed and ground in an agate mortar into fine powder and measured using a Bruker D8 advance in a (θ-θ) Bragg Brentano geometry, equipped with a Cu anode (λ= 1.5459 Å) and LynxEye XE detector. On the stacked diffraction patterns shown in Figure IV.3, all x < 0.8 compositions were indexed with the tetragonal P4 ̅ 21m cell.

Moreover, for La1+xBa1-xGa3O7+x/2 (x ≥ 0.8) compositions, their related diffraction pattern was observed with a splitting of the 𝑃4 ̅ 2 1 𝑚 hkls Bragg peaks. These diffraction patterns could be indexed with both (i) the La2Ga3O7.5 (x = 1) Ima2 melilite, and (ii) the La1.64Ca0.36Ga3O7.32 (x = 0.64) melilite, which crystallise in a pseudo-orthorhombic P1 cell, also induced by the ordering of interstitial oxides. Furthermore, the best match was obtained with the La2Ga3O7.5 (x = 1) Ima2 melilite. Z number), it is not possible to characterise the cationic disorder of these two elements over the A-sites. Moreover, due to the light oxygen electron number compared to La and Ba, it was also not possible to investigate the ionic disorder of the interstitial oxides (Oint) among the [GaO4]5 free channels, hence Oint occupations were fixed to the nominal composition on their reported positions. 103

For the x = 0.3, 0.675, 0.8 and 0.9 compositions SPD measured diffraction patterns, few extra peaks were noticed, which were indexed with different impurities: LaBa2Ga11O20 (S.G.

I2/m) (0.472(6)%wt) + LaGaO3 (S.G. Pbnm) (0.069(2)%wt) for x = 0.3. La1.3Ba0.7Ga3O7.15 for x = 0.675 (0.162(2)%wt) and 0.8 (0.088(3)%wt). LaGaO3 (S.G. Pbnm) (0.082(2)%wt) for x = 0.9.

In Figure IV.4 showing stacked SPD data of the measured compositions, Pawley refinements of these data revealed that the tetragonal melilite is retained for 0.3 ≤ x < 0.75 compositions while the x = 0.9 sample is fully orthorhombic. Moreover, the compositions between x = 0.75 and 0.85 exhibit a peak broadening, which was better modelled in Pawley fits by using both tetragonal and orthorhombic melilite structures. This suggests a stability limit of the 𝑃4 ̅ 2 1 𝑚 melilite and the beginning of its phase transition to the Ima2 superstructure starting at x = 0.75. Rietveld refinements of the acquired data were performed using Topas (V6) programme [13]. As mentioned above La, Ba and Oint occupancies were fixed to the nominal composition.

For patterns containing T or O phases, all the oxide displacement parameters were constrained to refine to a common value, whereas this constraint was applied to both structures independently for patterns containing both melilite polymorphs. An absorption correction was applied to all patterns Rietveld refinements, with µR values ranging from 1.34230(1) for x = 0.3 to 1.40990(1) for x = 0.9. In the following, Rietveld refinement conditions will be described separately in four compositions sections: (i) 0.3 ≤ x ≤ 0.725, (ii) x = 0.75, 0.8 and 0.85, (iii) x = 0.775, (iv) x = 0.9. compounds was shown to be different at higher temperatures (T ≥ 650°C), as indicated by the different activation energies, and was assigned to a phase transition from P1 to P4 ̅ 21m structure.

La1+xBa1

To study this possibility and better comprehend the conductivity of the samples, variable temperature NPD data were also acquired between room temperature and 820°C for the La1.9Ba0.1Ga3O7.45 (x = 0.9) sample, which is the only composition that consists of 100% Ima2 melilite polymorph at room temperature. To proceed for these measurements, multiple beads of La1+xBa1-xGa3O7+x/2 (x = 0.3, 0.6, 0.7, 0.8 and 0.9) compositions were first synthesised, then checked for purity two beads (ground together in powder form) at a time using laboratory PXRD. This process was repeated until large phase pure batches between 2.5g and 3g were accumulated for each composition. Room and high temperature neutron powder diffraction (NPD) measurements were then conducted on the D2B line at the ILL laboratory in Grenoble, Moreover, the thermal parameters of all atoms were refined as anisotropic (except the Oint which Biso was fixed at 1 Å 2 ). The overall composition of the oxides was subject to a penalty function which allows the Oint sites occupancies to refine while constraining the overall composition to near-nominal values. This strategy led to a total of 59 independently refined parameters (zero The cationic distribution was characterised as fully disordered for the tetragonal melilite, due to the presence of only one inequivalent A-site. The orthorhombic melilite structure which offers three possible A-sites thanks to its space group lower symmetry, allows a characterisation of the cationic distribution between La and Ba atoms over these sites. Benefiting from the constrained composition to refine close to the nominal, grants the possibility of refining the occupancies of each of the two La and Ba atoms. For both x = 0.8 and x = 0.9 compositions, La2 and La3 sites were found to contains double the Ba content present in the La1 site (see Table IV.3 and from Table A. 47 to Table A. 52 in the appendices Chapter A.IV). However, considering the three-sigma rule of their associated errors it is not possible to discern a partial ordered from a fully disordered system, meaning that no Ba site preference can be identified within the sensitivity limits of the refinement.

It has been known from literature that the La1+xCa1-xGa3O7+x/2 (0 ≤ x ≤ 0.64) solid solution was reported to crystallise in a pseudo-orthorhombic melilite cell (S.G. P1) for 0.55 ≤ x ≤ 0.64 To further investigate the cationic distribution of La and Ba, and a possible phase transition to a pseudo-orthorhombic P1 model for La1+xBa1-xGa3O7+x/2 (0.6 ≤ x ≤ 0.9) compositions, with a different A-sites cation ordering types (as reported for the La1+xCa1-xGa3O7+x/2 0.55 ≤ x ≤ 0.64 [5]). Two refinement strategies were then pursued: (i) converting the refined P4 ̅ 21m and Ima2

to P1 symmetry and using them as starting models with only La and Ba occupancies as refinable parameters; and (ii) using the reported pseudo-orthorhombic P1 structure of La1.64Ca0.36Ga3O7.32 as starting model with all atoms fixed Biso values to 1 Å 2 . These refinement procedures were also unsuccessful in answering the A-site cationic distribution question, as the refined occupancies associated errors were higher than the parameter itself, hence no meaningful values could be extracted. Finally, using the same strategy, La and Ba occupancies were fixed as in completely disordered system, and only the interstitial oxides positions and occupancies were let to refine. However, this procedure also had the same outcome and the related errors were higher than the parameter itself. These results mean that, even with quite different neutron scattering lengths between La and Ba (i.e. 8.24(4) fm and 5.07(3) fm respectively [17]), the amount and correlation of refined parameters is so great that the counting statistics are not sufficient to differentiate between these two elements.

It is known from the literature that intercalation of Oint atoms in the five-membered melilite framework forming rings centre, affects mostly the nearby oxides to satisfy its bonding conditions, hence inducing local disorder of these atoms [3], [5], [6], [11]. This is illustrated in

2(°)

820°C 770°C 720°C 525°C RT a) 2(°) b)
To identify the phases present at the different measured temperatures, Rietveld refinements were also run independently against both "HI" and "HR" data, and are described as follows:

La1.9Ba0.1Ga3O7.45 (x = 0.9) at 525°C: At this temperature, Rietveld refinements were carried out using only the orthorhombic model. In analogy with previously detailed x = 0.9 composition room temperature NPD refinement in section IV. As previously discussed in section IV.3.2.1, refinement of the La1.9Ba0.1Ga3O7.45 (x = 0.9) composition room temperature neutron data, revealed no preference for Ba atoms to be hosted in a specific A-site out of the three available. The interstitial oxide distribution also did not show strong evidence of a complete disorder over the melilite [GaO4]n framework, and good fits were secured with the orthorhombic Ima2 melilite structure. This was further confirmed by the 525°C refinement, which provided similar fit results and reliability factors (see Table IV.4).

Moreover, from VT-PXRD measurements, it appeared that at 720°C the sample is fully orthorhombic while being fully tetragonal at 770°C, which is confirmed by the extracted cell parameters. However, from initial refinements of NPD acquired data at these temperatures, diffraction patterns could not be fully fitted using only one of the two models. Generated Fourier difference maps of the 720°C refinement with a single orthorhombic cell did not reveal any residual nuclear density which could hint at interstitial oxide disorder. Moreover, several tests were run by filling the remaining Oint free channels with oxide atoms and refining the structure.

Even though these refinements slightly reduced the reliability factors from (Rwp= 4.44% GOF= 3.64) to (Rwp= 4.32% GOF= 3.55), the misfits were still present, and suggest a missing structure.

Thus, both tetragonal and orthorhombic melilites were added to the refinement of NPD data at both 720°C and 770°C temperatures. By doing so, a far better refinement was obtained with even lower reliability factors (see Table IV.4). Moreover, the fact that the refined weight % of tetragonal ranged from 35.8% (at 720°C) to 53.4% (at 770°C) while the orthorhombic melilite content decrease from 64.2% (at 720°C) to 46.6% (at 770°C) supports this refinement strategy.

The 820°C acquired data was the easiest to refine, as the use of only the tetragonal model was sufficient to describe the whole measured diffraction pattern.

The noticed structural trend in transiting from a low symmetry (Ima2) to a higher symmetry (P4 ̅ 21m) cells at higher temperatures, is actually consistent with the favoured greater disorder induced by the acquired thermal energy. A similar feature was noticed for the La1+xCa1- From this Figure, as x values increase a clear decreasing trend in the thermal stability of these melilites can be seen, this is consistent with the increasing metastability of these structures.

Moreover, one can also notice the stability of the Ima2 structure over a wider temperature range, which is in good agreement with the previously described melilite framework inability to host the Oint in a fully disorder framework (P4 ̅ 21m). the polymorphs stability limits against x "amount of substituted barium" and temperature drown from VT-PXRD measurement. The transition temperatures from the mixed P4 ̅ 21m + Ima2 to fully P4 ̅ 21m in the 0.725 < x < 0.8 region were extrapolated from the measured x = 0.8 and 0.9 compositions. The x = 1 compound decomposition temperature was taken from [11].

The tetragonal melilite was found to be no longer achievable phase pure by direct crystallisation from the melt starting x = 0.75 from La1+xBa1-xGa3O7+x/2 solid solution, as the Oint 1D ordered Ima2 melilite polymorph crystallises as a secondary phase, and forms at the expense of the P4 ̅ 21m smaller cell starting x = 0.9 composition. This means that its crystal structure is no longer stable for Ba substitution amounts higher than x = 0.9. In the melilite structures family, similar character was observed for the La1+xCa1-xGa3O7+x/2 solid solution, as when x values exceed 0.55 its crystal structure goes through a phase transition from P4 ̅ 21m to a pseudo-orthorhombic "trigonal" P1 cell, driven by the interstitial oxides ordering [5]. It is well known from the literature that the presence of interstitial oxide distorts its local environment pushing the edge-bridging oxygen atoms to the centroids of the five-neighbouring edge-sharing channels, yielding a satisfactory description of the bonding around this defect [5], [11] La1.54Sr0.46Ga3O7.27 and La2Ga3O7.5 compounds conductivity from [4], [11] overlaid for comparison. From this figure, the x = 0.6 sample exhibits the best conductivity (⁓ 10 -2 S.cm -1 ) for temperatures below 500°C, which gets slightly surpassed by the x = 0.7 composition at 500°C ≤ T, reaching 3.8×10 -2 S.cm -1 at 700°C. Although these compositions exhibit high conductivity values at intermediate temperatures, they remain almost one order of magnitude lower than the best known La1.54Sr0.46Ga3O7.27 and La1.64Ca0.36Ga3O7.32 melilite ionic conductors, which display a 10 -1 S.cm -1 value at 800°C. Moreover, one can notice that compounds which crystallise under the Ima2 structure or contain a substantial amount of the Oint ordered melilite polymorph (i.e. x = 0.8 and 0.9 compositions) possess lower conductivity values than the ones which crystallise under only the tetragonal P4 ̅ 21m melilite (i.e. x = 0.6 and 0.7 compounds). This is due to the interstitial oxide network difference in both polymorphs: the Ima2 melilite exhibits a 1D ordered Oint network along the a direction, which limits oxide diffusion to neighbouring channels in the b direction. In contrast with the tetragonal P4 ̅ 21m melilite, its Oint disordered network covers the whole 2D layered framework, which eases the charge carriers in the ab-plane. This argument is supplied by molecular dynamics calculations from [19], [20], which evidenced the 1D and 2D conduction mechanisms of both Ima2 and P4 ̅ 21m melilites, respectively. Furthermore, it appears that all measured samples feature a conductivity plateau (i.e. not evolving values) for temperatures higher than 500°C. This behaviour type could be related to several reasons: conduction mechanism change, phase transition, increase of the grain boundaries resistance or simply the maximum ion diffusivity was reached in these compositions as reported for several sodium ion conductors

Conclusion and perspectives.

The La1+xBa1-xGa3O7+x/2 solid solution synthesis was investigated in the present chapter. By using direct crystallisation of the melt as synthesis approach, the x limit previously set at x = 0.35 [6], was further extended to x = 0.9, with the x = 1 end member reported in [11].

Compositions of La1+xBa1-xGa3O7+x/2 (0 ≤ x ≤ 0.35) were reported to crystallise in the tetragonal P4 ̅ 21m melilite structure. In this study, from SPD data, this polymorph was shown to be further retained until the Ba substitution amount by La reached the value of x = 0.725, hence making this composition the highest tetragonal Oint concentration containing melilite among the of La1+xAE1-xGa3O7+x/2 AE= [Ca, Sr, Ba] melilite solid solution, and also the most interesting to characterise its conductivity. Higher substitution amounts exhibited the coexistence of two melilite types: tetragonal P4 ̅ 21m and orthorhombic Ima2 structures (for 0.75 ≤ x ≤ 0.85). This is no longer the case for La1.9Ba0.1Ga3O7.45 (x = 0.9) composition as the orthorhombic Ima2 melilite was found as the only stable phase at room temperature, consistent with the previously reported La2Ga3O7.5 melilite. This phase transition was linked to the inability of the small-cell tetragonal melilite to host high interstitial oxide concentration in a disordered way, while keeping satisfactory bonding conditions of all interstitial oxides, which was better seen in the anisotropic atomic displacement parameters of the Oint surrounding oxides. Local interstitial oxides environment relaxation was possible by the ordering of the Oint atoms along the a direction and among corner sharing five-membered [GaO4]5 network-forming pentagons. The ionic and cationic distribution was mapped by the help of NPD data collected at room temperature (for x = 0.3, 0.6, 0.7 0.8 and 0.9 compositions) and high temperature (for x =0.9 composition) among both P4 ̅ 21m and Ima2 melilites, which indicated a complete disorder of both A-site cations over their offered crystallographic sites, while no preference nor additional population of the interstitial oxides was found. This analysis was not possible to push further, as the refined errors of the used Ca pseudo-orthorhombic P1 model were very high. Finally, the bulk and total ionic conductivity of these samples was measured by AC impedance spectroscopy, and revealed a maximum value of 3×10 -2 S.cm -1 for x = 0.7 at 700°C, which is within one order of magnitude of the best melilite conductor, i.e. La1.54Sr0.46Ga3O7.27 reaching a maximum value of 10 -1 S.cm -1 at 800°C. The La1.6Ba0.4Ga3O7.2 (x = 0.6) compound on the other hand was found to be more conductive than the La1.54Sr0.46Ga3O7.27 melilite at lower temperatures (300°C ≤ T ≤ 500°C), however this is no longer the case for temperatures higher than 560°C as the La1.54Sr0.46Ga3O7.27 compound becomes more conductive due to the reached maximum conductivity plateau for the La1.6Ba0.4Ga3O7.2 (x = 0.6) melilite.

As perspectives for this work, the increase of doping limits in the La1+xAE1-xGa3O7+x/2 AE= Recent works on the two compounds described above and in the appendices chapter A.V reported these materials as potential phosphor hosts [3]- [5]. Moreover, their ionic conduction was also investigated without doping elements, which revealed promising conductivity values in the intermediate temperatures range [6], [7]. Furthermore, the oxide migration paths in both structures were explored by bond valence-based energy landscapes (BVELs) calculations [6], [7], disclosing the 2D and 3D conduction mechanisms in the Ca3Ga4O9 and Ca5Ga6O14 compounds respectively. Additionally, BVELs unveiled potential interstitial oxide positions which may improve the ionic conductivity when introduced as seen for the La1+xAE1-xGa3O7+x/2 AE= [Ca, Sr, Ba] melilites [8]- [10].

This chapter will subject first identification of the energetically favourable aliovalent dopant by Ca or Ga substitution in the Ca5Ga6O14 compound, synthesis and finding its dopant limits.

A study of the doped and parent compounds crystal structures will be conducted by coupling synchrotron powder diffraction (SPD), neutron powder diffraction (NPD), transmission electron microscopy (TEM), density functional theory (DFT) for structural prediction, to achieve the most accurate possible description of their structures, especially to study the effect of the doping on the structure, i.e. if the charge compensation will occur by introducing cation vacancies or interstitial oxides. The Ca5Ga6O14 compound was chosen instead of the Ca3Ga4O9 due to its framework being formed by only edge sharing five-membered GaO4 tetrahedra (melilite-type sheet), compared to the latter one which contains a mixture of five-and fourmembered GaO4 rings, hence making the first compound the most melilite-like one.

Dopant prediction and synthesis.

Dopant prediction by energy calculations.

As mentioned in Chapter I, structural prediction with the help of computational methods were reported to be successful in narrowing the heavy task of synthesis exploration [11]- [13].

The following calculations were performed by Meigeng Gao and Matthew Dyer (University of Liverpool, UK). To predict the energetically favourable aliovalent dopant by Ca or Ga substitution in the Ca5Ga6O14 compound, the Simdope code [14] was used to generate crystal structures according to the following substitutions:

• Ca4.5La0.5Ga6O14.25, Ca4.5Y0.5Ga6O14.25, i.e. two calcium atoms by two lanthanums or yttriums.

• Ca5Ga5.75Nb0.25O14.25, Ca5Ga5.5Ge0.5O14.25, i.e. one gallium by one niobium atom or two galliums by two germanium atoms.

The generated structures were relaxed and their related energies were calculated by DFT using the Vienna ab-initio Simulation Package (VASP) [15] programme. As shown in Figure 139

Attempts on extending the La-doping amounts by different synthesis routes.

To increase the dopant element concentration, i.e. to expend the x limit in the LaxCa5-xGa6O14+x/2 solid solution, full and congruent crystallisation from glass or undercooled melt was attempted as an alternative synthesis route, as demonstrated in previous studies [18]- [23]. To do so, the initially prepared mixture pellets were this time crushed to small chunks and melted using the ADL apparatus (described in the appendices Chapter A.I section A.I.1.1.2)

[24], [25]. A pellet piece (⁓ 35mg) was levitated using Ar or O2 gases, and heated using a pair of CO2 lasers (10.6 µm) until the liquid state of the sample was reached at 1350°C. The levitating bead was either subsequently quenched by turning off the lasers to obtain glass samples, or slowly cooled to room temperature in 30 seconds by decreasing the lasers power to secure its crystallisation from the melt. A third procedure was also attempted by allowing the molten sample to touch the nozzle and turning the lasers off; the contact surface acts as a nucleation centre which leads to crystallisation of the whole bead. In a final attempt, sol-gel synthesis was considered to extend the amount of x in the LaxCa5-xGa6O14+x/2 solid solution. This approach was previously demonstrated to considerably extend the dopant concentration in the La3Ga5-xGe1+xO14+x/2 langasite compounds from x = 0.3 to x = 1.5 [26]. Stoichiometric amounts of La(NO3)3•6H2O (STREM chemicals, 99.99%), Ga(NO3)3•6H2O (Alfa Aesar Puratronic, 99.99%) and Ca(NO3)2•4H2O (STREM chemicals, 99%) were weighted according to the La0.15Ca4.85Ga6O14.075 compositions (as a test), and dissolved in deionised water. The mixture was constantly stirred and heated at 100°C while adding citric acid in a 3:1 molar ratio, ethylene glycol was added just after in 1:1 molar ratio with citric acid; the solution was kept stirred and heated for 16h until a gel was formed, the gel was then calcinated at 1000°C for 12h. The resulting powder was then heated at 1200°C for 2h to achieve crystallisation; this led to a multiphase sample as both Ca5Ga6O14 and Ca3Ga4O9 structures crystallised.

For the following characterisations, solid state reaction was chosen to synthesise both La-free and La-doped materials, as it had the sharpest Bragg diffraction peaks compared to the other crystallisation approaches.

Structural determination and analysis.

Purity and composition verification. Furthermore, the La-doped compound shows a nice constant La atomic % variation across the measured points. However, this is not the case for Ca and Ga cations, as the measured atomic % varies much more than La across the different measuring points. In fact, this could be a matter of sample homogeneity at the pellet surface, i.e. residual sacrificial powder. A first indexation of both SPD patterns indicated that both samples are not phase pure as suggested by prior lab PXRD measurements. The x = 0 sample showed some low intensity additional Bragg peaks that could not be indexed. This impurity could originate from the sample dilution preparation, as it was not present in prior lab PXRD measurements. The x = 0.25 compound on the other hand showed the presence of CaO secondary phase, one explanation could be the formation of CaO due to gallium evaporation during the initial synthesis process.

The amount of CaO was later quantified at 0.56% (wt%).

A first constraint-free Rietveld refinement of the acquired SPD data was performed using Topas (V6) program [17]. For x = 0, with a total of 87 independently refined parameters, the refinement led to satisfactory reliability factors, with Rwp= 2.20%, GOF= 3.45 (see Figure V.9a

for refined plot and Table V.1 for refined structural parameters). SPD data of the x = 0.25 composition was first refined with no La substitution to the Ca5Ga6O14 crystal structure (87 independently refined parameter). Clear intensity misfits were observed on the refined plot, and made it obvious that something is missing from the cell. Lanthanum was then introduced in all three calcium sites with constrained occupancies of each mixed site to add up to 1, increasing the total number of refined parameters to 100. The constraint was defined in Topas as follows:

OccLa1*= 1-OccCa1 / OccLa2= 1-OccCa2 / OccLa3= 1-OccCa3
The addition of lanthanum in the cell dropped the reliability factors from Rwp= 2.27%, GOF= Refined La occupancies on the x =0.25 phase were consistent with previous results as the cationic disorder was manifested mainly on the Ca3 sites (Table V.4). Moreover, one can perceive a big jump in the thermal parameters of the O2, O8 and O9 atoms toward higher values going from the x = 0 to the x = 0.25 material (see Figure V.15a). Furthermore, when localising these oxygen atoms in the structure, it appears that they surround the Ca3 sites (see Figure Fourier difference maps of the x = 0.25 compound were generated using Topas (V6) [17] from its refined NPD data, and visualised using Vesta [29]. In Extracting as much information as possible from an incomplete and noisy data set can be challenging in particular in the case of disorder. The maximum entropy method (MEM) was introduced as an alternative strategy to the inverse Fourier transform for constructing the most probable electron/neutron density maps using as constraints a given X-ray/neutron diffraction data set when refinements or Fourier syntheses fail to describe accurately the whole system (i.e.

noisy data, light elements density covered by heavier elements, low elements concentration, static or dynamic disorder…). The use of the maximum entropy method has been demonstrated in many crystallographic works as a powerful calculation process in solving the problems stated above [30]- [35].

After the unsuccessful attempt at low temperature NPD data analysis in confirming or denying the interstitial oxide position at the one defined by RT-NPD analysis, as described in section V. Sample preparation and ionic conductivity properties.

Pellet densifying attempts.

In order to proceed to AC impedance measurements, a dense sample (ideal density >95%) Attempts to sinter the powder at higher temperatures could not be possible as the sample melts between 1300°C-1350°C. To attain materials with higher density, spark plasma sintering (SPS) operating at high temperature and high pressure was considered as a sintering route to achieve this goal. After several of attempts by Sebastien Chenu at the IRCER laboratory in Limoges, the SPS synthesis protocol for achieving 99% dense pellets was found to be as follows: the initially synthesised LaxCa5-xGa6O14+x/2 x = 0 and 0.25 compositions were ground to powder and then ball milled using a planetary mill for 10 min independently. The resulting powders were filled in graphite dies of 10 mm diameter each. The powder samples were then sintered by spark plasma sintering process, at 800°C under a 100MPa pressure for 2 minutes and then at 1150°C under a 100MPa pressure for 5 minutes (100°C/min for both heating steps). The synthesised pellets had a dark black colour due to the carbon diffusion from the graphite die (Figure V.23). Laboratory X-ray diffraction measurements were performed on freshly SPS [9], [22] and Chapter IV of this thesis.

From the Arrhenius plots presented in Figure V.24c, they indicate an increase in the ionic conductivity of the LaxCa5-xGa6O14+x/2 samples in the following order: x = 0, x =0.125, x = 0.25;

these results are consistent with the increase of the interstitial oxide concentration. At 800°C a maximum value of σ= 2*10 -5 S.cm -1 is reached for La0.25Ca4.75Ga6O14.125, which is two orders of magnitude higher than Ca5Ga6O14, which reaches a conductivity of σ= 5*10 -7 S.cm -1 at 800°C. Even though such an increase is observed between La-free and La-doped samples, the x = 0.25 compound still exhibits a much lower conductivity capacity than the previously described La1.7Ba0.3Ga3O7.35 melilite in Chapter IV and the best known La1.54Sr0.46Ga3O7.27 melilite conductor [9] displaying 0.1 S.cm -1 at 800°C. This difference can be explained by the much higher concentration and positional disorder of the interstitial oxides in the orthorhombic and tetragonal melilites in which, the first one sees its Oint forming one-dimensionally (1D) ordered chains over the a direction (in La2Ga3O7. The Ca12Al14-xGaxO33 mayenite solid-solution was found to crystallise in the Ca5Ga6O14 structure for 8 ≤ x by a glass crystallisation synthesis approach [7]. Conductivity of the x = 14 compound from this mayenite solution (i.e. Ca5Ga5.82O14-δ) was found to reach 10 -3 S.cm -1 at 800°C, which is two order of magnitudes higher than our La0.25Ca4.75Ga6O14.125 compound.

Moreover, EDS quantification of the Ca content at surface of the negative electrode and cross section of the sample poste impedance measurement, evidenced a high Ca concentration at the surface of the negative electrode, totally absent in the cross section of the sample [7]. The acquired PXRD data, to satisfy the nominal composition. The left amorphous amount was not quantified, as the samples were synthesised by crystallisation from glass precursors. Hence, another explanation could be diffusion of amorphous Ca left on the residual glass. Therefore, it is hard to compare our sample properties the one reported by the authors in [7] as of the different synthesis approached in the two studies, i.e. solid-state reaction in this work vs glass crystallisation in [7].

Conclusion and perspectives.

In this chapter, DFT calculations helped to target the synthesis exploration work, and suggested that lanthanum is the most favoured element for doping the Ca5Ga6O14 compound and making new oxide ion conductor materials. The synthesis of the doped compound by different methods revealed that experimentally only a low amount could be introduced into the crystal structure (i.e. LaxCa5-xGa6O14+x/2 xmax = 0.25). The crystal structure of both the La-free and maximum La-doped compounds were studied by a combination of SPD, TEM, NPD, MEM and DFT. From SPD data, the La positioning was defined to occur among both Ca1 and Ca3 sites. However, the amount of La in the Ca3 sites was far superior to that in Ca1 sites. This was confirmed by DFT, STEM-HAADF imaging showing brighter Ca3 spots, but also confirmed by STEM-EDS and EELS mapping of the La. The successful substitution of Ca 2+ by La 3+ cations in the Ca5Ga6O14 structure implies a charge balancing by either cationic vacancies or interstitial oxides. From SPD refinements and composition verification by microprobe, no strong evidence of cationic vacancies could be found nor the presence of secondary Ca-or Ga-rich phases, which ruled out this possibility. The hypothesis of Oint introduction was investigated by neutron diffraction data analysis. However, these investigations did not achieve direct identification of the interstitial oxide position: even by applying maximum entropy method calculations, the interstitial oxide was still not apparent. Nevertheless, by MEM a clear disturbance of the Ca3 channel local environment was observed in the constructed nuclear density. These obtained results were in qualitative agreement with the predicted structures by DFT with the most energetically suitable positions for the interstitial oxide to be held in, as the calculations indicated a significant distortion of the Ca3 channel environments. Finally, the AC impedance measurements indicated an increase of nearly two orders of magnitude from the La-free Ca5Ga6O14 to the maximum La-doped Ca5Ga6O14 compounds, which is consistent with the introduction of interstitial oxides.

As perspectives for this work, many exploring paths can be followed. For instance, Nd can be investigated in doping the Ca5Ga6O14 structure as its energy lay close to the lanthanum. The synthesis of RE-doped Ca3Ga4O9 phase could also be investigated for new oxide ion conductor materials, as the non-doped material exhibits a conductivity of almost 3×10 -3 S.cm -1 at 1000°C.

Therefore, finding the right aliovalent dopant element and benefiting from a melilite related framework (described in Chapter A.V) could allow the increase of this conductivity value by few factors.

General conclusion

The purpose of the presented work in this thesis is to develop new materials with high performing properties for different application types, and is motivated by the increasing demand for new materials from different parties. These solid-state chemistry studies group the melilites and melilite-related materials with potential interest for their optical and ionic conduction properties. The use of aerodynamic levitation coupled to two CO2 lasers (ADL) allowed the synthesis of glass precursors of these materials in the form of spherical beads by melting the composition first and quenching them with high cooling rates (⁓ 300°C/s) while levitating the sample. Crystallisation of the glass then took place using the adequate heat treatment (studied by DSC and VT-PXRD) to secure phase pure fully-dense ceramics. Using the ADL also enables direct crystallisation from the under-cooled liquid as a new synthesis approach to reach for new metastable materials unreachable by conventional solid-state reactions. The studied compositions and structures were characterised by coupling multiple diffraction techniques i.e. powder X-ray diffraction (laboratory and synchrotron), neutron diffraction, selected area electron diffraction, scanning electronic microscopy, transmission electronic microscopy; and solid-state nuclear magnetic resonance spectroscopy. The macroscopic properties on the other hand were investigated by luminescence spectroscopy and AC-impedance spectroscopy.

The new P21212 fully ordered superstructured SrREGa3O7 RE= [Ho -Yb] melilite family [1] was first investigated to extend its stability limits to other rare earths. The Dy and Lu analogues were successfully synthesised by crystallisation of glass precursor samples. However, it was not possible to synthesise the Tb compound in this new polymorph as this was attributed to the Tb 3+ inability to be held in a [6+1] coordination-type due to its bigger size.

Different hypothetical ordering-types of the A-site cations are discussed why they are disfavoured. Investigation on the thermal stability of this new melilite polymorph revealed the occurrence of a phase transition at high temperature into the parent fully disordered P4 ̅ 21m melilite, which suggested the possibility of stabilising this structure by rapid cooling to room temperature. The synthesis of this disordered polymorph was well achieved for the whole series RE= [Dy -Yb], previously unreported for Tm and Yb compounds. Moreover, the luminescence properties were investigated for the SrErGa3O7 P21212, P4 ̅ 21m and glass compounds. The results have showed the A-site cation ordering effect on their optical properties, as its Er emission band showed double the intensity of its P4 ̅ 21m and glass analogues. The main challenge of this study was to adapt the glass crystallisation process for the SrLuGa3O7 P21212 and SrYbGa3O7 P4 ̅ 21m compounds as secondary phases were easily induced.

In continuity of ordered/disordered systems, the Ca3Ga2-2xZnxGe4+xO14 (0 ≤ x ≤ 1) solidsolution crystallising in the langasite structural family, which is related to the melilite structure, synthesis was investigated by both full and congruent crystallisation from glass or the molten liquid. The P321 trigonal langasite was retained for the whole solid solution, hence achieving the first P321 Ca3ZnGe5O14 previously reported to crystallise under a monoclinic C2 polymorph [2]. This solid solution present three isoelectronic elements i.e. Ga 3+ , Zn 2+ and Ge 4+ , which makes its related cationic disorder characterisation challenging and not feasible by X-ray diffraction due to the absence of scattering contrast. To overcome this difficulty, neutron diffraction was used for the x = 0 and 1 end members which showed the occurrence of the cationic disorder between Ga/Ge (x = 0) and Zn/Ge (x = 1) among the B-and C-sites (i.e. 1a and 3f positions). Moreover, for the x = 0.5 compound a starting structural model was built by first quantifying the disorder from a unique 2D fitting of STEM-EDS images of each cation among the same sites. By proceeding in this way, justified chemical constraints were applied to the Rietveld refinement against this sample neutron data and divulged the same disorder trend seen in the end members. The main difficulties encountered in this project, apart from the highly challenging synthesis of phase pure sample, were the different neutron refinements strategies as of the low neutron scattering contrast between Ga and Ge for the Ca3Ga2Ge4O14 compound.

Also, the development of a whole new analytical protocol of the atomic-scale STEM-EDS maps.

The second part of this thesis was focussed on ionic conducting materials. By adopting direct crystallisation from the molten liquid, the highest interstitial oxide containing P4 ̅ 21m tetragonal melilite was successfully synthesised in the La1+xBa1-xGa3O7+x/2 solid solution with x = 0.725.

Moreover, the solid solution was further synthesised to x = 0.9, with x = 1 studied previously at CEMHTI [3], which crystallises under the Ima2 orthorhombic melilite polymorph.

Furthermore, the structural trend was studied by X-ray and neutron diffraction, revealing the complete La/Ba disorder over the possible A-sites, while the interstitial oxides remained disordered in the P4 ̅ 21m polymorph and are chain like ordered in the Iam2 melilite structure.

The study of these compounds by AC-impedance spectroscopy displayed the highest conductivities for La1.6Ba0.4Ga3O7.3 at 500°C (⁓10 -2 S.cm -1 ), equalling the best known melilite conductors: La1.54Sr0.44Ga3O7.27 (⁓10 -2 S.cm -1 ) La1.64Ca0.36Ga3O7.35 (⁓6.5×10 -3 S.cm -1 ) [4], [5] at the same temperature. However, at higher temperatures Arrhenius plots exhibited a plateau with the highest value of ⁓7×10 -1 S.cm -1 secured by the La1.7Ba0.3Ga3O7.35 compound at 800°C, which is less than an order of magnitude lower than La1.54Sr0.44Ga3O7.27 and La1.64Ca0.36Ga3O7.35 both reaching ⁓10 -1 S.cm -1 [4], [5].

Following these results, we were interested in developing new ionic conductor materials with a melilite-like structure. The Ca5Ga6O14 structure matched our demands as it has the same melilite layered network stacked antiparallelly with different positioning of the A-sites.

Lanthanum was found to be the most energetically favourable dopant element among the studied ones by DFT. The synthesis of the LaxCa5-xGa3O14+x/2 solid solution was successfully achieved by solid-state reaction with a maximum dopant amount of x = 0.25. Further synthesis investigations to extend the doping limits were conducted by glass crystallisation, direct crystallisation of the melt, and sol-gels; however, all these attempts were unsuccessful as LaCaGa3O7 or Ca3Ga4O9 impurities were part of the samples. Characterisation by X-ray synchrotron diffraction of the cationic disorder between La and Ca atoms was found to occur only among the Ca3 sites, which are the most open melilite-resembling channels. Moreover, from Rietveld analysis against SPD data no cationic vacancies were found to take place in the refined structure, which eliminates the possibility of charge balancing by cations vacancies. The interstitial oxide position was not possible to determine by neutron diffraction data analysis.

Even though a Fourier peak can be observed on Fourier difference maps from NPD Rietveld analysis, the maximum entropy method has showed its none presence in the reconstructed neutron density from the same set of NPD data. The most energetically favourable configuration for the interstitial oxide and lanthanum positioning in the structure were computed by DFT calculations, and revealed their arrangement among the Ca3 channels where the Oint is stabilised directly between two lanthanum atoms at the [GaO4]n sheets level, consistent with the observed Fourier peak from NPD data analysis and previous reported melilite conductors. Ionic conductivity of the doped sample exhibited an increase of two order of magnitudes over the Lafree compound: 2×10 -5 S.cm -1 (x = 0.25) vs 5*10 -7 S.cm -1 (x = 0) at 800°C. Moreover, due to the 0D arrangement aspect of the interstitial oxides, the conductivity of these materials is far below the one of those melilites crystallising under the small cell tetragonal polymorph.

Tthe use of aerodynamic levitation coupled to two CO2 lasers was shown to help achieve vitrification of different compositions unreachable by conventional melt quench process, which can then be used as metastable precursors to crystallise in new out of equilibrium structures.

Moreover, the ADL was also shown to facilitate direct crystallisation from an under-cooled melt for some compositions. Regarding these aspects, many reported unvitrifiable systems by conventional melt quench process, or even unexplored compositions are of interest to investigate their glass synthesis using the ADL. For instance, and as mentioned in Chapter II the Ba-based melilites especially the BaREGa3O7 RE= [Yb, Lu] compositions, where the size mismatch between the alkali and rare earth metals is maximised, can be interesting to investigated how the melilite framework distort to accommodate such a size difference. The synthesised Ca3Ga2-2xZnxGe4+xO14 (0 ≤ x ≤ 1) solid solution compositions exhibiting a highly disordered layered framework, are much of interest in complementing their study by functionalising these materials (e.g. by Cr 3+ ) and investigate their related optical properties, as

shown in nearby compositions Zn1+xGa2-2x(Ge,Sn)xO4:Cr 3+ crystallising in the spinel structures [6]. Additionally, the adopted 2D atomic scale STEM-EDS maps refinement approach of different cations from the same compound, was the key in elucidating the disorder between three isoelectronic elements in the Ca3ZnGe5O14 (x = 1) compound. Therefore, this new characterisation technique can be used in many different materials where their related disorder characterisation remains a challenge, as in high entropy oxides (HEO). Finally, knowing that an alkali free melilite was reported, i.e. La2Ga3O7.5, but also from Chapter IV reporting the La1.725Ba0.275Ga3O7.3625 as the tetragonal P4 ̅ 21m melilite with the highest interstitial oxide content, both achieved by proceeding direct crystallisation from an under-cooled melt. This procedure could be extrapolated to the Ca-based and Sr-based LaAEGa3O7 melilites to extend their relative doping amounts, which may improve their already high conductivity values.

The ABC3O7 melilites, AB2O4 spinels, ABO3 perovskites and A3B5O12 garnets are well studied structures in the literature due to their crystalline structures ability to accommodate a variety of different nature, size and oxidation state elements in different coordination types [7][8][9][10], which leads to a multiple of interesting properties [11][12][13][14]. In this context, the occurrence of previously described langsite structures in chapter III are of interest materials. These structures family are mainly known for their piezoelectric properties [15,16]. Nevertheless, these compounds family, especially the La3Ga5(Ge/Si)O14 compound, are readily synthesised as large-scale transparent single-crystals [17]. Several studies have developed new optically active langasite compounds, for example the rare earth doped La3SbZn3Si2O14 composition which showed white light emission [18], or the cationic framework ordered La3Ga5MO14:Eu3 + (M = Zr, Hf, Sn) as red-emitting LED phosphors [19]. However, langasite materials with high small rare earth (Ho -Lu) concentration fully occupying the A-sites positions were never reported due to their challenging synthesis. By proceeding crystallisation from a glass precursor or an under-cooled melt it could be interesting to investigate the synthesis of these langasite compositions, i.e. RE3Ga5GeO14 RE = (Ho -Lu), in the hunt of new optically active materials.

Additionally, investigating the possible synthesis of RE3-xAExGa5-xGe1+xO14 with possible different ordering-types between the rare earth and the alkali earth metals when the size mismatch between these two is maximised, as seen in chapter II and reported in [20] for the melilite structures, knowing the structural similarities between these two structures.

or slowly cooled down to room temperature to crystallises it from the melt. The use of CO2 lasers makes it possible to reach very high temperatures estimated around 3000°C. Moreover, this contactless synthesis approach between the sample and the nozzle allows to avoid the contamination and nucleation problems cited above. Furthermore, the synthesised beads have usually a diameter between 1 and 5mm, which make them very small in size, hence reaching high cooling rates (between 1000°C -300°C / s depending on the levitating gas). The sample and reference chambers are heated simultaneously with a dedicated heating source for each. DSC records the heat flow difference between the sample and reference as they are both heated at once. When the sample goes through a structural or matter state evolution (i.e.

crystallisation, phase transition, fusion…), it requires a different energy than the reference to keep both at the same temperature, which is manifested by either an exothermal or endothermal peak.

Differential scanning calorimetry (DSC) is one off the first characterisation techniques to be run after the glass synthesis, as it permits to determine the most important physical quantities , step size = 0.0001°) thanks to its high flux (5×10 11 photons/second at 30 keV). Moreover, its short wavelength (λ= 0.458084 Å) allows to explore a longer Q (Å -1 ) range, which provides more information about the atomic occupancies and thermal parameters. SPD data illustrated in Chapter V were measured on the CRISTAL beamline at soleil synchrotron in France with an incident wavelength of λ= 0.67153 Å over the angular range of 1°-60° (2θ) and a step size of 0.004°. A.I.2.2.3. Neutron diffraction.

Elements with a small number of electrons are usually hard to distinguish from X-ray diffraction, especially if the material contain both heavy and light elements, as X-ray diffraction is based on the interaction with the electronic density of the atoms. Usually the suitable solution to extract valuable information about these atoms is to proceed neutron diffraction as their scattering is not the same (e.g. oxygen is much more visible in neutron diffraction than X-ray diffraction). Moreover, this technique can also be used when two elements have close atomic number but different neutron scattering lengths, which make it possible to characterize their respective occupancies on the same site. Furthermore, neutron diffraction doesn't show strong peak intensity extinction at high angle as seen in XRD; this advantage can be linked to the independent relation between the scattering lengths and diffraction angle. It is worth noting that large amounts of sample (⁓5g) are used in order to keep reasonable acquisition time.

Neutron powder diffraction (NPD) data presented in Chapter III were acquired on the instrument MEREDIT at the Nuclear Physics Institute, Czech Republic, which provides an incident wave length of λ= 1.46 Å and a measuring range between 4°-144° (2θ) and a step size of 0.08° with a measuring time of 970s/step. As for NPD data displayed in Chapters IV and V, measurements were conducted on the D2B line in the ILL laboratory, France. The incident wavelength of this neutron line is λ= 1.60 Å, with a measuring range of 4°-160° (2θ), a step of 0.05°, and a total measuring a time of 14400 seconds.

The measured data at the D2B line were provided in the form of two data sets: high intensity "HI" and high resolution "HR". HI data are the integration of the whole 2D pattern, whereas observed structure factors (issues due to incomplete and noisy data) [1]. The principal of MEM calculations relies on the probability's theory (Bayesian statistics). pr(X1|X2): probability that X1 is true under the condition that X2 is true.

-Sc: Hypothesis or Scene to validate (the density in the unit cell).

-D: New data of a certain observation (the diffraction data).

-I: the prior information (about Sc before getting D), the prior density (either flat or corresponding to any "relevant" structural model). with k a positive constant and 𝜌 𝑛 set of probabilities associated to these statements.

The deduction {pr(Sc|DI

A.I.2.2.6. Nuclear magnetic resonance (NMR).

Solid state nuclear magnetic resonance (NMR) spectroscopy, is a powerful characterisation technique in probing the local structure/environment of a chosen nuclei. Moreover, this technique is based on the Zeeman Effect. NMR studies of a nuclei requires a nuclear spin I ≠ 0 of the probe atom. The spinning nature of an atom nucleus generates a moment I consequently a magnetic moment µ. In the absence of an external magnetic field, the nuclear spins are degenerate, meaning that they are disoriented and possess the same energy. When an external magnetic field B0 is applied, it provokes a splitting into 2l+1 possible orientations separated by

Larmor frequency (ν0).

ν 0 = 𝛾B 0 2𝜋 (Equation A.1)
In solids the magnetic field around each nucleus is affected by the electronic cloud of the neighbouring nuclei, causing different interactions types (i.e. chemical shift interaction, direct dipole-dipole interaction, J-coupling interaction, quadripolar interaction) interfering with the Zeeman Effect.

A.I.3. Structural solution and refinements.

A.I.3.1. The Rietveld method.

The acquired laboratory, synchrotron or neutron diffraction data were subject of analysis by the Rietveld method, which simulates a diffraction pattern from a theoretical model (structure)

and compare it to the measured diffraction pattern. The simulated intensities at a certain 2θ value (here we call it i) are calculated using the following mathematical formula: -𝑌 𝑐𝑎𝑙𝑐 𝑖 : Calculated intensity at position (in 2θ).

𝑌 𝑐𝑎𝑙𝑐 𝑖 = ∑
-𝑌 𝑏𝑎𝑐𝑘 𝑖 : Background calculated intensity at the i th position (in 2θ).

-𝑆 𝜙 : Scale factor proportional to the number of unit cells contributing to the scattering divided by the unit cell volume.

-𝐽 𝜙𝑘 : Multiplicity factor of the k th reflection.

-𝐿𝑝 𝜙𝑘 : Lorentz-polarisation factor.

-𝑂 𝜙𝑘 : Preferred orientation correction factor.

-𝑀: Beam absorption correction function.

-|𝐹 𝜙𝑘 |: Structural factor.

-Ω 𝑖𝜙𝑘 : Profile function.

The background is usually defined either manually, or by a polynomial function type (Chebyshev, Legendre). In powder diffraction problems, a Pseudo-Voigt profile function is commonly used to describe the patterns intensity distribution around a peak k, as it combines both Gaussian (from the instrument, i.e. U V W) and Lorentzian (from the sample, i.e. microstructure and crystallite size X Y) contributions. In this work a TCHZ profile function was used as it considers the diffraction angle dependent Gaussian and Lorentzian broadening variations.

To judge the quality of a Rietveld refinement and how the theoretical model compares to the experimental data, a first look at the difference curve (𝑌 𝑜𝑏𝑠 𝑖 -𝑌 𝑐𝑎𝑙𝑐 𝑖 ) can help identifying the poorly fitted regions; the flatter this difference curve is the better it is. Moreover, after each refinement cycle, reliability factors (Rp, Rwp, RBragg, χ 2 ) are calculated which also provides information about the fit quality; the lower these values are the better it is. These factors are calculated using the following formulas:

-R-profile: 𝑅 𝑝 = 100. In this PhD work Topas academic (V6) [2] was used as main refinement program.

A.I.3.2. ab-initio structure solution.

To understand a compound macroscopic property a better understanding of its crystal structure is indeed needed. First, the acquired powder X-ray diffraction pattern is indexed against the ICDD data base, comparing the existing structures cell parameters to the measured peak position. If the pattern is fully indexed, Rietveld refinements can be proceeded to refine the crystal structure. However, if the indexation part fails, meaning that no structure from the used data base can be associated to the experimental diffraction pattern, structural solution take place to elucidate the crystal structure of this new compound.

In solving a new material crystal structure, three major steps must be followed:

-First step is finding the cell parameters, also called indexation, this step can be fulfilled using Dicvol [3] programme implemented in WinPlotR [4] from the FullProf [5] programme.

The resulting solutions are associated with merit figures defined by Wolff and Smith [6], [7], which allows to choose the best solution with the highest merit. A Lebail [8] or Pawley [9] refinement is carried out at the end of this step to extract the (zero shift, precise cell parameters and the profile parameters). Most importantly it allows to refine, with the most accuracy possible, the peaks intensities which indicates the hkl extinction conditions; hence, narrowing the number of possible space groups to one or few of them. In this thesis the Space group Test implemented in JANA2006 [10] program was used. As easy as it may sounds to use a programme for the finding the right space group, from powder samples diffraction data, this task can be very challenging due to peak overlapping, in which case depending on the sample a different technique can be employed to elucidate the hkl extinction conditions.

-Second step after finding the right cell parameters and space group, is to locate the positions of the different atoms inside the structure. This type of information is provided by the diffracted peak intensities, and can be exploited by different methods (direct, Patterson, maximum entropy…) using different approaches (charge flipping, simulated annealing…) implemented in a variety of programs, JANA2006 [10], Topas [2], FOX [11]…etc. Usually the heaviest atoms are placed first as they have the strongest scattering contribution. The lightest atoms are latter localised by Fourier difference maps analysis and added to the structure.

-The third and final step is to use the Rietveld method to refine the different remaining atomic parameters (atomic positions, occupation rates in case of disordered materials, related thermal parameters. This step is of a big importance to give the best averaged structural description of the measured sample.

A.I.4. Microstructure and atomic scale observations.

A.I.4.1. Scanning electron microscopy (SEM).

To check the samples surface morphology, chemical composition and homogeneity; scanning electronic microscopy (SEM) coupled to energy dispersive X-ray spectrometer, measurements were conducted on a Field Emission Gun-SEM MERLIN (ZEISS). As shown in -Secondary electrons (SE): When the incident beam hits the sample, the latter valence electrons are ejected (called secondary electrons). In this mode the only information provided are the sample's morphology and topology.

-Backscattered electrons (BSE): The elastic interaction between the incident beam and the sample's nucleus, results in a bounce back of the beam's electrons (called backscattered electrons). In this mode the chemical homogeneity can be observed as the quantity of backscattered electrons is dependent of the Z atomic number, this means that in imaging, brighter regions have a correspond to a higher atomic number.

-X-ray elemental analysis: the chemical composition of the measured sample can be determined in this mode. This is possible from the generated X-rays from the inelastic interaction between the electron beam and sample's core electrons.

A.I.4.2. Transmission electron microscopy (TEM).

To observe samples from the nanometre to the atomic scale, TEM is a powerful technique that can help in achieving this task, however the sample thickness needs to be thin enough, a few tens of nanometres, in order for the beam to go through. The samples preparation methods have been described in the electron diffraction part. Two imaging modes have been proceeded in this thesis, TEM and STEM-HAADF (see Figure A. 6a and Figure A. 6b. In TEM mode, the bright field imaging is obtained by selecting only the transmitted beam, the generated image of the crystals in Bragg diffraction conditions show a dark contrast, while the brighter contrast indicates crystals in non-diffraction conditions or none-crystalline sample. The bright field mode mostly provides key information about the sample microstructure (morphology, crystallinity, crystallite size and dispersion). Dark field mode on the other hand, is operated by selecting one or multiple diffracted beams, which allow a selective imaging of a chosen phase in a multiphased sample. Moreover, the crystals at the origin of the selected diffracted beams will appear brighter in the acquired image.

Atomic scale imaging was performed in the high-resolution Scanning Transmission Electron

Microscopy-High Angle Annular Dark Field (STEM-HAADF) mode, on a double corrected JEOL ARM200F (JEOL Ltd.) Cold FEG Transmission Electron Microscope (TEM). Before proceeding to the atomic scale imaging, the sample must to be oriented in the desired direction with the help of the electron diffraction. STEM-HAADF imaging is constructed by the collection of wide-angle scattered electrons (angles > 50 mrad) using an annular detector (Figure A. 6b). The images obtained are in chemical contrast, i.e. the heaviest elements or phases will appear brighter. In order to obtain more information on the sample cationic distribution, elemental maps at the atomic scale were performed by EDS (Energy Dispersive X-ray Spectroscopy) or EELS (Electron Energy Loss Spectroscopy).

Figure A. 6. Schemes of TEM imaging concept in bright (a), dark field (b) modes and STEM-HAADF mode (c).

Figures were takesn from [12] and [13].

A.I.5. Properties measurements.

A.I.5.1. Photoluminescence measurements.

Photoluminescence is the occurrence light emission under photon absorption. While an emission measurement on a certain spectral range, the source radiation wavelength is fixed.

Photoluminescence spectra were recorded at room temperature using a Horiba-Jobin-Yvon Nanolog spectrofluorimeter, equipped with a 450 W Xe lamp source coupled to a double monochromator for excitation, and an iHR320 spectrometer coupled to an infrared PMT detector sensitive from 950 to 1650 nm (Hamamatsu). 4) a *Site was put to be fully occupied without refining each atom occupancy a : constrained to refine to the same Biso values. a Constrained to refine to the same value.

Figure VI.2. Four Ca2CoSi2O7 cells projection within the c-axis showing the [Co(Si)2]O7 framework distortion described in two ways: a) combination of framework distorted parent melilite cells (blue and orange squares) isolated by a 2D step-like framework (black lines) of undistorted A-sites pentagonal channels, b) twodimensional stack (along the b-axis) of 1D sequences of : (i)XX*Xˈ (y= 0.25), (ii)Y X*ˈX* (y= 0.5), (iii) XˈXX*ˈ (y= 0.75), with X, Xˈ, Y, X*, X*ˈ tilling described in c). In all panels the green and purple shading highlight both undistorted and distorted [(Co/Si)O4]5 pentagonal channels respectively.

Résumé de l'Introduction générale

La conception et le développement de nouveaux matériaux sont nécessaires dans la société d'aujourd'hui pour différents types d'applications : médicales [1][2][3][4][5][6], stockage et conversion de l'énergie [7][8][9][10], industrielle [11], [12] …etc. Le défi principal à relever pour répondre à la demande continuelle de nouveaux matériaux est de trouver une méthode de synthèse qui permette d'atteindre l'état hors-équilibre des matériaux pour accéder à de nouvelles phases cristallines. Au laboratoire CHEMTI, une méthode originale et unique a été développée : la cristallisation complète et congruente à partir d'un verre massif ou d'un liquide surfondu.

L'utilisation de la lévitation aérodynamique couplée à un chauffage par deux lasers CO2 permet de fondre des échantillons avec des températures de fusions supérieures à 2000°C. Ce dispositif permet également d'atteindre des vitesses de refroidissements atteignant 1000°C/s, permettant de figer l'état désordonné de la matière jusqu'à solidification de cette dernière. Par ailleurs, la vitesse de refroidissement peut aussi être contrôlée pour maitriser la cristallisation des échantillons à partir du liquide fondu à haute température.

Cette technique originale de synthèse a été utilisé au cours de cette thèse qui est divisée en cinq chapitres, avec une répartition par thématiques de matériaux :

• Matériaux pour l'optique.

• Matériaux pour l'énergie.

Le premier chapitre de ce manuscrit consiste en un état de l'art des différentes méthodes de synthèses employées pour l'obtention de nouveaux matériaux. Un intérêt particulier est donné aux méthodes de synthèse par cristallisation du verre ou du liquide fondu, avec différents exemples de matériaux clés réalisés.

Le chapitre II traite de la synthèse, caractérisation structurale et stabilité thermique de nouvelles phases cristallines de type SrREGa3O7 RE = [Dy-Lu / Y] apparentées à la structure des mélilites.

Le troisième chapitre de ce manuscrit concerne la synthèse et la caractérisation du désordre chimique dans la nouvelle solution solide Ca3Ga2-2xZnxGe4+xO14 (0 ≤ x ≤ 1). L'un des points forts de ce chapitre est la quantification du désordre chimique entre trois cations isoélectroniques (Ga, Zn, Ge) dans le composé Ca3GaZn0.5Ge4.5O14 (x = 0.5) par affinement 2D de cartographies STEM-EDS des différents cations, acquises à l'échelle atomique.

Résumé du Chapitre I : État de l'art

La science des matériaux est un vaste champ de recherche qui lie à la fois des aspects chimiques L'utilisation de la lévitation aérodynamique permet aussi la cristallisation de phases cristallines hors-équilibre à partir du liquide surfondu par contrôle de la vitesse de refroidissement (diminution de la puissance des lasers de façon progressive). Cette procédure a été utilisée lors de la synthèse du composé cristallin La2Ga3O7.5 [7], non accessible par réaction à l'état solide.

Ce composé a la particularité de représenter la limite x = 1 de la solution solide La1+xAE1-xGa3O7 apparentée a la famille des structures mélilites, cristallisant dans une surstructure orthorhombique de la maille parent tétragonale, avec la plus haute teneur d'oxygènes interstitiels répertoriée pour cette famille de structure. Par ailleurs, ce matériau représente des valeurs de conductivité anionique intéressantes (0.01 S.cm -1 à 800°C), seulement un ordre de grandeur inférieure aux meilleurs conducteurs anioniques de la famille des mélilites (i.e.

La1.54Sr0.46Ga3O7.27 et La1.64Ca0.36Ga3O7.32 atteignant des valeurs de 0.1 S.cm -1 à 800°C).

Les différents types de conducteurs anioniques sont décrits plus en détails dans le chapitre I, avec une attention particulière portée à la famille des mélilites. Une analyse par diffraction des rayons X par rayonnement synchrotron nous a permis de classer les domaines de composition cristallisant dans la structure P4 ̅ 21m (0 ≤ x ≤ 0.725), Ima2 (0.9 ≤ x ≤ 1) ainsi que les domaines mixtes (0.725 < x < 0.9). Le défi de cette étude par DRX synchrotron, a été l'affinement Rietveld du diffractogramme de la composition (x = 0.775) qui représentait une asymétrie de pic très large. Pour attaquer ce problème, plusieurs méthodes ont été déployées : description d'asymétrie de pic par le modèle de Stephens, harmoniques sphériques et l'approche multi-mailles. Le désordre chimique entre La/Ba et les oxygènes interstitiels dans les matériaux synthétisés a été confirmé par des affinements Rietveld effectués sur des diffractogrammes neutrons à température ambiante, mais aussi à hautes températures pour le composé (x = 0.9).

Résumé du

La caractérisation des propriétés de conductivité anionique effectuée par spectroscopie d'impédance a indiqué une valeur maximum de 3×10 -2 S.cm -1 atteinte pour la composition La1.7Ba0.7Ga3O7.35 (x = 0.7) à 700°C, légèrement inférieure à celle des meilleurs mélilites (i.e.

La1.54Sr0.46Ga3O7.27 atteignant une valeur de 10 -1 S.cm -1 à 800°C). Ceci dit, les tracés d'Arrhenius des compositions (0.5 ≤ x < 0.9) témoignent d'un plateau de la conduction, où les valeurs de cette dernière n'évoluent quasiment plus à hautes températures. Ce phénomène a été étudié plus en détails par diffraction des rayons X in situ à température variable et par microscopie électronique à balayage, confirmant une évolution de la microstructure avec la température, ce qui pourrait expliquer la stagnation du comportement de conductivité mesuré à haute température.

Résumé du Chapitre V : Dopage au lanthane dans la structure Ca 5 Ga 6 O 14 de type mélilite pour de nouveaux conducteurs anioniques Les propriétés de conduction anionique montrent une augmentation de deux ordres de grandeur de la conductivité de la phase non dopée vers la phase dopée. Cependant, les valeurs de conductivité de ces composés restent relativement faibles avec une valeur maximum atteinte de 2×10 -5 S.cm -1 à 800°C pour la phase La0.25Ca4.75Ga6O14.125 (x = 0.25).

Résumé de la Conclusion générale

Les travaux présentés dans cette thèse ont pour but le développement de nouveaux matériaux hautement performants pour diverses applications. Ces études de chimie du solide portent sur les structures de type mélilites, mais aussi des matériaux avec des structures apparentées aux mélilites présentant un intérêt potentiel pour leurs propriétés optiques et de conduction ionique.

L'utilisation de la lévitation aérodynamique couplée au chauffage par laser CO2 a permis de synthétiser des précurseurs vitreux de ces matériaux sous forme de billes sphériques en fondant

INTRODUCTION

The melilite gallates SrREGa 3 O 7 with the largest RE cations, i.e., RE = La to Y, are well-known for their luminescence properties observed on single crystal or powder materials. 1-5 These compounds are readily synthesized by conventional ceramic methods and adopt the tetragonal melilite structure with a uniform [Ga 3 O 7 ] framework layer and fully disordered Sr/RE ("A-site") cations. In contrast, the compositions with RE smaller than Tm have not been widely studied, because they are challenging to synthesize, and they appear to have more complex structures that have not been fully characterized. 6,7 The introduction of small A-site cations (or more precisely, the imposition of a low A/B ionic radius ratio 8 )i s known to induce distortions of the melilite framework, for example in the åckermanites Ca 2 MSi 2 O 7 (M =Mg 2+ ,Co 2+ ) 9-11 and the gallates CaREGa 3 O 7 (RE = La, Nd), 8,12 which both have high concentrations of Ca 2+ on the A sites. These melilites undergo complex incommensurate structural distortions due to the size mismatch between the Ca/RE sublattice and the tetrahedral framework layer, producing a modulated distribution of A-site environments ranging from six-to eight-coordinate in CaNdGa 3 O 7 , which are better adapted for the local coordination of Ca 2+ than the single eight-coordinate A site exhibited in the undistorted parent phase.

An initial study of SrREGa 3 O 7 in the small-RE range (RE = Eu-Yb, Y) was motivated by the search for new luminescent transparent ceramics. 7 Transparent ceramics showing luminescence properties are key materials in the development of numerous applications such as laser gain media and scintillating inorganic materials. 13-18 Indeed, they combine the advantages of transparent media, such as volume excitation/emission, with ceramic optical emission properties, i.e., narrow and intense emission bands. Transparent ceramics are usually synthesized through complex powder sintering processes, requiring high temperature and high pressure to remove residual porosities acting like light scattering centers and consequently limiting the transparency of the resulting material. 16,19,20 An alternative synthesis approach, full crystallization from glass, was recently proposed to achieve transparent ceramics. 21-27 This process can lead to fully dense ceramics, i.e., ceramics without porosity, if the density difference between the glass and the crystalline phases remains limited, thus preventing the appearance of cracks during crystallization. The full and congruent crystallization process also leads to very thin grain boundaries. 22 Therefore, the possibility to achieve fully dense ceramics with thin grain boundaries, two of the main requirements for transparent ceramics synthesis, has enabled the use of full glass crystallization to access new transparent ceramic compositions. This was particularly demonstrated for innovative materials showing noncubic symmetry, as long as the birefringence effect remained limited. 7,21,22,28,29 Moreover, crystallization from glass is a process operating at relatively low temperatures compared to conventional powder sintering and solid state processes, thus offering the possibility to access new metastable crystalline phases as demonstrated for BaAl 4 O 7 , 21,30 28,31 and Bi 0.8 Nb 0.8 Te 2.4 O 8 transparent ceramics. 32 Using this method, we were successful in synthesizing new transparent to SrREGa 3 O 7 ceramics with both small RE cations (RE = Eu, Gd, Tb, Dy, Ho, Y, Er, Tm, and Yb) and substantial nonstoichiometries (Sr 1-x RE 1+x Ga 3 O 7+x/2 with RE = Eu, Gd, and Tb). 7,26 Some members of the transparent ceramic SrREGa 3 O 7 family were found to have additional features in their PXRD patterns, implying additional complexity in their crystal structures, but this was not investigated in detail. 7 Here, we investigate the structure and the phase stability of the SrREGa 3 O 7 (RE = Y, Dy, Ho, Er, Tm, Yb, and Lu) melilites. In contrast to the modulated CaREGa 3 O 7 melilites, we find that these materials can crystallize in a new cationordered 3 × 1 × 1 melilite superstructure, which produces three distinct A-site environments and enables the large size difference between Sr and the small RE 3+ cations to be accommodated by the tetrahedral framework. Furthermore, by tuning the synthesis conditions, it is possible to isolate disordered polymorphs for the RE = Dy, Ho, Er, Tm, and Yb members. The superstructure description is detailed by means of synchrotron and neutron powder diffraction Rietveld refinements, which are coupled to observations from scanning transmission electron microscopy-high angle annular dark field (STEM-HAADF) imaging and X-ray energy dispersive spectroscopy (EDS) elemental mapping. Moreover, atomicresolution STEM-HAADF imaging and EDS elemental mapping enable direct observation of Sr 2+ and RE 3+ cation ordering in the melilite structure. Last, the broad optical transmission range (from the UV up to the mid-infrared) and photoluminescence properties of these new SrREGa 3 O 7 melilites are measured. A significant influence of the Sr/RE ordering/disordering is reported on the RE emission band features in the glasses and ordered and disordered ceramics.

Sr 1+x/2 Al 2+x Si 2-x O 8 , 22 Sr 1-x/2 Al 2-x Si x O 4 ,

EXPERIMENTAL SECTION

2.1. Synthesis Procedure. The small rare-earth compounds SrREGa 3 O 7 (RE =D y -Lu, Y) and the known tetragonal melilite SrTbGa 3 O 7 were synthesized by a full crystallization from glass process. First, high purity SrCO 3 , RE 2 O 3 , and Ga 2 O 3 powders (Strem Chemicals, purity >99.9%) were weighed in stoichiometric amounts and ground together in an agate mortar using ethanol to homogenize the mixture. The resulting powder was then dried, pressed into pellets, and broken into fragments of ∼50 mg. The fragments were then levitated individually in an argon gas jet and melted at approximately 1650 °C (determined by optical pyrometry) using a pair of CO 2 lasers (10.6 μm), 33 held for several seconds to allow homogenization, and then quenched radiatively to room temperature by shutting off the lasers (an estimated cooling rate of 300 °Cs -1 ) to produce the precursor glasses as spherical beads. Full crystallization of the glass precursors was then achieved by a single heat treatment performed under air in a conventional muffle furnace at temperatures between 805 and 815 °C. Crystallization protocols for each specific composition are detailed in section 3.1.

2.2. Thermal Analysis. Differential scanning calorimetry (DSC) was performed on a Setaram MULTI HTC 1600 instrument. Powder samples of ∼200 mg, obtained by crushing several beads of the same composition, were contained in platinum crucibles and scanned at a rate of 10 K min -1 in flowing argon.

2.3. Powder Diffraction. Laboratory X-ray powder diffraction (PXRD) analyses were performed in Bragg-Brentano geometry using a D8 Advance Bruker laboratory diffractometer (Cu Kα radiation) equipped with a LynxEye XE detector. In situ high-temperature diffraction data were collected under air using two different setups depending on the maximum temperature required. For measurements up to 1200 °C, variable temperature VT-PXRD data were recorded using an HTK1200N Anton Paar furnace. The powder sample was placed in a platinum-lined corundum sample holder. Data were collected from 10 to 40°(2θ) with a 0.024°step size and an acquisition time of 1 s/step. Phase transitions were tracked while heating from 740 to 900 °C for RE =H o -Lu, from 740 to 1000 °C for Dy, and from 740 to 1100 °C for Tb, using 5 °C steps. Data were also acquired during cooling from the maximum temperature down to 400 °C (300 °C for RE = Ho). For measurements up to 1600 °C, VT-PXRD data were recorded every 50 °C from room temperature up to 1500 °C using an Anton Paar oven chamber (HTK1600N model) from 19 to 38°(2θ) with a 0.016°step size and an acquisition time of 1 s per step. Synchrotron powder diffraction (SPD) was carried out on the 11-BM beamline at the Advanced Photon Source (APS, Argonne National Laboratory, U.S.) for compositions RE = Ho, Er, Tm, Yb, and Lu. Data were acquired at room temperature from powder loaded in a 0.8 mm diameter Kapton tube with an incident wavelength of λ = 0.41423 or 0.45787 Å over an angular range of 1-50°(2θ) with a step size of 0.001°. Note that the precursor glass powders were scaled up to ∼1 g for these experiments by combining several crushed beads. Neutron powder diffraction (NPD) data were obtained at the Laboratoire León Brillouin (LLB, Saclay, France) on the 3T2 diffractometer at room temperature for RE = Yb using an 8mm-diameter vanadium tube. Data were collected with wavelength of λ = 1.229 Å over the 10-120°2θ range with a 0.05°step size, for a total of 22 h acquisition time. A large (∼5 g) powder sample was produced for this experiment by crushing a large number of individual beads. Structure refinements were performed from powder diffraction data using TOPAS Academic version 6. 34 2.4. Electron Diffraction and Imaging. Selected area electron diffraction (SAED) experiments were carried out on a Philips CM20 transmission electron microscope (TEM) to determine the cell parameters and space group of the transparent polycrystalline ceramics. Atomic-resolution STEM-HAADF micrographs and EDS elemental mapping were performed on a JEOL ARM200F (JEOL Ltd.) Cold FEG TEM operating at 200 kV, equipped with a double spherical aberration corrector and fitted with a JEOL SDD CENTURIO EDS system. The cationic ordering in SrYbGa 3 O 7 was imaged on the atomic scale using STEM-EDS elemental mapping and STEM-HAADF imaging mode with a 68-174.5 mrad inner-outer collection angle. The probe size used is 0.13 and 0.1 nm, respectively. The samples were first prepared by mechanical polishing with a tripod and inlaid diamond discs until a 50 μm thickness. The thin foils were then obtained by argon ion milling (PIPS GATAN).

2.5. Optical Transmission and Photoluminescence Spectroscopies. Optical transmission spectra were recorded on polished samples in the UV-visible-near-infrared (NIR) and infrared ranges using an Agilent Cary 5000 UV-vis-NIR double beam spectrophotometer and a PerkinElmer Frontier FTIR spectrometer, respectively. Photoluminescence spectra were recorded at room temperature on bulk and powder samples using a Horiba-Jobin-Yvon Nanolog spectrofluorimeter, equipped with a 450 W Xe lamp source coupled to a double monochromator for excitation, and an iHR320 spectrometer coupled to an infrared PMT detector sensitive from 950 to 1650 nm (Hamamatsu). Special attention was paid to collect the emission spectra under the same experimental conditions to allow their accurate comparison.

RESULTS

3.1. Glass-Crystallization Synthesis of Ceramic Powders. The precursor glasses prepared by the aerodynamic levitation laser-melting procedure (see section 2.1) were confirmed to be amorphous by PXRD prior to a provisional thermal analysis by DSC conducted on heating up to 920 °C. Fully amorphous samples were obtained for all of the compositions attempted, with the exception of the end member RE = Lu, which contained weak Bragg peaks consistent with the presence of a small amount of crystalline melilite (Figure S1). The glass crystallization temperatures, signified by a strong exothermic peak in the DSC, were found to occur in the range 804-860 °C (see section 3.4); the decrease of the rare-earth size from Tb-Lu induces a systematic increase of the glass transition and crystallization temperatures (associated with increased rigidity of the glass network). 35 Glass powders were finally heat treated for 2 h at 815 °C and cooled down in the furnace (for RE =Tb-Yb, Y) or heat treated for 2 h at 805 °C and quenched by placing the Pt crucible in water (for RE = Lu) to produce polycrystalline samples.

Laboratory PXRD of these samples showed that two distinct crystal structures had formed, according to the identity of the rare earth ion. For the larger rare earths (RE = Tb, Dy, Ho and Y), the PXRDs were readily indexed to the familiar tetragonal melilite structure (P4̅ 2 1 m with a ≈ 7.9 and c ≈ 5.2 Å). However, the smaller rare earths (RE = Er, Tm, Yb, Lu) exhibited a more complex PXRD pattern which contained the main reflections of the melilite structure, and an additional set of weak reflections. These patterns were indexed using Dicvol, 36 revealing a 3-fold expansion of the melilite unit cell along the a axis to produce a new orthorhombic supercell of dimensions (a ≈ 23.70 Å, b ≈ 7.92 Å, and c ≈ 5.21 Å). The detailed determination of the 3 × 1 × 1 melilite structure by powder crystallography and electron microscopy is described first in sections 3.2 and 3.3. The compositional and thermal stability of this superstructure, as determined by variable temperature PXRD and DSC measurements, is then described in section 3.4.

Attempts to synthesize the small-rare earth compositions (RE =Ho-Lu) directly by classic solid-state reaction were not successful. For example, a variable-temperature PXRD experiment showed that a reaction mixture of SrCO 3 -Yb 2 O 3 -Ga 2 O 3 produces SrGa 2 O 4 and Yb 3 Ga 5 O 12 as the only ternary phases before melting at 1500 °C( Figure S2). As reported by Boyer et al., 7 it is possible to synthesize SrREGa 3 O 7 transparent ceramics of these compositions by full crystallization from glass (Figure S3a), starting from SrREGa 3 O 7 glass beads produced as described in section 2.1 and annealing them in a second step: the transparent ceramics thus produced exhibit the same PXRD patterns as for the powder samples described above.

3.2. Solution and Refinement of the 3 × 1 × 1 Superstructure. SrREGa 3 O 7 synchrotron X-ray diffraction (SPD) and selected area electron diffraction (SAED) patterns were consistent with laboratory PXRD, confirming the presence of a superstructure with a supercell corresponding to a tripling of the a axis in a 3 × 1 × 1 expansion (Figure 1)of the tetragonal melilite parent cell (Figure S4). The only observed reflection conditions were h00, h =2 n, and 0k0, k = 2n, consistent with space group P2 1 2 1 2. Note that we did not see any evidence of satellite peaks in the SrTmGa 3 O 7 SAED patterns, which implies that the crystal structure is commensurate (in contrast to small-alkaline-earth melilites such as CaLaGa 3 O 7 and CaNdGa 3 O 7 , which exhibit incommensurate structural distortions). 8,12 We selected SrYbGa 3 O 7 as a representative sample for detailed structural analysis due to the high stability of the 3 × 1 × 1 superstructure at this composition (see section 3.4), and its favorable neutron diffraction characteristics (relatively low neutron absorption by Yb and good scattering contrast between Yb/Sr). The structure was solved by chargeflipping 37,38 (implemented in JANA2006 39 through the Superflip software 40,41 )f o l l o w e db yF o u r i e rd i fference mapping, as described in the Supporting Information. The final Rietveld analysis was performed against SPD and NPD data simultaneously. Initial refinement of the Sr/Yb occupancies of the A sites produced three distinct A sites with equal multiplicity: a mixed Yb/Sr site ("Yb1/Sr1," refined occupancy 0.498(1)/0.501(1)), a Yb-dominated site ("Yb2" (0.977(1)/0.023(1)), and a Sr-dominated site ("Sr3" (0.025(2)/0.975( 2)). The amount of site inversion being very limited, these values were then fixed to ideal occupancies (0.5/0.5, 1/0, and 0/1, respectively), which did not affect the goodness of fit. All atomic coordinates were then refined in addition to anisotropic thermal parameters (Sr/Yb positions only) or isotropic thermal parameters (Ga and oxide positions) to give reliability factors R wp = 4.427%, R p = 3.772%, and χ 2 = 1.035. The Rietveld refinement is presented in Figure 2, Table 1, and Table S1, with the principal interatomic distances presented in Table 2 and Table S2.

The refined SrYbGa 3 O 7 melilite superstructure is presented in Figure 3. Its crystal structure retains the topology of the parent melilite structure, where corner-sharing GaO 4 tetrahedra form two-dimensional Ga 3 O 7 sheets with the A cations accommodated in pentagonal channels that align parallel to the stacking axis. In the tetragonal parent structure (e.g., the structure of SrLaGa 3 O 7 , shown in Figure 3b), the Sr/La site cations are fully disordered, and the channels are symmetrically equivalent with the eight nearest-neighbor A-O distances in the range 2.51-2.94 Å. 6,42 In contrast, in SrYbGa 3 O 7 , the ordering of large/small A site cations (eight-coordinate ionic radii of 1.25 and 0.985 Å for Sr 2+ and Yb 3+ , respectively) over three different sites causes the Ga 3 O 7 framework to distort (Figure 3a). This produces three distinct channel types which have equal multiplicity.

The A sites in the Sr-containing channels Yb1/Sr1 (halfoccupied by Sr 2+ ) and Sr3 (fully occupied by Sr 2+ ) can be considered as distorted versions of the eight-coordinate squareantiprismatic A-sites found in the parent melilite SrLaGa 3 O 7 (Figure 3d ande). In the Sr3 channels, the bond valence sum (BVS) for Sr 2+ is 1.76, which is comparable to that found in the undistorted SrLaGa 3 O 7 (BVS = 2.04), despite its broad distribution of Sr-O distances in the range 2.430(4)-3.195(4) Å (Figure 3e). It is clear that Yb 3+ would be severely under-bonded at this site (BVS for Yb 3+ = 1.23). The Yb1/Sr1 sites have A-O distances clustered neatly in the range 2.342(4)-2.702(4) Å (Figure 3d). These sites retain a formal coordination number of 8 but are smaller than the Sr3 sites and smaller than the A-sites of SrLaGa 3 O 7 . Here, the calculated BVS values indicate a compromise between the bonding preferences of Sr 2+ (which is formally overbonded, with BVS = 2.68) and Yb 3+ (formally under-bonded, with BVS = 1.87). Such values are comparable with those found in the previously published structure of disordered SrYGa 3 O 7 (where BVS for Sr 2+ = 2.37; Y 3+ = 1.81). 6 In contrast to the Sr3 and Yb1/Sr1 sites, the Yb2 sites (fully occupied by Yb 3+ ) are substantially different from those found in SrLaGa 3 O 7 and can be considered to have [6 + 1] coordination defined by six short Yb-O distances in the range 2.228(4)-2.517(4) Å that form a triangular-prismatic first coordination sphere, and one long Yb-O distance of 2.967 (4). Note that the next-shortest Yb2-O distance is 3.711(3) Å (Yb2-O11), which is beyond the range usually considered for bonding. This site is small enough to accommodate Yb 3+ with a BVS of 2.68, whereas coordination of Sr 2+ would be disfavored (BVS for Sr 2+ = 3.84). The six short Yb-O distances cause a severe narrowing of the pentagonal channel, as shown by the deviation of its geometry from the ideal case of SrLaGa 3 O 7 (Figure 3c). The refined A-O distances for all three sites are shown in Table 2. The relationship between the arrangement of the A sites in two dimensions and the corresponding framework distortion is discussed in more detail in section 4.1. To investigate the possibility of local deviation in the Yb/Sr distribution (e.g., the presence of areas enriched in Yb or Sr), EDS mapping and STEM-HAADF imaging were performed on the atomic scale, on the SrYbGa 3 O 7 sample oriented along the [001] direction (Figure 4a and Figure 5). Along this direction, the columns of atoms are composed of the same crystallographic A site (Yb1/Sr1 with a 50/50 occupancy or Yb2 as fully occupied by Yb or Sr3 as fully occupied by Sr; Figure 3a). STEM-EDS elemental mapping of the three cations, Ga, Sr, and Yb, on the atomic scale (where each point corresponds to a column of atoms with the same chemical nature) shows GaO sites (blue), pure Yb2 sites (red), pure Sr3 sites (green), and mixed Yb1/Sr1 sites highlighted by yellow arrows (Figure 5). This result confirms and allows the cationic organization proposed by powder diffraction to be visualized.

Scanning transmission electron microscopy-high angle annular dark field (STEM-HAADF) is a Z-contrast imaging mode whose signal is essentially dominated by Rutherford scattering, with a cross-section proportional to Z 2 (Z being the atomic number). 43-45 For thin objects (several tens of nanometers), an analytical expression of the Z dependence of the image intensity can be approximated by an exponential function of the form I ∝ Z n with n in the range between 1.6 and 2, depending on the annular dark field (ADF) detector geometry (collection angle). On the atomic scale, for a column composed of several elements (i) with a ratio m i and Z i being the atomic number of the element i, this formula becomes I ∝ ∑ i (m i Z i n ). Consequently, one of the advantages of this imaging mode is the possibility to distinguish between chemically different atomic column sites. However, the intensities are highly sensitive to the number of atoms in the atomic column. Considering this point, atomic resolution STEM-HAADF images have been acquired with a SrYbGa 3 O 7 crystal oriented along the [001] direction in order to stack the same number of atoms along all the atomic columns, whatever their chemical nature (Figure 4a). The cation ordering was then determined by indexing the atomic columns from the brightest to the darkest contrasts in relation with the heaviest sites to the lightest atoms: Yb2 (Z = 70) > Yb1/Sr1 50:50 mixed (Z̅ ≈ 56) > GaO (Z̅ = 39) ≈ Sr3 (Z = 38). Only the Sr and GaO atomic columns are difficult to distinguish accurately due to their very close atomic numbers. However, by comparison with the EDS elemental maps (Figure 5) and the embedded simulated STEM-HAADF image (top right corner of Figure 4a), all the crystalline sites are identified. The simulated STEM-HAADF image of the SrYbGa 3 O 7 superstructure, oriented along the The thermal parameters of Yb1/Sr1, Yb2, and Sr3 were refined as anisotropic (see details in Table S1). [001] zone axis, was obtained using the JEMS software 46 from the cif file of the superstructure. It is a simple projection of the structure convolved with the electron probe intensity of the microscope. The channeling effects have not been simulated. A perfect match in terms of distances and positions between the experimental STEM-HAADF images and the melilite structure resolved from synchrotron and neutron powder diffraction experiments was found with no sign of modulation or default in the crystallographic site organization. Recent works 47,48 have demonstrated that a quantification of the total intensity of the scattered electrons (V) for individual atomic columns can enable the nature of unknown columns to be assigned via the formula V ≈∑ i (m i Z i n ) with n ≈ 2 and m i being the weighting of the different elements i composing the atomic column. This formula has been employed to determine the local Yb1/Sr1 distribution over the mixed site, i.e., the deviation around the ideal average 50/50 value determined from powder diffraction. Multiple factors such as thickness variation, the level of noise, and channeling can affect the signal. To limit these artifacts, the intensity profiles were extracted for each projected position from the same STEM-HAADF image, assuming the thickness of the sample to be almost constant through the image (8 nm × 6 nm), as well as the different factors affecting the signal. The signal obtained for each atomic column was fitted with a background signal and a Gaussian function determined for each type of crystallographic s i t e( S r 3 ,Y b 2 ,Y b 1 / S r 1 ;Figure 4b). 49 The chemical composition of atomic columns of the same crystallographic site (Sr3, Yb2, Yb1/Sr1) can be compared to each other by looking at the corresponding volumes under the peaks which are proportional to the total intensity of electrons scattered toward the ADF detector. According to the formula V ≈ ∑ i (m i Z i n ) with V being the volume under the peak and Z being the atomic number of the site, the factor n has been determined for each crystallographic site considering the mixed Yb1/Sr1 site with an average 50/50 occupancy. The n values obtained for the sites Sr3, Yb1/Sr1, and Yb2 were 2.1, 1.99, and 1.94, respectively, in agreement with the literature that predicts an n factor close to 2. Considering these n values, a Z atomic number has been calculated for each measured atomic column, and its distribution is presented on the Figure 4c. The three different crystallographic A sites are well distinguished, and their average Z values agree with the occupancies Yb/Sr: 1/0 (Z Yb = 70), 0/1 (Z Sr = 38), and 0.5/ 0.5 (Z Yb/Sr ≈ 56), respectively. The pure Sr3 and Yb2 crystallographic sites show a small Z distribution (±13% and ±7%, respectively) which can be linked to deviation due to the different factors previously described which affect the signal. In comparison, the variation of the Z value to the Yb1/Sr1 mixed atomic columns (±14%) is similar to the pure Sr crystallographic site, corresponding to a low variability of the chemical composition between each mixed Yb1/Sr1 atomic column, which represent between 40 and 100 cells along the c axis (i.e., 20 to 50 nm in thickness). The PXRD experiments started from precursor glasses, which were heated in 5 °C steps from 740 °C, until the point where thermal decomposition of the melilite into binary (RE 2 O 3 ) and ternary (garnet-type) oxides was observed. This was then followed by measurements on cooling to room temperature, as shown in Figure 6. A measurement time of 30 min step -1 was used to ensure the reliable detection of low-intensity superstructure peaks, resulting in an average heating rate of approximately 0.17 °C min -1 . The RE = Lu member was found to have the lowest thermal stability with decomposition products appearing at 830 °C, which is only ∼50 °C higher than its glass crystallization temperature, and this was the only sample to decompose substantially during the measurement. The RE = Ho, Er, Tm, and Yb members were found to have higher decomposition temperatures in the range 850-870 °C. This, together with their lower glass-crystallization temperatures, means that a wider temperature window is available for their synthesis. Members with rare earths larger than Ho were found to be the most stable with respect to decomposition: RE = Y, Dy, and Tb were found to decompose at 890, 965, and 1010 °C, respectively. For comparison, RE = Gd is not susceptible to thermal decomposition, as demonstrated by successful melt-growths of single crystals. 50 This indicates that the boundary of the metastable small-rare-earth melilites lies between RE = Gd and Tb (see Figure 8).

The onset temperatures of the parent (A-site disordered) tetragonal melilite and 3 × 1 × 1 superstructure peaks revealed three categories of behavior that depend on the size of the rare earth cation. (i) The smallest RE members (RE = Yb and Lu) were found to crystallize directly into the 3 × 1 × 1 melilite superstructure upon heating. In these compounds, the superstructure was retained throughout the experiment on cooling to room temperature. (ii) The intermediate-RE members (RE = Er and Tm) crystallized first into the parent melilite structure, which was then retained up to high temperature. However, on cooling below 720 and 790 °C, respectively, they transformed into the 3 × 1 × 1 superstructure, which was then retained all the way to room temperature. (iii) The largest RE members (RE = Tb, Dy, Y and Ho) crystallized into the parent melilite structure and retained this structure throughout the experiment. Note that, in all cases, the products obtained at room temperature were consistent with the results of ex situ crystallization described in section 3.1.

The DSC scans, measured in parallel with the in situ PXRD over the range 25-925 °C, used a constant temperature scan rate of 10 °C min -1 on heating and cooling (Figure 7), substantially faster that the average rate of the in situ PXRD experiments. The DSC data collected on heating are dominated by the strong exothermic peaks from glass crystallization in the range 804 °C( RE = Tb) to 858 °C (RE = Lu), as shown in Figure 7a. However, with the exception of the end members (RE = Tb and Lu), the cooling curves were found to exhibit a small exothermic peak whose position varied systematically with composition, as shown in Figure 7b. The onset temperatures of these peaks are strongly correlated with the identity of the RE cation: a maximum of 853 °C was observed for RE = Yb, with a near-monotonic decrease to 548 °C for RE = Dy. For Er and Tm, their peaks at 713 and 800 °C, respectively, agree closely with the superstructure ordering temperatures observed on cooling in situ by PXRD. Postmeasurement ex situ PXRD scans showed that all of these samples, with the exception of RE = Tb (which showed no exothermic peak on cooling), had crystallized in the 3 × 1 × 1 superstructure (Figure S5). The exothermic event observed on cooling thus corresponds to a structural phase transition from the tetragonal parent melilite structure to the orthorhombic 3 × 1 × 1 melilite superstructure.

These thermal analysis results demonstrate that the 3 × 1 × 1 superstructure can be formed for the larger rare-earth members RE = Dy, Y, and Ho if they are crystallized with appropriate heating and cooling rates (Figure S6). Furthermore, they suggest that it should be possible to recover the parent tetragonal polymorphs of the intermediate-and small-RE members (Er-Yb) at room temperature by rapid cooling from the disordered domain (Figure S6). To test this, we used a conventional muffle furnace to heat powdered precursor glasses of each composition (RE = Er, Tm, and Yb) in a platinum crucible at 10 °C min -1 to ∼50 °C above their transition temperatures T o (defined by the exothermic peak in the DSC cooling scan) and then immediately quenched them to room temperature by removing them from the furnace. PXRD confirmed that the tetragonal parent melilite structure had been isolated for each of these compositions (Figures S7,S8). Attempts to quench SrLuGa 3 O 7 in this way, from ∼10 °C below its decomposition temperature, only produced the 3 × 1 × 1 superstructure. This is consistent with the absence of a phase transition peak in the DSC cooling scan of this compound: our results indicate that this structure is cationordered through its entire stability range. (using SPD data) and RE = Dy (using laboratory PXRD; Figures S9-S12). For RE = Ho, Er, and Tm, the lattice parameters, atomic positions, and isotropic thermal parameters were refined (with all oxygen atoms assigned the same thermal parameter; Tables S3-S12), and the fractional occupancies of Sr and RE on the three A sites were refined with a global compositional constraint to match the nominal stoichiometry. This produced good fits to the data for all compositions (for structural parameters and agreement factors, see Tables S3-S8 and Figures S10,S11). These refinements all revealed a partitioning of Sr and RE over the three A sites that is consistent with the structure of SrYbGa 3 O 7 . Like SrYbGa 3 O 7 , the next-smallest member, SrTmGa 3 O 7 , was found to exhibit complete cation ordering on the A sites, while refinements of the larger RE =D y -Er members revealed a small amount of disorder between the RE2 and Sr3 sites. This can be seen most clearly for SrErGa 3 O 7 , where Er occupancy refined to 0.50 for RE1/Sr1, 0.866(3) for RE2, and 0.130(4) for Sr3. These structures are still strongly cation-ordered, but these small deviations from the SrYbGa 3 O 7 model are consistent with the weakening stability of the 3 × 1 × 1 superstructure as the RE radius increases (sections 3.4 and 4.2). It is possible that this apparent partial Sr/RE site inversion, indicated by the Rietveld refinements, actually corresponds to the presence of fully disordered microstructural domains in these samples: this appears to be the case for RE = Y, where HRTEM imaging and associated FFTs show clearly, in a single grain, the coexistence of ordered and disordered nanodomains of size 20-30 nm with the same [001]* orientation (Figure S13), suggesting that disorder is introduced on the nanometer scale, rather than on the unit cell scale. The possible existence of such ordered/ disordered domains in the RE =D y -Er members provides an alternative explanation for the partial disorder over the RE2 and Sr3 sites, which is apparent in their refined (average) structures.

The SPD data revealed SrLuGa 3 O 7 to have a lower crystallinity than the other members with significantly broader Bragg peaks, consistent with its high glass-crystallization temperature and small thermal stability window. For this composition only, deviations of the Ga-O distances from their corresponding values in SrYbGa 3 O 7 were restrained by a penalty function in order to obtain a physically plausible model. Additionally, it was necessary to split the Lu3 site to avoid an unphysically large thermal parameter at this site. Although this produced a satisfactory fit to the SPD data (R wp = 9.18%, R p = 6.87%, see Table S9), these factors render the RE = Lu model less precise than those of the other highly crystalline RE members and may indicate complex local disorder in this sample.

The disordered polymorphs, which were synthesized for RE =D y -Yb by quenching from high temperatures (see section 3.4), have ionic radius ratios of the A (Sr/RE) and B (Ga) cations that lie close to the incommensurately ordered structural domain proposed by Wei et al. 8,12 for the small alkaline-earth melilites CaREGa 3 O 7 . To test this possibility, we conducted SAED measurements on disordered SrTmGa 3 O 7 (Figure S4), which confirmed the tetragonal P4̅ 2 1 m indexation and contained no evidence of incommensurate satellite reflections. We then proceeded with Rietveld analysis using laboratory PXRD data with the tetragonal P4̅ 2 1 m model of the parent melilite SrLaGa 3 O 7 as a structural template (Figures S10,S11). Unit cell parameters and atomic coordinates were refined with no additional constraints. Across the series, the trend in lattice parameters follows the expected lanthanide contraction and is consistent with the trend observed in the superstructured polymorphs (see normalized lattice parameters, Figure S14 and Table S13, S15, S17, S19). The mean Sr/ RE-O distances were found to lie in the range 2.590(8)-2.600(5) Å, which is consistent with the parent SrLaGa 3 O 7 melilite (mean Sr/La-O 2.655 Å; Tables S14, S16, S18, and S20).

3.6. Optical Properties. The optical transmission spectra in the UV-vis-NIR range (200 to 2700 nm) of the SrREGa 3 O 7 glasses and ceramics have already been reported in anterior works. 7 Optical transparency of both glasses and ceramics actually spans from ∼300 nm up to ∼7 μm (at an arbitrary transmittance value of 10% for 1 mm thick samples), as can be seen in and confirmed by the transmission windows presented in Figure S15. Optical scattering losses can be observed on all of the ceramics in the short-wavelength region of their transmission spectra, as expected. Maximum transmission also drops from 80% for the glasses down to 40-60% for the ceramics, except for the SrYbGa 3 O 7 ceramic, which maintains above 70% of transmission in the mid-infrared range. Moreover, a clear structuration (narrower bandwidth and sharper peak intensity) of the absorption bands characteristic to the RE cations is also noticed: around 1480-1530 nm for the Er 3+ ion, 1900-2000 nm for the Ho 3+ ion, 1600-1800 nm for the Tm 3+ ion, and 975 nm for the Yb 3+ ion, for instance (Figure S16). This confirms the structural environment ordering around the RE cation induced during the full crystallization from the glass. To better evidence this influence, emission photoluminescence spectroscopic measurements were focused on the SrErGa 3 O 7 melilites. The fluorescence spectroscopy of the Er 3+ ion is indeed well-known and exploited in numerous applications (e.g., in optical fiber amplifier for telecommunications). The emission spectra recorded in the 1400-1650 nm region under excitation at 520 nm on glass and ceramic melilite bulks reveal a strong enhancement of the emission intensity in the ceramic material (Figure S17). In addition, one can observe a raising of several structured peaks along the Er 3+ broad emission band in the ceramic, resulting from the more defined structural ordering around the Er 3+ ions.

Photoluminescence emission spectra have been also recorded on the SrErGa 3 O 7 glass and ordered and disordered ceramic powdered samples, as presented in Figure 9. Strictly the same experimental conditions and amounts of finely crushed powders were employed to enable accurate comparison of their emission spectrum. In comparison with the emission spectra recorded on bulk polished samples (Figure S17), no significant difference of emission intensity is noticed here between the glass and ceramics emission band. Then, one can also notice a stronger structuration of the band in the ordered ceramic vs the disordered ceramic, whose band shape is very similar to that recorded in the glass.

■ DISCUSSION 4.1. Origin of the 3 × 1 × 1 Superstructure. While the preference of the large (Sr) and small (RE) cations for different coordination sites explains the occurrence and relative stabilities of the ordered and disordered structures in this series (see section 4.2), it does not explain why the 3 × 1 × 1 superstructure retains a substantial degree of disorder, i.e., why Sr and RE are ordered over three different sites (Sr-only, REonly and mixed), instead of segregating completely over two Inorganic Chemistry sites (Sr-only and RE-only), which would give a fully ordered structure. This can be considered by expanding the view of the 3 × 1 × 1 superstructure (Figure 10) to reveal the full complexity of the cation ordering. The most striking feature is that the small highly distorted RE2 sites, populated exclusively by RE, are arranged in two dimensions on a pseudohexagonal sublattice which maximizes their separation (Figure 10a). This arrangement means that the highly distorted pentagonal channels that host them are not required to share edges with each other. In contrast, the larger Sr and Sr/RE1 sites are not arranged pseudohexagonally and instead form one-dimensional stripe-like sublattices parallel to the b axis.

The underlying melilite structure can be described as a hexagonal tiling ("MacMahon's net" or "Cairo pentagonal tiling" corresponding to a pair of orthogonal interpenetrating hexagonal nets), 51,52 as illustrated in Figure 10b. Here, it can be seen that two tile types A and B are required to describe the structure fully, and these tessellate in stripes along the b axis (Figure 10b) in sequence ABA′ (where A′ = 180°rotation of A) to produce the observed 3-fold unit cell expansion. Tile A is a half-ordered structural fragment containing 1 × Sr site, 1 × RE site, and 2 × mixed sites. Tile B is a fully ordered structural fragment containing 2 × Sr sites and 2 × RE sites. ABA′ is, therefore, 2/3-ordered. For the purpose of discussion, a fully disordered structural fragment (tile C) is also illustrated in Figure 10c.

The stability of ABA′ tiling can be explained by comparison with the simpler hypothetical structures produced by its individual components A and B. It can be seen that AA′ (= BC) tiling supports a wide separation of the small highly distorted RE2 sites with no requirement for edge-sharing between the highly distorted RE2 pentagonal channels, but it produces a low overall population of these sites (1/4), with half of the cations accommodated on mixed sites. This hypothetical half-ordered structure is disfavored, because it does not maximize the number of small RE2 sites available for the [6 + 1] coordination of RE 3+ . In contrast, the hypothetical fully ordered structure afforded by BB tiling yields the highest possible population of RE2 sites (1/2), but it is disfavored because it requires each of these highly distorted channels to share edges (as indicated by the black outline in Figure 10c). It follows that the ABA′ tiling is a compromise between the local bonding preferences of the small RE cation (which demands a high population of [6 + 1] RE2 sites) and the limited flexibility of the host framework, which cannot distort to support two such sites in close proximity locally. The 3 × 1 × 1 superstructure thus retains 1/3 of its A sites as mixed sites, which are larger and less distorted than RE2, as a buffer between the fully ordered fragments. This maximizes the RE2 [6 + 1] population, while keeping the Ga 3 O 7 framework strain to within acceptable limits.

4.2. Competition between Ordered and Disordered Polymorphs. The trends in thermodynamic and structural stability in the SrREGa 3 O 7 series depend strongly on the ionic radius of the RE cation (Figure 8). The 3 × 1 × 1 superstructure is most stable when the cation mismatch is largest: the Lu member is ordered over its entire stability range, and the Yb member has a very strong tendency toward ordering with only a narrow window between its cationdisordering and decomposition temperatures. As the RE ionic radius increases, the stability of the superstructure decreases until the disordered polymorph becomes dominant when RE is larger than Er. This trend can also be seen in the fact that SrErGa 3 O 7 and SrTmGa 3 O 7 are readily synthesized in their ordered polymorphs by ex situ crystallization in a muffle furnace, while in SrDyGa 3 O 7 and SrHoGa 3 O 7 the 3 × 1 × 1 superstructure can only be obtained by precise control of the annealing protocol (see section 3.4). SrYGa 3 O 7 presents an intermediate case, with isolated fully ordered nanodomains forming on ex-situ crystallization. Eventually, when the RE radius becomes sufficiently large (RE = Tb), cation ordering is no longer observed. This trend is consistent with the nature of the superstructure itself: the distortion of the Ga 3 O 7 framework to generate a set of highly distorted pentagonal channels that accommodate RE in [6 + 1] coordination requires A site cations that are small enough to occupy such a site. This implies that the formation of the 3 × 1 × 1 superstructure not only is dependent upon Sr/RE size mismatch but is also conditional upon the absolute size of the RE cation. For example, this may explain why the Ba-based melilites BaNdGa 3 O 7 (A-site ionic radius radio r Ba /r Nd = 1.28, assuming 8-fold coordination) and BaSmGa 3 O 7 (r Ba /r Sm = 1.32) 6 adopt the tetragonal P4̅ 2 1 m structure despite having Ba/ RE radius ratios that are similar to that of SrYbGa 3 O 7 (r Sr /r Yb = 1.28), as Nd 3+ and Sm 3+ are too large to tolerate [6 + 1] coordination. The opposite case is presented by CaErGa 3 O 7 : 6 this compound is reported to adopt the tetragonal parent structure despite the presence of the small Er 3+ cation, which may be because the relatively weak size contrast between Ca 2+ and Er 3+ (r Ca /r Er = 1.12) is insufficient to drive long-range ordering. These examples suggest that both a large A-cation size contrast (e.g., AE 2+ /RE 3+ ≈ 1.28) and a sufficiently small RE cation (Dy 3+ or smaller) must be present together to stabilize the 3 × 1 × 1 superstructure.

Alternative framework distortions that are available to smallcation melilite gallates are the 5D modulated structures of CaLaGa 3 O 7 and CaNdGa 3 O 7 . In these compounds, a pair of modulation vectors parallel to the basal axes of the tetragonal melilite parent cell generate a set of six-, seven-and eightcoordinate A sites (versus eight-coordinate-only in the tetragonal parent phase). The population of these sites by Ca and RE is nonrandom, with Ca showing a preference for the six-coordinate sites (e.g., these sites are approximately 60% occupied by Ca and 40% by Nd in CaNdGa 3 O 7 ). In these compounds, the average A-site cation radius (e.g., 1.115 Å for CaNdGa 3 O 7 ) is comparable to that found in SrYbGa 3 O 7 (1.123 Å), and this drives the distortion of the framework to reduce the average size of the channels, although the sixcoordinate channels exhibited by CaNdGa 3 O 7 (six A-O distances of 2.4-2.7 Å and two of 2.9-3.1 Å) are not as small or distorted as those found in the 3 × 1 × 1 superstructure of SrYbGa 3 O 7 (six distances of 2.22-2.52 Å and one of 2.97 Å). The relatively low contrast in ionic radii between Ca/Nd (= 1.01) may not provide a sufficient driving force for full cation ordering such as that found in the 3 × 1 × 1 superstructure (Sr/Yb = 1.28). Note that the absence of satellite peaks in the SAED patterns of quenched SrTmGa 3 O 7 (which adopts tetragonal parent structure, as described in section 3.2; Figure S4) is consistent with the conclusions of Wei et al., 8 who describe the relationship between structural modulation and A/B cation radius ratio: while it is close to the proposed boundary, the average A site cation radius in SrTmGa 3 O 7 is not sufficiently small to induce modulation.

In summary, the interplay between the tetragonal parent structure, the 5D modulated structures, and the 3 × 1 × 1 superstructure is governed by the average size of the A-site cations (a small average radius is required for the modulated structures and 3 × 1 × 1 superstructures); the contrast between the A site radii (high contrast favors the 3 × 1 × 1 superstructure over the modulated structures); and the absolute ionic radius of the RE cation (3 × 1 × 1 superstructure is only stable if RE <T b 3+ ), as shown schematically in Figure 11.

4.3. Effect of Structural Ordering on Optical Properties. The structural ordering of the SrREGa 3 O 7 melilites leads to a decrease of their optical transmission in the bulk form (Figure S15), resulting from light scattering losses at the grain boundaries, as well-known and described in the literature. 15,53 This effect is particularly pronounced in the short wavelength region and can also affect the maximum transmission of the bulk ceramic. The photoluminescence spectroscopic properties of RE doped glass ceramics have been intensively studied in the past 20 years. 54-57 It is commonly accepted that structural ordering around the RE ions resulting from controlled crystallization of their parent glasses can significantly modify their emission features by increasing their emission intensities, for instance. Such enhancement can be particularly strong (over 100×) when energy levels of the RE ions are more efficiently excited through energy transfers between the RE ions after their incorporation into the crystalline phase. Their migration within the material can also lead to an optimized RE interionic distance favorable to these energy transfers. The absorption and emission band shapes of RE ions in a structured environment are expected to be affected, by showing a narrower line width and more intense absorption/emission peaks, similarly to that observed in single crystals. 54-57 Here, a clear structuration of the absorption bands of the SrREGa 3 O 7 ceramic melilites is observed (Figure S16), thus illustrating this structural ordering around the RE ions. Then, the increase of intensity observed in the emission spectra recorded on the SrErGa 3 O 7 bulk ceramic (Figure S17) can be mostly attributed to the light scattering induced by grain boundaries and the experimental technique used to excite and collect emitted light. Both excitation and emission light pathways are indeed expanded in the transparent bulk ceramic in comparison with the glass. This assumption is clearly supported by the emission spectra presented in Figure 9, where the glass and ceramic melilites were finely crushed to obtain comparable grain size, minimizing therefore the scattering related to the sample textures/morphologies. The observed increase of Er 3+ emission intensity in the ceramic vs the glass powdered melilites is then not as high as that observed in the bulk's measurement (Figure S17).

Nevertheless, as one can observe in Figure 9, there is a notable difference of spectral emission line shapes between the disordered and ordered ceramics. The strong structuration of the emission band observed in the ordered melilite ceramic can be compared, to some extent, to the sharp spectral bands of Er 3+ in YAG single crystals and transparent ceramics, 58 indicating a long-range ordering. The structural environment of the RE ions is well-defined and identical across the material, resulting in these sharper band features. On the other hand, the emission line shape of the disordered ceramic is continuously broadened and very similar to that of the glass, indicating that the RE environment in the glass and disordered are close.

The near-and mid-infrared emission bands of the SrREGa 3 O 7 melilites make them potential candidates for the development of infrared solid state lasers and compact sources for dentistry, surgery, remote sensing, environment, and security and defense, 59-64 which should motivate further spectroscopic study of these materials in the 2-5 μm range, for example using low temperature conditions and/or timeresolved spectroscopy.

CONCLUSION

We have shown that the glass crystallization method can be used to synthesize a series of small rare-earth melilites SrREGa 3 O 7 (RE =D y -Lu, Y) with control of their crystal structures and luminescence properties. These compounds are found to be metastable, with thermal decomposition temperatures in the range 800-850 °C for the smallest rare-earths Ho-Lu, which makes them challenging to access by conventional high-temperature ceramic methods. By tuning the crystallization conditions, we have shown that it is possible to isolate two different crystal structures for each composition. The first is a conventional tetragonal melilite structure with fully disordered A site cations, which forms readily for the larger rare-earth members RE =D y -Er but can also be obtained for the smaller rare-earth members (all except RE = Lu) by rapid quenching from a high temperature. The second accessible crystal structure is a 3 × 1 × 1 melilite superstructure with Sr and RE ordered over three distinct A sites of equal multiplicity (Sr-only, RE-only, and mixed Sr/RE), which is strongly favored for the smallest rare-earth members RE = Tm, Yb, and Lu, but can also be isolated for the larger members Dy-Er and Y by appropriate control of heating and cooling rates during crystallization. In this structure, cation ordering is driven by the bonding requirements of the small RE cation, which adopts a highly distorted [6 + 1] coordination. The host Ga 3 O 7 framework accommodates these [6 + 1] sites in a pseudohexagonal arrangement which maximizes their separation but limits their population to 1/3 of the A sites. This competition between the bonding demands of RE 3+ and the flexibility of the host framework favors the retention of the mixed Sr/RE site (population 1/3) which acts as a buffer between fully ordered structural fragments. The 3 × 1 × 1 superstructure offers an alternative way to order small A cations in the melilite structure, which contrasts with the previously reported modulated distortions in Ca-based analogues CaLaGa 3 O 7 and CaNdGa 3 O 7 , which are partially cation-ordered. We propose that the particular combination of average A-site size (ionic radius), A-site size contrast, and absolute size of the RE cation are the key parameters that control the ordering type in these structures and note that the 3 × 1 × 1 structures and modulated structures occupy two distinct regions of this parameter space. Finally, we show that the control of cationic ordering around Er 3+ ions in SrErGa 3 O 7 ceramics influences the luminescence properties, revealing a comparable structural environment in both disordered ceramics and glasses, while samples that adopt long-range ordering of Sr/Er in the 3 × 1 × 1 superstructure produce sharper spectral bands that are reminiscent of YAG single crystals or transparent ceramics. With their broad optical transmission range (extending up to 6-7 μm wavelengths) and ease of fabrication, the SrREGa 3 O 7 glass and ceramic melilites appear to be promising RE host materials for active photonic applications. a : constrained to refine to the same Uiso values Controlled crystallization of glass precursors in ternary or quaternary phase fields is a demonstrated route to technologically useful transparent ceramics by offering suitable control of t h em i c r o s t r u c t u r et om i n i m i z el i g h ts c a t t e r i n g . 1-8 We previously reported long-lasting red luminescence in the spinel Zn 1+x Ga 2-2x Ge x O 4 :Cr 3+ , 9 followed by the synthesis of transparent glass ceramics at similar compositions by controlled crystallization of Na 2 O-ZnO-Ga 2 O 3 -GeO 2 glass precursors. In these materials, Zn 2+ ,G a 3+ , and Ge 4+ undergo a nanoscale phase segregation to leave a dispersion of ZnGa 2 O 4 nanocrystals embedded in a GeO 2 -rich glassy matrix, 10 producing bulk glass ceramics with high transparency in the visible and infrared spectral regions. Such materials can be functionalized by the addition of Cr 3+ to induce long-lasting red luminescence in the full volume of the ceramic. 11 Other multinary oxide phase fields containing Zn, Ga, and Ge are therefore of interest for their potential to host controllable phase separation phenomena and hence optically transparent functionalizable glass ceramics. The existence in the phase diagram of a stable high-symmetry crystal structure able to host multiple cations, thus fulfilling the role of ZnGa 2 O 4 , which may be an advantage in this respect. Solid solutions of the langasite-type compounds Ca 3 Ga 2 Ge 4 O 14 and Ca 3 ZnGe 5 O 14 are therefore of interest as potential nano-crystallization products from CaO-ZnO-Ga 2 O 3 -GeO 2 precursor glasses.

■ ASSOCIATED

The langasite structure, of general formula A 3 BC 3 D 2 O 14 ,isa layered framework structure type constructed from cornersharing (C,D)O 4 tetrahedra and BO 6 octahedra; the BO 6 octahedra also bridge adjacent layers, forming 8-coordinate interlayer sites for A cations, which are arranged in channels along the stacking axis (Figure 1). The structure type, which is of interest for properties arising from its polarity, 5,6,12 optical transparency, 3,4 or ability to host interstitial oxide ions, 13 can accommodate multiple cations with different coordination preferences: the A sites tend to host alkaline-and rare-earth cations, while transition metal and p-block cations tend to be distributed across the corner-linked B, C, and D sites. Ca 3 Ga 2 Ge 4 O 14 is readily synthesized in bulk and adopts the common trigonal langasite structure (space group P321). In contrast, Ca 3 ZnGe 5 O 14 appears to be difficult to synthesize in bulk, and has only been isolated in the form of small single crystals as a byproduct from the synthesis of Ca-Cu 0.95 Zn 0.05 Ge 2 O 6 ; 14 it adopts a distorted langasite framework, corresponding to a twofold expansion of the parent unit cell and reducing the symmetry from P321 to its monoclinic subgroup C2 (a distortion that is also observed in certain temperature and pressure regimes for other langasites such as La 3 Nb 0.5 Ga 5.5 O 14 ). 15,16 The trigonal and monoclinic unit cells are projected together onto the same underlying langasite structure in Figure 1.

In both compounds, the absence of X-ray scattering contrast between Ga 3+ /Ge 4+ and Zn 2+ /Ge 4+ means that the distribution of these cations over the three framework sites (B, C, and D) cannot be obtained directly by conventional (non-anomalous) X-ray diffraction methods, and instead indirect routes (e.g., analysis based on refined bond distances) have been used to deduce the nature and extent of cation ordering. 17 Such isoelectronic pairs can be distinguished directly by neutron diff raction (NPD), as demonstrated for La 3 Ga 5-x Ge 1+x O 14+x/2 , 13 but NPD alone cannot be used for direct analysis of more complex systems with three or more isoelectronic cations distributed over the framework sites B, C, and D. Atomic-resolution STEM-EDS mapping offers a solution to this problem by detecting each element type directly with a spatial resolution of around 2-3 Å. While this technique is most often used qualitatively, intensities of atomic columns can be extracted by Gaussian curve fitting which is most often applied to 1D line profiles to provide quantitative information about atomic site occupancies. 18 Furthermore, Gaussian fitting of entire 2D map sections has been demonstrated for SrTiO 3 thin films 19 and then applied to distinguish multiple elements with close atomic number in FeCoNi alloys. 20 The 2D fitting approach has the advantage of considering the actual nature of the two-dimensional data set: it reduces errors associated with the subjective selection of the location and boundaries of a line profile (which is problematic where the atomic columns of interest do not lie on a perfectly straight line, or where adjacent columns overlap to contribute unwanted intensity to the profile) and produces contour maps that are more intuitive for crystallographic problems.

It can be challenging to characterize cation ordering in crystalline systems where the scatterers have a similar atomic number or where there are more than two cation species involved in the ordering, especially when the ordering is incomplete. The ability to resolve such problems is important in many contexts, for example, where cation ordering controls structural polarity, 21 suppresses thermal conductivity, 22 or influences lithium battery cyclability. 23 Here, we report the synthesis of a complete solid solution (1-x)Ca 3 Ga 2 Ge 4 O 14 -(x)Ca 3 ZnGe 5 O 14 (0 ≤ x ≤ 1) by full crystallization from glass, with full structural characterization by synchrotron powder Xray diffraction (PXRD) and neutron diffraction, and quantitative use of atomic-resolution STEM-EDS on powder specimens based on the development of a 2D fitting procedure to extract quantitative information on the distribution of Zn 2+ , Ga 3+ , and Ge 4+ over the available framework sites in the x = 0.5 member Ca 3 Zn 0.5 GaGe 4.5 O 14 .

EXPERIMENTAL SECTION

2.1. Synthesis Procedure. Samples of composition Ca 3 Ga 2-2x Zn x Ge 4+x O 14 were synthesized either by direct crystallization of the melt (for x = 0), or by full and congruent crystallization from glass (for 0.25 ≤ x ≤ 1). First, stoichiometric amounts from high-purity precursors CaCO 3 99.95%, Ga 2 O 3 99.998%, ZnO 99.999%, and GeO 2 99.9% (all from Strem Chemicals) were weighed according to the nominal composition for 0 < x ≤ 1. For x =0 ,a n excess of 2% (wt %) of GeO 2 was added to the initial mixture to compensate for partial volatilization (see Figure S1). The precursors were then ground together for several minutes in an agate mortar using ethanol to improve the homogeneity of the mixture. The resulting powder was dried and pressed into pellets, then divided into fragments of ∼35 mg each. Pellet chunks were melted individually by aerodynamic levitation (ADL) in an argon gas jet coupled to two CO 2 lasers (10.6 μm). These samples melted between 1250 and 1350 °C (depending on the composition), and were further heated up to 1500 °C to ensure their homogeneity, then subsequently quenched by turning the lasers off, reaching high cooling rates (estimated around 300 °C/s) in order to achieve vitrification, and leading to glass precursors in the form of spherical beads for Ca 3 Ga 2-2x Zn x Ge 4+x O 14 with compositions 0.25 ≤ x ≤ 1. For Ca 3 Ga 2 Ge 4 O 14 (x = 0), the argon gas flow was adjusted so that the levitating molten bead touches the nozzle. The contact surface thus acts as a nucleation center for crystallization of the entire bead when the lasers are turned off. This process produced a higher crystallinity of the sample compared to glass-crystallized samples of the composition, as confirmed by laboratory PXRD, showing narrower diffraction peaks for the molten liquid crystallized sample compared to the glass-crystallized sample (see Figure S3). The amorphous (0.25 ≤ x ≤ 1)/crystalline (x =0 ) state of resulting beads was further confirmed by laboratory PXRD (see Figures S2 andS3). The glass precursor samples were then crystallized in air at temperatures between 800 and 815 °C (characteristic crystallization temperatures obtained by DSC, as shown in Figure 2a), for 2-3 h (see Section 3.1).

2.2. Thermal Analysis. Differential scanning calorimetry (DSC) was performed on a Setaram MULTI HTC 1600 instrument to determine the glass transition and crystallization temperatures of each composition. A ∼300 mg powder sample was used, contained within a platinum crucible, with argon as the purging gas and a heating and cooling rate of 10 °C/min, samples were heated up to 900 °C. The measured temperatures have an incertitude of ±2 °C.

2.3. Powder Diffraction. Room temperature laboratory PXRD was performed using a Bruker D8 Advance laboratory diffractometer (Cu K α radiation) equipped with a LynxEye XE detector in Bragg-Brentano geometry, with powders dispersed on a low-background silicon wafer. In situ variable temperature PXRD was performed using a Bruker D8 Advance laboratory diffractometer (also Cu K α radiation, Bragg-Brentano geometry) equipped with a Vantec detector and an Anton Paar HTK1200N furnace. Powders obtained from crushed glass beads were placed in a platinum-lined corundum sample holder and heated under air. Data were collected from 30 to 600 °C in one heating step, and then to 1200 °C using a 10 °C step size, an angular range of 20-39°(2θ) with a 0.016°step size and counting time of 0.7 s/step. Synchrotron powder diffraction (SPD) measurements were collected on the 11BM beamline (Argonne National Laboratory) in the United States, for samples of composition Ca 3 Ga 2-2x Zn x Ge 4+x O 14 , where x = 0, 0.25, 0.5, 0.75, and 1. Crystallized beads were crushed to powder (one bead per composition) and filled into 0.8 mm diameter Kapton capillaries. Data were acquired with an incident wavelength of λ = 0.458084 Å from 1 to 50°(2θ) with a step size of 0.001°and a 0.1 s measuring time per step. Neutron powder diffraction (NPD) data were acquired for samples of composition Ca 3 Ga 2-2x Zn x Ge 4+x O 14 x = 0, 0.5 and 1, on the instrument MEREDIT at the Nuclear Physics Institute, Czech Republic, with λ = 1.46 Å in the range 4-144°(2θ), using a step size of 0.08°and a measuring time of 970 s per step. Samples were scaled up to ∼5 g for x = 0, 0.5 and ∼4 g for x =1,by crushing and combining ∼100 individually crystallized beads for neutron diffraction experiments. Structural analysis and Rietveld refinements 24 were performed using TOPAS Academic (v.6). 25 Bond valence sums (BVS) were calculated by the method of Brown and Altermatt. 26 2.4. Transmission Electron Microscopy. The cation distributions were investigated at the atomic scale via high-resolution scanning transmission electron microscopy-high angle annular dark field (STEM-HAADF) imaging and energy dispersive X-ray spectroscopy (EDS) elemental mapping. These experiments were performed on a JEOL ARM200F (JEOL Ltd.) Cold FEG transmission electron microscope (TEM) operating at 200 kV, equipped with a double spherical aberration corrector and fitted with a JEOL SDD CENTURIO EDS system. In STEM-HAADF imaging mode, a 68-174.5 mrad inner-outer collection angle and a 0.1 nm probe size were used while in STEM-EDS mapping a probe size of 0.13 nm was chosen. Fine sample powder was first homogeneously dispersed in ethanol, and then one droplet of this suspension was deposited on a TEM amorphous holey carbon-coated copper grid and left to dry.

RESULTS

Synthesis by Crystallization from Glass and

Molten Liquid. Classic solid-state reaction routes were first investigated in the synthesis of Ca 3 Ga 2 Ge 4 O 14 (x = 0); however, we were not able to prepare single-phase powders by this route (see Supporting Information Section I for more details). Crystallization from glass was then considered as an alternative synthesis route, as this approach was shown to help accessing new metastable crystalline phases. 2-4,27 Initial attempts to make precursor glass of composition Ca 3 Ga 2 Ge 4 O 14 (x = 0) used a conventional melt-quenching technique, by melting the reaction mixture in a platinum crucible at 1300 °C for 1 h, then quenching by placing the bottom of the crucible in a bath of water without any samplewater contact. After thermal treatment, these glasses showed a heterogeneous crystallization, leading to a mixture of gallate and germanate phases. In contrast, glass beads produced using the faster cooling rates offered by the ADL apparatus were found to crystallize into single-phase langasite materials after heat treatment at 815 °C. By further tuning of the ADL experimental conditions, we found that direct crystallization of the molten bead (see Section 2.1) produced single-phase langasite materials with sharper diffraction peaks (see Figure S3). We used the directly crystallized materials for all structural characterizations of the composition x =0 .

Single-phase langasite materials were obtained for 0.25 ≤ x ≤ 1 by crystallization of precursor glasses obtained by ADL. The highest quality samples were obtained by crystallizing the beads in bulk form rather than crushed (powder) form due to surface crystallization of the secondary phases CaZnGe 2 O 6 and Ca 2 ZnGe 2 O 7 (see Figure S4): in situ PXRD of Ca 3 ZnGe 5 O 14 (x = 1) glass powder shows the crystallization of the langasite phase above 670 °C, which occurs simultaneously with crystallization of these minor impurities (Figure 2a). In Figure S5, we show a comparison between DSC heating curves of Ca 3 ZnGe 5 O 14 (x = 1) glass, measured under powder and bulk form. The powder sample exhibits a lower T c , consistent with a more facile surface crystallization mechanism. As shown in Figure 2b, DSC measurements were conducted on a single glass bead for each composition to determine their glass transition (T g ) and glass crystallization (T c ) temperatures (see Table S1). To achieve full and congruent crystallization from glass, the resulting glass beads for 0 < x ≤ 1 were heated at 815 °C for 2 h (0 < x < 1) and at 800 °C for 3 h (x = 1), under bulk form to prevent surface crystallization of impurities. Beads prepared in this way contained langasite-type Ca 3 Ga 2-2x Zn x Ge 4+x O 14 as the only crystalline phase. 17) Å, and β = 90.817(4)°), 14 was described as a fully ordered structure where Zn 2+ cations are accommodated on the octahedral (B) sites, while Ge 4+ cations occupy the remaining tetrahedral (C-and D-) sites. To further investigate the possibility of a monoclinic distortion for glass-crystallized samples close to this composition (x = 1), SPD measurements were conducted on samples of composition x = 0, 0.25, 0.5, 0.75, and 1.

Across the solid solution, all SPD patterns (Figure S6) could be indexed with the parent hexagonal langasite cell with a systematic peak shift (Figure 3a), and no extra peaks became apparent as the composition approaches x = 1, indicating that the P321 structure is retained for all compositions. Figure 3b shows a direct comparison between the acquired SPD pattern of Ca 3 ZnGe 5 O 14 (x = 1), and a simulated SPD pattern of Ca 3 ZnGe 5 O 14 (reported C2 structure) 14 under the same measuring conditions. The simulated C2d i ffraction pattern contains many additional Bragg peaks that are not present in the acquired pattern, which is fully indexed to the hexagonal P321 Ca 3 Ga 2 Ge 4 O 14 cell.

Rietveld refinements were carried out using the Ca 3 Ga 2 Ge 4 O 14 structure reported by Mill et al. 17 (SG P321, a = 8.076 Å, c = 4.974 Å) as a starting model for all compositions, keeping the same number of total refined parameters for each sample (15 background terms, zero shift, scale factor, 6 profile parameters (TCHZ profile function), axial divergence and 17 atomic parameters, resulting in 41 refined independent parameters). The B-, C-, and D sites were fixed to be fully occupied by cations with no refinement of the Ga 3+ ,G e 4+ ,o rZ n 2+ partial occupancies. The refined cell parameters (from SPD data) show opposing trends in the a and c parameters, giving a very weak decrease in unit cell volume but a marked increase in c/a ratio with increasing x (Figure 3c). Such behavior is consistent with the substitution of Ga 3+ (ionic radius of 0.62 and 0.47 Å in 6-and 4coordination, respectively) by a mixture of smaller Ge 4+ (0.53 and 0.39 Å) and larger Zn 2+ (0.74 and 0.60 Å), 28 and is also seen in other langasite-type solid solutions such as La 3 Ga 5-x Ge 1+x O 14+x/2 . 13 The refinements led to satisfactory reliability factors for the entire measured series (see Figures S8-S10 for SPD Rietveld refinement plots and Tables S2-S6 for refined structural parameters).

As shown in Figure 3b, the Ca 3 ZnGe 5 O 14 (x = 1) sample synthesized by glass crystallization produces far fewer Bragg reflections than the previously reported monoclinic (C2) structure, and can be indexed fully to the trigonal (P321) structure. We also compared the Rietveld fits obtained from both structural models. Provisional refinement of both models produced misfits due to an hkl-dependent peak broadening in the measured pattern. This was modeled using the Stephens description 29 for trigonal and monoclinic symmetries, respectively, thus reducing the R wp and χ 2 values from [8.98%, 2.01] to [7.36%, 1.35] for the P321 model and from [8.93%, 1.99] to [6.68%, 1.10] for the C2 model (see Figures S10 andS12 for SPD refinements and Tables S6-S9 for refined structural parameters). The unit cell of the C2 model, refined to an essentially orthorhombic symmetry corresponding to a decrease of β from 90.817(4)°(published starting model) 14 to 89.955(1)°. Even though the C2 model provides a marginally better fit to the whole pattern when the Stephens broadening functions are applied, the lower symmetry of this structure allows more refinable parameters (68 + 10 parameters from Stephens description) than the P321 space group (41 + 5 parameters from Stephens description), and the refined model is almost indistinguishable from its trigonal counterpart, as shown in Figure S7 an overlay of both refined structures against the same acquired SPD data. We therefore consider the trigonal P321 structure to be the simplest and most appropriate description of glass-crystallized Ca 3 ZnGe 5 O 14 (x = 1).

To test the stability of the Ca 3 ZnGe 5 O 14 (x =1 )P321 structure against T(°C) and a possible phase transition (P321 → C2), variable temperature PXRD (VT-PXRD) measurements were carried out on a glass-crystallized Ca 3 ZnGe 5 O 14 (x = 1) sample, from room temperature to 700 °C in steps of 100 °C. As shown on Figure S12, the cell parameters display a linear increasing trend and no discontinuous changes were noticed (as demonstrated in 16 for some langasite compositions under pressure, where their cell parameters trend shows a discontinuity due to a phase transition from P321 to C2), suggesting that the hexagonal polymorph is retained until its decomposition.

3.3. Distribution of Two Cations in x = 0, 1 End Members by Neutron Diffraction. The end-member compositions (x = 0, 1) host only two cation species on the framework (B, C, D) sites, with different neutron scattering lengths (8.185(20) fm, 7.288(2) fm, and 5.680(5) fm for Ge, Ga, and Zn, respectively), 30 allowing the use of NPD to refine the Ga/Ge and Zn/Ge ratios directly. Rietveld refinements

Inorganic Chemistry

against NPD data were constrained to keep each mixed site fully occupied and an overall composition matching the nominal; see Figure 4a,b for refined plots, and Tables 1 and2 for refined structural parameters. The refinements of neutron data for the x = 0 sample showed that the cationic disorder is distributed over the octahedral 1a and tetrahedral 3f sites (as previously reported in refs 17, 31), while the tetrahedral 2d site remains fully occupied by Ge. Refined occupancies led to 0.51(8)Ga/0.49 (8)Ge on the 1a site and 0.50(3)Ga/0.50(3) Ge on the 3f site, which displays a complete disorder over these two crystallographic sites (see Tables 1 and2). This is consistent with a non-quantitative 71 Ga QPASS NMR spectrum collected from the Ca 3 Ga 2 Ge 4 O 14 sample, which showed resonances from 6-and 4-coordinate gallium (as described in Supporting Information Section II). Rietveld refined NPD data for the x = 1 fully substituted end member also confirmed that the cationic disorder occurs between the 1a and 3f sites, while the 2d site remains fully occupied by Ge atoms. The refined occupancies over the mixed sites, 0.52(4)Zn/0.48(4)Ge on the 1a and 0.16(1)Zn/ 0.84(1)Ge on the 3f, show that only Zn atoms are randomly dispersed over the two coordination types, 52(4)% on the 1a 6-coordinated site and 16(1)% on the 3f 4-coordinated site. The B-and C-site cation oxide distances show notable differences going from the Ca 3 Ga 2 Ge 4 O 14 langasite to the fully Zn/Ge-substituted compound Ca 3 ZnGe 5 O 14 (Tables 3 and4).

The B-site M-O3 bond length increases from 1.926(3) Å (Ga1/Ge1-O3) to 1.984(6) Å (Zn1/Ge1-O3), which allows an 8.7% increase of the polyhedral volume, while both C-site M-O3 and M-O2 bonds lengths decrease from 1.787(4) Å (Ga2/Ge2-O3) and 1.853(5) Å (Ga2/Ge2-O2), to 1.767(6) Å (Zn2/Ge2-O3) and 1.862(6) Å (Zn2/Ge2-O2), respectively, leading to the 3f site tetrahedron a volume decrease of 2.1%. These results are consistent with the refined occupancies of each site for both end members, where Ga 3+ is fully exchanged by the larger Zn 2+ cation on the 1a site and only one-third by the same larger cation on the 3f site, while the other two-thirds are substituted by a smaller Ge 4+ cation. The hypothesis of a fully ordered hexagonal langasite structure for both end members was considered by Rietveld refinement with different fixed Ga/Ge and Zn/Ge occupancies on both 1a and 3f sites against NPD data. In Figure S13a,b, a shallow χ 2 minimum can be detected when the amount of Ga 3+ and Zn 2+ approaches 50% occupancy of the 1a site for x = 0 and 1, respectively. Moreover, subtle peak intensity misfits at low angle can be spotted when Ga 3+ or Zn 2+ scattering density is focused on one of the two cationic disordered sites, inducing over-or undercalculated peak intensities (Figure S13c,d). The intensity misfits are more visible for the Zn 2+ compound x =1 , compared to the Ga 3+ compound x = 0 due to their close neutron scattering lengths. 30 Furthermore, BVS calculations (Tables 3 and4), indicate that only the 2d site is suitable for Ge 4+ , BVS = 3.91(3) and 3.89(4) with a mean Ge3-O distance of 1.758(4) and 1.759(3) Å for both x = 0 and x =1 compounds, respectively. For the 1a and 3f sites, the BVS values indicate that all three cations are either under-or overbonded in the two different coordination types, which is consistent with the partial cation disorder observed by Rietveld refinement. The trend in bond distances and atomic site occupancies from NPD is discussed together with the bond distance trend from SPD across the full series (x = 0, 0.5, 1) in Section 4.

3.4. Distribution of Three Cations in x = 0.5 by STEM-EDS and Neutron Diffraction. To analyze the distribution of three isoelectronic cations over multiple crystallographic sites, as required for the intermediate composition Ca 3 GaZn 0.5 Ge 4.5 O 14 (x = 0.5), neutron diffraction must be combined with another complementary technique. Here, our approach is to extract direct quantitative information about the cation distributions by atomic-resolution STEM-EDS, and use this to construct a Rietveld model with appropriate (chemically justified) constraints on the refined cation occupancies.

In order to visualize the 2D structural projection of the Ca 3 GaZn 0.5 Ge 4.5 O 14 , the sample was oriented along the [001]* direction (Figure 5a) and imaged in STEM-HAADF mode at the atomic scale (Figure 5b,c). Along the [001]* direction, each column of atoms is composed of only one type of crystallographic site with the same density (see Figure 1).

In STEM-HAADF mode, the intensity of the acquired images is proportional to the thickness of the sample (e), the density (ρ) and the average atomic number (Z): I ∝ eρZ n , where n is in the range 1.6-2. The thickness of the sample was measured at 60 nm by electron energy loss spectroscopy (EELS), which represents close to 120 superimposed unit cells (120 atoms per column). It was estimated to remain unchanged across the entire imaged area (≈5n m× 5 nm). In these conditions, the intensity in the STEM-HAADF images is essentially due to the average atomic number (Z) of the crystallographic site. The 3e sites, being composed of the lightest cations (Z Ca = 20), appear the darkest while the 1a, 3f, Calculated with a distance cut off at 3 Å Inorganic Chemistry and 2d sites appear brighter due to the presence of heavier cations (Z Ge = 32, Z Ga = 31, and Z Zn = 30). However, as Ge, Ga, and Zn are of similar atomic number (Z Ge ≈ Z Ga ≈ Z Zn ), it is not possible to determine the distribution of these three cations on the 1a, 3f, and 2d crystallographic sites using only the intensities of the STEM-HAADF images. Consequently, EDS mapping at the atomic scale was carried out (Figure 6). The maps acquired on several zones of the same grain were aggregated in order to improve the signal-to-noise ratio and to tend toward an average model. A Wiener filter was then applied to highlight the atomic positions. The 3e site is clearly visible and composed only of Ca as expected, while the 2d site contains only Ge, and the 3f and 1a sites are mixed, which is consistent with the refi ned structures of Ca 3 Ga 2-2x Zn x Ge 4+x O 14 both end members x = 0 and x =1 . The Ga and Ge signals appear clearly on both the 1a and 3f sites, while the Zn signal seems to be focused on the 1a sites; visually, it is difficult to confirm its presence on the 3f site. In order to gain more information and determine the Ga, Ge, and Zn cation ratio on the 1a and 3f sites, a 1D analysis was performed by extracting an intensity profile through the sites from the EDS maps. The width of the profile (the orange rectangle overlaid on Figure 6b) was optimized in order to integrate as much signal as possible without introducing interference from the neighboring 1a and 3f column signals. In such a configuration, with a small distance between the cation sites 1a-3f (≈1.9 Å), it is not possible to integrate the full signal for each crystallographic site (Figure 6b).

Using a Gaussian decomposition and assuming that the area under the curve is proportional to the element content, the ratios of the elements Ge, Ga, and Zn between sites 1a and 3f were determined (Figure 7). The Gaussian coordinates were defined for the 1a and 3f sites from the Ge profile, which is best defined thanks to its high concentration, and then fixed for all the other element profiles (Ga and Zn) in order to integrate the signal in the same positions. As the Zn content is low, its profile was first refined using only one Gaussian contribution at the 1a coordinates (see Figure S14). However, a single Gaussian could not describe the entire profile, and a second Gaussian was added at the 3f position, indicating a small amount of Zn also present on this site. The calculated ratios between the 1a and 3f sites for the three cations were: (Ge 1a / Ge 3f = 0.9) (Ga 1a /Ga 3f = 1.17) (Zn 1a /Zn 3f = 2.6). Considering the nominal composition Ca 3 GaZn 0.5 Ge 4.5 O 14 , which has been checked by EDS analyses, and a 2d pure Ge site, the compositions of the mixed 1a and 3f sites have been determined and reported in Table 6: 0.23 (10)Zn/ 0.54(5)Ge/0.28(8)Ga and 0.09(4)Zn/0.67(2)Ge/0.24(3)Ga, respectively. These results show a very good agreement with refined occupancies from NPD data. Nevertheless, this 1D approach has certain limitations such as the application of a Wiener filter on the elementary maps, which can induce a bias, as well as the inability to integrate the signal through the entire sites due to the small distance between the neighboring 1a and 3f sites. Such problems can be reduced by a two-dimensional fitting approach such as that demonstrated by Lu et al., 19,20 so that a wider region of the map is used for quantitative analysis.

We chose to analyze two regions from the central part of the 2D elemental images to minimize possible errors or deformation at the borders. These two regions are centered on 1a sites and extending to their first 3f and 2d neighbors, defining polygonal regions with minimal contributions of other sites (see Figure S15). We then performed a refinement for each cation (Zn, Ga, and Ge) using the simplest possible model of a background offset and a sum of two-dimensional Gaussian lines for each site. Each 2D Gaussian is characterized by its x and y positions, width at half maximum, and amplitude.

The Ge data (with the best signal-to-noise ratio due to the high concentration of Ge in the cell) were refined first to extract the peak positions, width and amplitude for each of the 1a and 3f sites (note that the three 3f sites surrounding the 1a sites were constrained to keep the same peak width, for each of the two selected zones independently). The Zn and Ga data were then refined with constrained peak position and peak width from the Ge ones, hence extracting only the amplitude as refined value for these two cations on the 1a and 3f sites. Refinements of the STEM-EDS maps from zone 1 are shown in Figure 8. The equivalent zone 2 refinements are shown in Figure S16. The compositions of each column were extracted using the same calculation logic as the one used for the 1D refinements and normalizing the occupancies to 1.

Following the quantitative analysis by STEM-EDS, we constructed a Rietveld model for refinement against NPD data. Using the observation that the 2d site is dominated by Ge (Figure 6d and Figure 8), and by analogy with the x = 0 and 1 members (Tables 1 and2), we fixed the 2d site in x = 0.5 to be 32 and measured STEM-HAADF images, respectively. The corresponding crystal structure projection is overlaid on the top-right corner of the image, where blue, green, pink and orange points represent the 3e, 1a, 3f, and 2d crystallographic sites, respectively. fully ordered with Zn 2+ exclusively in octahedral coordination. In contrast, glass-crystallized Ca 3 ZnGe 5 O 14 contains a significant amount of site inversion with Zn 2+ partially occupying the tetrahedral 3f sites. This can also be seen by comparison of the B-, C-, and D-site polyhedral volumes of the two structures. In Table 7, we show a comparison between the octahedral (1a), tetrahedral (3f and 2d) Zn-O distances in glass-crystallized (trigonal) and single-crystal (monoclinic) Ca 3 ZnGe 5 O 14 : in the trigonal structure, these distances are significantly shorter for the 1a site, and slightly longer for the 3f, while they show similar values for the 2d site, consistent with refined partial occupancies of only the 1a and 3f by smaller Ge 4+ and bigger Zn 2+ . We note that the symmetryreducing monoclinic distortion is not a prerequisite for this type of Zn 2+ /Ge 4+ ordering, which implies that the monoclinic distortion of the lattice is induced by the cation ordering and its associated changes in the average size of the framework polyhedra.

At the other extreme of the solid solution, Ca 3 Ga 2 Ge 4 O 14 (x = 0), there are some minor differences in the extent of Ga 3+ / Ge 4+ ordering between the melt-crystallized materials that we report here, and single-crystal materials described in the literature, 33 despite the retention of trigonal P321 symmetry (see Table 8). In melt-crystallized Ca 3 Ga 2 Ge 4 O 14 ,G a 3+ ions are distributed over the octahedral 1a and tetrahedral 3f sites, while the tetrahedral 2d sites are occupied exclusively by Ge 4+ ; only 25(4)% of the total Ga content is in octahedral coordination, whereas the remaining 75(4)% is tetrahedrally coordinated. This is consistent with the reported Ga/Ge coordination environments in Ca 3 Ga 2 Ge 4 O 14 glass determined by EXAFS. 34 In single-crystal Ca 3 Ga 2 Ge 4 O 14 , 33 anomalous Xray scattering methods have shown that only ∼10% of the Ga 3+ cations are present in octahedral coordination (1a), with the remainder present at the tetrahedral (3f) site. In both materials, the tetrahedral 2d site is occupied exclusively by Ge 4+ , which may help to maximize separation of the most highly charged cations, and hence minimize electrostatic repulsion between them. This confirms that the synthesis route can influence the extent of Ga 3+ /Ge 4+ ordering in these structures, with melt-crystallization favoring a higher degree of disorder in this case, compared to the single crystals synthesized by a Czochralski method. 33 In complex glass-crystallized compositions with three isoelectronic cations (Zn 2+ /Ga 3+ /Ge 4+ ) distributed over the three possible octahedral and tetrahedral framework sites, exemplified by Ca 3 GaZn 0.5 Ge 4.5 O 14 (x = 0.5), which is reported here for the first time, a combined approach between NPD refinements and quantitative 2D fitting to atomicresolution STEM-EDS maps was applied. The analysis of Ca 3 GaZn 0.5 Ge 4.5 O 14 shows that the structure evolves progressively as the solid solution is traversed. This is seen in the unit cell parameters (Figure 3c) and the Rietveld refined M-O distances at the 1a (octahedral), 3f (tetrahedral), and 2d (tetrahedral) framework sites (Figure 10): as Zn 2+ is substituted into the structure, there is a marked increase in the volume of the MO 6 octahedra which goes against the overall decreasing trend in unit cell volume, indicating that the 1a site is becoming preferentially populated by larger cations. It was possible to quantify directly the cation distribution in Ca 3 GaZn 0.5 Ge 4.5 O 14 (x = 0.5) by 2D fitting to atomic- resolution STEM-EDS images followed by NPD refinements: this confirmed directly that Zn 2+ shows the strongest preference for octahedral coordination, while Ga 3+ and Ge 4+ have similar proportions in octahedral and tetrahedral coordination (and that, in common with the end-member compositions, the 2d tetrahedral site is occupied exclusively by Ge 4+ ). This distribution is essentially consistent with the relative ionic radii of these cations. Across the solid solution, there is also a notable increase of the refined oxygen thermal parameter values, from B iso = 1.18(4) Å 2 (x = 0) and 1.66(5) Å 2 (x = 0.5) to 2.17(7) Å 2 (x = 1), consistent with the observed cationic disorder and the increase of the size mismatch at the B and C sites due to the Ga 3+ substitution by Zn 2+ and Ge 4+ . Characterization of the cation distributions in complex bulk materials containing several cations with close atomic and neutron scattering factors is a nontrivial problem that is usually approached by coupling different characterization techniques. For example, a recent study of the high entropy spinel (Cr 0.2 Mn 0.2 Fe 0.2 Co 0.2 Ni 0.2 ) 3 O 4 with five different first-row transition metal cations distributed over two crystallographic sites, combines multiple complementary diffraction and spectroscopic techniques to fully characterize the material. 35 Our analysis of the Zn 2+ /Ga 3+ /Ge 4+ distribution over three crystallographic sites in Ca 3 GaZn 0.5 Ge 4.5 O 14 demonstrates that the quantitative use of atomic-resolution STEM-EDS mapping, using a 2D fitting program to directly extract the occupancies of each element, has the potential to be very useful for such problems that can simplify crystallographic analysis and can be applied in many different contexts if sufficiently high-quality data can be obtained from a suitable crystallite orientation. Here, we have shown that it is possible to fit the different elemental contributions from atomic columns with extremely small spatial separations (e.g., atomic columns spaced by approximately 2 Å are clearly resolved in the case of Ge 4+ ,a s shown in Figure 6) and with relatively low cation concentrations (e.g., a Zn 2+ 3f site occupancy of 0.1). For Zn 2+ and Ga 3+ , which have weaker STEM-EDS signals due to their low populations in Ca 3 GaZn 0.5 Ge 4.5 O 14 ,2Dfitting makes it possible to extract independent occupancies from the adjacent 1a and 3f sites. Such high spatial resolution and sensitivity should make it possible to study many different structure types in this way.

CONCLUSIONS

We have synthesized a new solid solution Ca 3 Ga 2-2x Zn x Ge 4+x O 14 (0 ≤ x ≤ 1) by direct crystallization from an under-cooled melt (x = 0) and glass crystallization (0.25 ≤ x ≤ 1), and characterized the evolution of structure and cation distribution across the solid solution by coupling SPD and NPD to atomic-resolution STEM-EDS. We showed that the trigonal langasite structure (space group P321) can be retained across the whole solid solution, even for the composition Ca 3 ZnGe 5 O 14 (x = 1), which was previously reported in a distorted monoclinic langasite structure (space group C2). Using NPD, we found that the simpler endmember compounds Ca 3 Ga 2 Ge 4 O 14 (x = 0) and Ca 3 ZnGe 5 O 14 (x = 1) have isoelectronic cations (Ga 3+ /Ge 4+ and Zn 2+ /Ge 4+ , respectively) distributed over the tetrahedral 3f and octahedral 1a sites, while the tetrahedral 2d sites are occupied exclusively by Ge 4+ . This partial disordering of Zn 2+ and Ge 4+ over two crystallographic sites in glass-crystallized Ca 3 ZnGe 5 O 14 marks a major difference from its previously reported monoclinic structure, which is fully ordered with Zn 2+ in purely octahedral coordination (1a) and Ge 4+ purely tetrahedral (3f). The partial disordering of Zn 2+ /Ge 4+ , introduced by the crystallization from glass synthesis technique, presumably accounts for the suppression of the monoclinic distortion and stabilization of the trigonal structure in this material.

In the more complex case of Ca 3 GaZn 0.5 Ge 4.5 O 14 (x = 0.5), where three isoelectronic cations (Zn 2+ ,Ga 3+ and Ge 4+ ) can be distributed over three possible sites, we used atomic-resolution STEM-EDS to image their distributions directly, and then extracted their site occupancy values quantitatively via 2D fitting by adapting the Fit2D program (developed originally for fitting 2D NMR spectra). This allowed us to construct a suitable Rietveld model for refinement against NPD data using chemically justified site occupancy constraints. These results confirmed that the tetrahedral 2d site is occupied exclusively by Ge 4+ at x = 0.5 (in common with the simpler x = 0, 1 end members), while Zn 2+ ,G a 3+ and the remaining Ge 4+ are distributed over the octahedral (1a) and tetrahedral (3f) sites in proportions that correlate to their ionic radii: the Zn 2+ ions show the greatest tendency toward octahedral coordination, while a higher proportion of Ga 3+ and Ge 4+ are present at the 3f sites. To our knowledge, this is the first time that quantitative 2D fitting of atomic-resolution STEM-EDS maps has been applied to this type of problem in a bulk oxide material. In principle, this approach can be applied to other materials classes where it is important to understand the distributions of cations with similar scattering factors (e.g., adjacent transition metals, lanthanides or p-block elements) over multiple crystallographic sites within a structure.

■ ASSOCIATED CONTENT

* sı Supporting Information II. 71 Ga NMR study of Ca 3 Ga 2 Ge 4 O 14 . 71 Ga NMR is a powerful tool to probe the Ga local structure in terms of coordination and also to provide a quantification of its different environments 1,2 . 71 Ga solid-state NMR spectroscopy was performed on the x = 0 member only (Ca 3 Ga 2 Ge 4 O 14 ) at 20 T with a Bruker Avance Neo spectrometer equipped with a 0.7 mm magic angle spinning (MAS) double resonance Bruker probe-head. The powdered sample was spun at a MAS frequency of 100 kHz. Given the wide spectral broadening of the 71 Ga NMR environments, a radiofrequency field of 125 kHz was used, which corresponds to 90° and 180° central-transition selective pulses of 1 µs and 2 µs, respectively. A spin-echo experiment was recorded using a full echo acquisition (interpulse delay of 150 µs), a recycling delay of 2 s, and with 26,000 scans. Furthermore, a two-dimensional QPASS (Quadrupolar Phase-Adjusted Spinning Sidebands) 3 experiment was performed in order to improve the spectral resolution of the Ga environments by separating the overlapping spinning sidebands. Eight sets of timings (constant full duration of seven rotor periods) were needed for a proper separation, with a recycling delay of 2 s, and 8,000 scans per set of timings. The spectra were referenced to a 1 mol gallium nitrate solution.

As shown in Figure II.1 (below), the spectrum obtained from the spin-echo experiment lacks resolution because of overlapping spinning sidebands, even at ultra-high MAS frequency (100 kHz). The "spinning sidebands-free" QPASS spectrum allows to achieve ultimate spectral resolution and clearly identifies two contributions located at ca. 0 ppm and 100 ppm corresponding to 6-coordinated and 4-coordinated Ga respectively. However, the complexity of the QPASS experiment does not allow a precise quantification of the two Ga environments. The observed 71 Ga lineshapes have smoothed profiles as opposed to singularities expected for fully ordered crystalline phases, indicative of geometrical and chemical disorder of both Ga environments in the second coordination sphere. Haytem BAZZAOUI

Synthèse et Caractérisation de Nouveaux Matériaux Oxydes par Cristallisation Complète et Congruente du verre ou du liquide fondu

Le développement de nouveaux matériaux à propriétés performantes est un axe majeur de la recherche actuelle. Au cours de cette thèse, de nouveaux matériaux hors équilibre ont été développés par des approches de synthèses innovantes : la cristallisation complète et congruente à partir du verre ou du liquide fondu. De hautes températures ont été atteintes par lévitation aérodynamique couplée à un chauffage par lasers CO2. Les matériaux synthétisés visent des propriétés optiques et/ou de conductivités anioniques. L'étude structurale des mélilites SrREGa3O7 RE= [Dy -Lu, Y] synthétisées par cristallisation complète et congruente à partir d'un précurseur vitreux a permis de mettre en évidence une mise en ordre entre les cations Sr 2+ et RE 3+ sur trois sites cationiques, ce qui induit un triplement du paramètre a de la maille mélilite parent tétragonale, et donc la stabilisation d'une nouvelle maille orthorhombique. De plus, l'étude de la stabilité de cette structure orthorhombique à hautes températures en mode in situ a montré l'existence d'une transition de phase vers la maille parent tétragonale désordonnée de la mélilite. En revanche, l'étude du désordre chimique dans la solution solide de langasite Ca3Ga2-2xZnxGe4+xO14, un minéral lié à la famille de la mélilite et cristallisant sous une maille trigonale s'est avérée insuffisante par diffraction des rayons X et neutrons en raison de la présence de trois cations isoélectroniques (Ga 3+ , Zn 2+ , Ge 4+ ). Pour répondre à cette problématique, une analyse unique a été déployée : l'affinement de cartographies STEM-EDS 2D de chaque cation, permettant l'établissement d'un modèle de départ pour l'analyse Rietveld. De nouveaux matériaux conducteurs anioniques ont été étudiés dans les solutions solides La1+xBa1-xGa3O7+x/2 et LaxCa5-xGa6O14+x/2. Ils cristallisent dans des structures mélilite ou dérivées. La première solution solide a été synthétisée par cristallisation à partir du liquide fondu à haute température et a révélé la rétention du polymorphe tétragonal de la mélilite avec la plus haute concentration en oxide interstitiel (La1.725Ba0.275Ga3O7.3625 x= 0.725). En outre, le composé La1.6Ba0.4Ga3O7.15 (x= 0.6) montre la plus haute valeur de conductivité anionique à 500°C, égalant les meilleurs conducteurs mélilites connus (La1.64Ca0.36Ga3O7.32 et La1.54Sr0.46Ga3O7.27). Finalement, l'étude de la deuxième solution solide a montré une substitution maximum x= 0.25 atteinte par réaction solide-solide. La complexité de cette étude repose sur la caractérisation structurale de ce composé qui a nécessité des calculs DFT pour identifier la structure la plus énergétiquement favorable. Mots clés : Cristallisation du verre / liquide fondu à haute température, Nouveaux matériaux métastables, Matériaux hors équilibre, Analyse structurale par affinement Rietveld, Microscopie électronique en transmission à résolution atomique.

Synthesis and Characterisation of new Oxide Materials by full and Congruent Crystallisation from Glass or the Molten liquid

The development of new materials with high performing properties is a major theme in today's research. In this thesis, new out-of-equilibrium materials were developed by unique synthesis approaches: full and congruent crystallisation from glass or from an under-cooled melt. High temperatures were reached by aerodynamic levitation coupled to two CO2 lasers. The synthesised materials target optical and/or ionic conductivity properties. The structural study of the SrREGa3O3 RE= [Dy -Lu, Y] melilites, synthesised by full and congruent crystallisation from glass precursors, characterised the ordering of Sr 2+ and RE 3+ cations over three distinct sites, inducing a tripling of the a cell parameter of the parent tetragonal melilite, leading to the stabilisation of a new orthorhombic cell. Moreover, the stability of this orthorhombic polymorph studied in situ against temperature, showed the occurrence of a phase transition to the parent fully disordered tetragonal melilite. In contrast, the cationic ordering in the Ca3Ga2-2xZnxGe4+xO14 langasite solid solution, a melilite-related mineral crystallising in a trigonal cell, could not be probed directly by diffraction methods (X-rays and neutrons) due to the presence of three isoelectronic cations (Ga 3+ , Zn 2+ , Ge 4+ ). In order to fulfil this task, a unique analysis approach was performed: refinement of atomic resolution 2D STEM-EDS maps for each cation. Last, new ionic conductor materials were investigated in the melilite La1+xBa1-xGa3O7+x/2 and melilite-related LaxCa5-

  .1). (ii) Non-topochemical, which on the other hand does not involve any intermediate stage (e.g. a parent compound) and the final material is synthesised directly [2] (see Figure I.1).

Figure I. 1 .

 1 Figure I.1. Comparison between conventional and soft chemistry synthesis approaches, redrawn and adaptedfrom[2].

Figure I. 2 .

 2 Figure I.2. Energy curve of a system comparing its metastable, unstable and stable states.

Figure I. 3 .

 3 Figure I.3. a), b) Planar projection of quartz network in its both amorphous and crystalline states respectively, drawn from [24]. c) STM image of a partially crystallised SiO2 film. d) coloured STM image (showed in (c)) highlighting the random distribution of [SiO4]n rings in the amorphous SiO2 vs the well-defined [SiO4]6 rings in the crystallised quartz, from [27].

Figure I. 4 .

 4 Figure I.4. Illustration of the crystallisation process evidencing the temperature depending phenomena ofnucleation and crystals growth using a DSC curve. The insert SEM images were taken from[30].

Figure I. 5 .

 5 Figure I.5. a) Differential scanning calorimetry curve upon heating of the BaAl4O7 glass composition and the crystal structure projection of the two synthesisable polymorphs in inserts. b) Photograph of polished glass and crystallised beads of the same composition. c) Transmittance measurements comparison between glass and the two polymorphs. All from [33].

Figure I. 6 .

 6 Figure I.6. a) Photograph of a large crystallised bulk ceramic of Sr1+x/2Al2+xSi2-xO8 (x =0.2) composition. b) Photograph of different Sr1+x/2Al2+xSi2-xO8 (0 ≤ x ≤ 0.2) bulk crystallised compositions evidencing the evolution of transparency as a function of disorder. c)Photograph of a glass crystallised Bi0.8Nb0.8Te2.4O8 compound in the form of large disc (60 mm in diameter). The insert inside the disc shows an EBSD-SEM map of the material evidencing crystalline domains sizes. The insert at the bottom right shows a ceramic fibre of the same composition.These figures were taken from[37] and[38].

Figure I. 7 .

 7 Figure I.7. a), b) Crystal structure projection of the A2B'(B2O7) P4 ̅ 2 1 m melilite compounds within the a-axis and c-axis respectively. c) Photograph of the SrREGa3O7 polished glass and ceramic materials. d) Transmittance curves after thickness normalization at 1 mm from both the SrGdGa3O7 (black) and SrYGa3O7 (blue) ceramics. The red dot curve corresponds to the transmittance fit based on the theoretical model. Both c)and d) panels were taken from[53].

8 -

 8 coordinated, B 6-coordinated, C and D 4-coordinted sites. Its crystal structure can be described as a layered structure with an ABAB stacking along the c-axis. The langasites underlaying framework is formed by open [(C,D)O4]5 pentagons (A-layer at zA=0.5), linked by BO6 octahedra (B-layer zB=zA+0.5). The A-site cations sits in the B-layers filling the [(C,D)O4]5 pentagons centre, similar to the melilite structure (see Figure I.8

Figure I. 8 .

 8 Figure I.8. Langasite and melilite crystal structure projection respectively within, a) and b) c-axis, c) and d) aaxis, evidencing the similarities between these two structure types.

Figure I. 9 .

 9 Figure I.9. Schematic of a solid oxide fuel cell (SOFC) showing its different components, from[START_REF] Taroco | Ceramic Materials for Solid Oxide Fuel Cells[END_REF].

) 3 (

 3 MO4)6X2 A= [Ln, Na, K, Ca, Sr Ba, Mn, Cd, Pb] M= [Si, Ge, P, V] and X= [O, OH, F, Cl, Br, I] [87] apatite compounds structure can be described as isolated MO4 tetrahedra stacked along the c-axis creating three distinct channels. Two are fully occupied by independently stacked A(1) and A(2) atoms, while the third one consists of an oxygen atom row (see Figure I.10). Contrary to what has been stated above for fluorite and perovskite conductors, relying on the introduction of oxygen vacancies to achieve fast oxide ion conduction, the apatite materials depend on introducing interstitial oxygens to act as mobile charge carriers. Lanthanum-based silicates or germanates oxide apatites, were found to be good ionic conductors at intermediate temperatures. In this aspect, the Ln9.75Sr0.25(SiO4)6O2.895 and La9.5(Ge5.5Al0.5O24)O2 alkaline doped apatites show an increase of their conductivity by an order of magnitude compared to their La10(SiO4)6O3 analogue at 700°C [88] (see Figure I.12).

Figure I. 10 .

 10 Figure I.10. a) AO2 fluorite structure, where the blue and red spheres represent the A cations and oxygen atoms respectively. b) simple ABO3 perovskite cell, with A and B atoms corresponding to the blue and brown spheres respectively, while the red spheres correspond to the oxygen atoms. c) Apatite crystal structure projection within the c-axis, evidencing the three channels type, with brown, green and red spheres corresponding to the A(1), A(2) and oxygen atoms. d) Simplified γ-type BIMEVOX structure, where blue spheres represent V and the dopant element (held in an octahedral site), orange and red spheres correspond to Bi and oxygen atoms.

  structure in the right stoichiometry to keep a charge balanced composition. The interstitial oxides are held in the GaO4 infinite framework pentagons centre at the [GaO4]n sheets level by local expansion of the gallium coordination into GaO5 units, forming an Oint two-dimensional network over the ab-plane (see Figure I.11a), which allows fast conduction mechanism by a

Figure I. 11 .

 11 Figure I.11. Crystal structure projection along the c-axis of both: a) fully disordered P4 ̅ 21m and b) ordered Ima2 melilites.

Figure I. 12 .

 12 Figure I.12. Arrhenius plots of the total conductivity of, (1) Zr0.9Y0.1O1.95 (YSZ), (2) Ce0.9Gd0.1O1.95 (GDC), (3) Bi0.75Y0.25O1.5 (Stabilized δ-Bi2O3), (4) La0.8Sr0.2Ga0.83Mg0.17O2.815 (LSGM), (5) Ba2In2O5 (Brownmillerite), (6) Bi4Cu0.15Ti0.15V1.7O11-δ (BICUTIVOX), (7) La9.75Sr0.25(SiO4)6O2.895 (Si-apatite), (8) La9.5(Ge5.5Al0.5O24)O2 (Geapatite), (9) La1.54Sr0.46Ga3O7.27 (Sr-melilite) and (10) La1.64Ca0.36Ga3O7.32 (Ca-melilite). Solid and dashed lines correspond to vacancies and interstitial conductor materials. This figure was taken from[START_REF] Diaz-Lopez | A Study of Novel Electrolyte Materials with Interstitial Oxides as Mobile Species[END_REF].

Figure II. 1 .

 1 Figure II.1. SrYbGa3O7 melilite structure projection within the c-axis of both, a) disordered and b) ordered polymorphs.

  (see Figure II.1). This superstructure retains the same layered framework, with three different types of distorted [GaO4]5 pentagonal channels, in order to accommodate the rare earth, strontium and mixed A-sites. The RE cation being smaller than the Sr atom, its local structure is the most distorted of the three as it adopts a [6+1] coordination defined by six short RE-O distances in the range 2.2 -2.5 Å that form a triangular-prismatic first coordination sphere, and one long distance of 2.9 Å. The Sr and RE/Sr sites are less distorted and remain 8-coordinated with moderately similar cation-oxide first neighbour bond distances to the SrLaGa3O7 parent P4 ̅ 21m melilite (see Figure II.2).

Figure II. 2 .

 2 Figure II.2. Local coordination and their A-O bond distances of a) Yb site (red histogram), b) Sr site (green histogram) and c) mixed Yb/Sr site (patterned red/green histogram). The black dashed histograms are givenfrom A-O distances of the parent disordered SrLaGa3O7 melilite.

Figure II. 3 .

 3 Figure II.3. Laboratory X-ray powder diffraction data of SrREGa3O7 (RE = Tb-Lu, Y) glass samples synthesized by aerodynamic levitation coupled to laser heating (ADL).

  Figure II.5 the PXRDs of the post-DSC samples contain peaks from the P21212 supercell for all rare-earths, except Tb which express no sign of superstructure peaks. Moreover, due to the absence of X-ray scattering contrast between strontium and yttrium ions (ZSr= 38, ZY= 39), it might be expected that the superstructure peaks would have very weak intensities, i.e. arising purely from the Ga3O7 framework distortion; hence, hard to resolve from a noisy pattern.

  ordered melilite between RE = Dy and Lu + Y. More details about the synthesis of both ordered and disordered polymorph are indicated in section II.3.

Figure II. 4 .

 4 Figure II.4. Differential scanning calorimetry (DSC) measurements of SrREGa3O7 (RE = Tb -Lu, Y) glass composition, where Tg, Tc and To are glass transition, crystallization and ordering temperatures respectively. a)Heating plots using a 10°C/min heating rates from room temperatures to 925°C. b) Cooling plots using a 10°C/min cooling rates from 925°C to room temperatures.

Figure II. 5 .

 5 Figure II.5. Post DSC PXRD data (in natural logarithm scale) of SrREGa3O7 (RE = Tb -Lu, Y) compounds, where black tick marks correspond to the SrDyGa3O7 P4 ̅ 21m disordered melilite phase, while the orange tick marks represents the additional P21212 ordered melilite reflections.

  To investigate the thermal stability of the P21212 melilite supercell, in situ VT-PXRD measurements were performed on glass precursors across the series of compositions SrREGa3O7 RE = [Tb-Lu, Y], from room temperature to 740°C in one step and then to the point where the melilite starts to decompose into RE2O3 and garnet type oxides (900°C for RE = [Ho-Lu], 1000°C for RE = Dy and 1100°C for RE = Tb) using a 5°C step, in the angular rage of 10°-40° (2) with a 0.024 step size and a measuring time of 1s/step. In Figure II.6, the first thing to notice is the very small temperature domain of stability for the Lu compound (over ⁓ 25°C), as it crystallises and decomposes at 800°C and 825°C respectively, which explains why its phase pure synthesis is challenging. The other rare earth cations display a wider temperature range between their crystallisation and decomposition temperatures, Yb over 90°C, Tm 100°C, Er 110°C, Ho 105°C, Y 115°C, Dy 225°C, Tb 270°C. The reported results in Figure II.6 can be divided in three distinct categories: (i) Category 1: smallest rare-earths (RE = Yb, Lu) crystallising directly in the ordered polymorph upon heating with no phase transition observed on cooling. (ii) Category 2: intermediate-size rare-earths (RE = Er, Tm) crystallising into the parent P4 ̅ 21m melilite and then undergoes a phase transition to the P21212 ordered melilite on cooling at 720°C and 790°C respectively. (iii) Category 3: the largest-sized rare-earths (RE = Tb-Ho, Y) crystallising in the disordered melilite upon heating and retaining the P4 ̅ 21m structure whether on heating or on cooling with no sign of supercell peaks.The VT-PXRD results for Dy, Ho and Y contrast with the thermal analysis described in section II.2, which showed that following a suitable heat treatment, the ordered melilite could be obtained for these compositions. To study the reversibility of the observed phase transition, a Tm glass melilite sample was subject to two heating/cooling cycles measured by in situ VT-PXRD (see FigureII.7). From this figure the appearance of the ordered melilite is completely reversible, as it gets disordered on heating at slightly higher ordering temperature (⁓ 820°C > 790°C), which then on the cooling forms again the P21212 melilite polymorph at 790°C.

Figure II. 6 .

 6 Figure II.6. Variable temperature powder X-Ray diffraction (VT-PXRD) on SrREGa3O7 (RE= Tb -Lu, Y), starting from the glass precursors. Peaks representing the initial melilite (substructure) crystallization, the 3x1x1 structural ordering (superstructure), and the onset of decomposition are indicated by symbols described in the Yb panel. Peaks labelled † arise from the alumina sample holder. The precursor glass for RE = Lu contained a small amount of crystallized melilite, indicated by ǂ.

Figure II. 7 .

 7 Figure II.7. Two heating/cooling cycles in situ VT-PXRD measurements on the SrTmGa3O7 glass sample.

  diagram-like graph (Figure II.8).

Figure II. 8 .

 8 Figure II.8. SrREGa3O7 (RE= Tb -Lu) melilites stability diagram drawn from DSC and VT-PXRD resumes, coupled to previous results from Jan Skakle et al [16] (RE=La -Gd). The ordering region was drawn accordingto the highest stability temperature of each compound from both DSC and VT-PXRD.

  in-situ PXRD) Ordering T (in-situ PXRD) Ordering T (DSC, ex-situ PXRD) Glass crystallization T (in-situ PXRD) Glass crystallization T (DSC, ex-situ PXRD)

×4 Z= 1 ,

 ×41 with: 4 the A-sites multiplicity, and Z=6. For the P21212 melilite only • Isotropic thermal parameters for all atoms. For both melilites. • Isotropic thermal parameters of O atoms constrained to have the same (refined) value. For both melilites. This led to a total of 94 independently refined parameters (15 background terms, sample height for lab data or zero shift for SPD data, axial divergence, 6 profile parameters from TCHZ function + 4 peak broadening parameters added to the (310) peak, 67 atomic parameters) for the ordered melilite, and 43 independently refined parameter (15 background terms, sample height for lab data or zero shift for SPD data, axial divergence, 6 profile parameters from TCHZ function, 16 atomic parameters) for the disordered melilite. All these refinements led to satisfactory reliability factors as displayed in

Figure II. 9 .

 9 Figure II.9. Rietveld refinement of a) SrYbGa3O7 ordered melilite (Rp= 4.09% Rwp= 5.36%) (SPD data) and b) SrYbGa3O7 disordered melilite (Rp= 2.87% Rwp= 3.83%) (lab data). Observed (black dot), calculated (red line), and difference (blue line) profiles are shown. The set of green vertical lines corresponds to reflection positions.

  Across the RE compositions series, the refined cell volumes show a clear decreasing trend going from Dy to Lu end members, which is coherent with the rare-earth size decrease (Figure II.10a). Moreover, Figure II.10b indicates notable differences in the cell parameters evolution

Figure II. 10 .

 10 Figure II.10. a) Normalised (to Dy) cell volumes from both refined P21212 and P4 ̅ 21m structures coupled to RE = La for comparison. b) comparison between the refined ordered melilite tripled parameter and the disordered melilite analogue parameter.

Figure II. 11 .

 11 Figure II.11. a) [001]* HRTEM image and b), c), d) associated FFTs of the SrYGa3O7 melilite parent synthesised by full crystallization from glass showing the coexistence of both cation-ordered and cation-disordered domains.

  The calculated (Sr,RE)/Ga ratios of SrREGa3O7 RE = [Dy -Yb] compositions lie just at the edge of incommensurate structure region of this map (see Figure II.12). To test this possibility, and plausible appearance of an incommensurate modulated structure of the original disordered synthesised melilite, SAED measurements were conducted on A-site disordered SrTmGa3O7 as a representative composition for the series. As shown in Figure II.13, electron diffraction measurements show a complete absence of satellite reflections and the pattern was fully indexed with the classic P4 ̅ 21m melilite.

Figure II. 12 .

 12 Figure II.12. Redrawn phase diagram from [27], showing the boundary between commensurate and incommensurate [A2]2[B I ]2[B II 2O7]2 melilite structure domains correlated to the ionic radius ratio of the betweenthe A and B cations. With the coloured solid points represent our study.

Figure II. 13 .

 13 Figure II.13. [001]* Selected Area Electron Diffraction (SAED) pattern of the SrTmGa3O7 parent melilite synthesised by full crystallisation from glass, with the indexation of its tetragonal structure (a=7.9 Å, c = 5.2 Å, P4 ̅ 21m). Evidencing a total absence of satellite peaks. The arrows point the reflections assigned to double diffraction.

  Figure II.14, the Yb and Sr exhibits a pure site each, with a third mixed Sr/Yb site, consistent with the refined disorder from SPD data and the one reported by Marina Boyer in her PhD[35].

Figure II. 14 .

 14 Figure II.14. Atomic-scale STEM-EDS elemental maps of the cations (a) Yb (red), (b) Sr (green), (c) Ga (blue) and (d) the overlaid EDS maps showing the mixed sites (50/50 Yb1/Sr1) in red/green highlighted by yellow arrows. (e) SrYbGa3O7 superstructure projection of the cationic sites along the [001] axis. Ga atoms are drawn in blue, Sr3 sites in green, Yb2 sites in red and the mixed sites (50/50 Yb1/Sr1) in red/green. (f) STEM-HAADF image of the SrYbGa3O7 superstructure along the [001] zone axis. On all the images the yellow arrows highlight the mixed Yb1/Sr1 sites (50/50 average occupancy).

Figure II. 15 .

 15 Figure II.15. The cationic substructure of the P21212 ordered melilite, where a) shows the chain-like and stripelike arrangement of mixed Sr/RE and Sr-only sites, while b) shows the pseudo-hexagonal sub-cell of the RE-only sites.

  (Figure II.16a), the ordered polymorph can be deconstructed to two tiling types: A and B (see Figure II.16), as the combination of A, B and Aˈ (corresponding to a 180° rotation of A tile), are needed to describe the whole structure. Tile A is half ordered with two mixed sites and two Sr and RE dedicated sites (one each), where tile B is fully ordered containing only two single natured site types, Sr and RE. The combination of only A tiling (= combination of only Aˈ tiling) or a combination of both A and Aˈ (AAˈ) tiling (see Figure II.16c and Figure II.16d), supports a wider separation of the distorted RE sites, providing a RE distorted pentagons edge-sharing free framework. However, it minimises the amount of RE-only populated sites (1/4), leading to a half-ordered melilite.The BB tiles grouping on the other hand, would result in a fully ordered structure with the maximum amount of RE-only sites (1/2). Nevertheless, the disfavoured edge-sharing distorted RE sites would be outcome from this configuration (indicated by the black outline in Figure II.16e). This is also seen in the ABA tiling combination, which also consequence edge-sharing distorted RE sites. The compromise of maximising the amount of RE sites while keeping a GaO4 framework with no edge-sharing RE distorted sites, was found by the arrangement of ABAˈ tiling. The P21212 melilite structure thus retains 1/3 of its A-sites as mixed sites, which are larger and less distorted than RE2, as a buffer between the fully-ordered fragments. This maximizes the RE2 [6+1] population, whilst keeping the Ga3O7 framework strain to within acceptable limits.

Figure II. 16 .

 16 Figure II.16. a) Observation of the structural ordering of the ordered melilites projected within the c-axis with ABAˈ tiling. The A, Aˈ and B tiles in b) are combined in c), d), e), f) and g) to create the possible ordering combinations.

  All of the (AE,RE)Ga3O7 gallate melilite published structures, which were synthesised by ceramic methods, are summarised in Figure II.17. From this figure, Ba melilites shows the biggest unexplored compositions, while the parent P4 ̅ 21m Ca-based melilites were reported prior the discovery of the 5D modulation in the La and Nd calcium melilites. This makes both Ba and Ca-based compositions interesting to investigate for new melilite structures.

Figure II. 17 .

 17 Figure II.17. Phase diagram indicating the different structural orderings reported for the (AE,RE)Ga3O7melilite family, according to the ionic radii of their A site cations. The parent structure and 5D-modulated structure regions have been compiled from the literature[16],[27],[28]. Note that the parent structure region for AE = Ca is marked with an asterisk, as it was reported prior to the discovery of structural modulation in CaLaGa3O7 and CaNdGa3O7.

Figure II. 18 .

 18 Figure II.18. Near infrared emission band of the SrErGa3O7 glass, ordered and disordered ceramics measure on a) bulk, b) powdered samples, under excitation at 520 nm (Xe lamp source).

an 8 -

 8 coordinated (Wyk. Pos. 3f), B 6-coordinated (1a), C and D both 4-coordinated sites (3f and 2d respectively), organised in channels of the same site nature along the c-axis "stacking axis" (see Figure III.1). The variety of the crystallographic sites in this structure can accommodate many cation types, offering the potential for complex cation ordering schemes.

Figure III. 1 .

 1 Figure III.1. Crystal structure projection of the A3BC3D2O14 langasite structure family along the a) c-axis, b) baxis, showing both the P321 cell (straight black lines) and C2 cell (dashed black lines).

  Figure III.1), with a completely ordered langasite framework, where Zn 2+ fully occupies the

Figure III. 2 .

 2 Figure III.2. In situ powder X-ray diffraction (VT-PXRD) data of a CaCO3-Ga2O3-GeO2 mixture, with respect of Ca3Ga2Ge4O14 nominal composition, between room temperature and 1200°C. a), b) Inserts show the indexed diffraction patterns at room temperature and 1200°C, with the different colour tickmarks corresponding to, CaCO3 (black), Ga2O3 (blue), GeO2 (red), Ca3Ga2Ge4O14 (green) and CaGeO3 (orange).

Figure III. 3 no

 3 Figure III.3 no Bragg diffraction peaks were observed, confirming the amorphous state of the synthesised samples.

Figure III. 3 .

 3 Figure III.3. Laboratory X-ray powder diffraction data of Ca3Ga2-xZnxGe4+xO14 (x = 0, 0.25, 0.5, 0.75, 1) glass samples synthesized by aerodynamic levitation coupled to laser heating (ADL).

Figure III. 4 .

 4 Figure III.4. Variable temperature powder X-ray diffraction (VT-PXRD) measurements of, a) glass of composition Ca3Ga2Ge4O14 (x = 0), b) glass of a slightly deviated composition from Ca3Ga2Ge4O14 (x = 0) with an excess of ⁓ 2% (%wt) of GeO2 added in the nominal composition. Green tickmarks represent the Ca3Ga2Ge4O14 indexation.

Figure III. 5 .

 5 Figure III.5. Variable temperature PXRD measurements on the Ca3ZnGe5O14 x =1 glass composition showing its crystallisation upon heating, where * and † represent the clinopyroxene CaZnGe2O6 and melilite Ca2ZnGe2O7 impurities respectively. Green tick marks represent the P321 Ca3ZnGe5O14 indexation.

Figure III. 6 .

 6 Figure III.6. Conducted DSC measurements on Ca3Ga2-2xZnxGe4+xO14 x = 0 (black), 0.25 (red), 0.5 (blue), 0.75(green) and 1 (purple) powder samples, using a 10°C/min rates upon heating.

Figure III. 7 .

 7 Figure III.7. a) Comparison between a) DSC measurements of Ca3ZnGe5O14 (x = 1) under bulk (black) and powder form (red). b) laboratory PXRD measurements of post DSC measured samples in a). Green tickmarks represent the LeBail refined Ca3Ga2Ge4O14 P321 structure

Figure III. 8 .

 8 Figure III.8. Crystallised Ca3Ga2Ge4O14 (x = 0) sample from a) glass at 820°C in an open atmosphere furnace, b) molten liquid on the ADL equipment, by turning the lasers off while the droplet is touching the nozzle. Green tick marks represent Ca3Ga2Ge4O14 indexation. c) the extracted FWHM's for each peak from a) and b), extracted by individual peak fitting.

  Figure III.1 for a comparison between the monoclinic C2 and the trigonal P321 cells), it can be described as a fully ordered structure where Zn 2+ cations only occupy the octahedral B-sites, whilst the Ge 4+ fully occupies the remaining tetrahedral C-and D-sites. The direct melt crystallised (x = 0) and glass crystallised (0.25 ≤ x ≤ 1) samples were first analysed by laboratory PXRD. As shown in Figure III.9a across the solid solution, all diffraction patterns were indexed with the parent P321 Ca3Ga2Ge4O14 langasite structure.However, for composition near x = 1 "Ca3Ga2-2xZnxGe4+xO14" Bragg diffraction peaks became broader, which could be hinting at atomic disorder, peak splitting with a possible phase transition to C2 symmetry, or even microstructural strain (see Figure III.9b). To further investigate this observed peak broadening in lab data and the possibility of a monoclinic distortion for compositions near x = 1 "Ca3Ga2-2xZnxGe4+xO14", synchrotron powder diffraction (SPD) measurements were conducted on samples of composition x = 0, 0.25, 0.5, 0.75, 1. First a bead of each sample composition was synthesised and crushed into fine powder, then loaded into 8 mm diameter Kapton capillaries. The prepared samples were sent to the APS Argonne laboratory for the SPD measurement to be conducted on the 11BM beamline.

Figure III. 9 .

 9 Figure III.9. a) Normalised stacked diffraction patterns of Ca3Ga2-2xZnxGe4+xO14 (x = 0, 0.25, 0.5, 0.75, 1) compositions measured by laboratory powder X-ray diffraction. b) Zoom on the 37.7°-39.5°(2θ) region evidencing the observed peak broadening as x values increases. Pink tick marks correspond to the Ca3Ga2Ge4O14 indexation.

Figure III. 10 .

 10 Figure III.10. a) SPD data of Ca3Ga2-2xZnxGe4+xO14 x = 0 (black), 0.25 (red), 0.5 (blue), 0.75 (green) and 1 (purple) compositions, with dark blue tickmarks corresponding to Ca3Ga2Ge4O14 indexation. b) Zoom view on the (100), (001), (101) and (21 ̅ 0) (S.G P321) peaks shown in (a), highl the peaks shift. c) Normalised simulated monoclinic Ca3ZnGe5O14 C2 [2] (in black) and measured Ca3ZnGe5O14 glass crystallised sample (in red), synchrotron powder diffraction (SPD) plots, with their respective cell indexations in orange and blue tick marks. d) Normalised refined cell parameters (from SPD data) of the P321 langasite structure across the solid solution series to the parent Ca3Ga2Ge4O14 cell parameters.

  refined models showed to be almost indistinguishable, see Figure III.11 for the overlay of both structures. From these two key points: (i) the complete absence of extra diffraction peaks arising from the monoclinic distortion on the measured Ca3ZnGe5O14 SPD pattern despite its excellent signal to noise ratio, and (ii) the almost undistinguishable Rietveld refined models P321 and C2, the trigonal cell P321 was then kept to describe the structure of this composition.

Figure III. 11 .

 11 Figure III.11. Overlay between Rietveld refined C2 (black atoms) and P321 (green atoms) structures for the Ca3ZnGe5O14 (x = 1) composition against SPD data, along, a) c-axis, b) b-axis of the C2 structure.

Figure III. 12 .

 12 Figure III.12. Rietveld refinement of a) Ca3Ga2Ge4O14 (x = 0) (SPD data, Rp= 7.617% Rwp= 9.506%) and b) Ca3ZnGe5O14 (x = 1) (SPD data, modelled strain Rp= 7.02% Rwp= 8.75%). Observed (red dot), calculated (black line), and difference (blue line) profiles are shown. The set of green vertical lines corresponds to reflection positions.

Figure III. 14

 14 Figure III.14.71 Ga NMR spectra acquired on a sample of composition Ca3Ga2Ge4O14 (x = 0) by a MAS spinecho (green) and a QPASS (blue) experiments, showing the two coordination types of Ga in the sample.

  Ga and 67 Zn spectrum, solid state NMR of these two nuclei informs us about the local disorder occurring among the B-C-and D-sites of this langasite structure, which are key information in building a starting Rietveld model for neutron data refinement presented in the next section.

Figure III. 15 .

 15 Figure III.15. a) 67 Zn CPMG MAS spectrum recorded at 17.6 T with a spinning frequency of 14 kHz. b) Simulation of the experimental spectrum considering two 67 Zn resonance with distribution of the quadrupolar interactions (average coupling of 7.3 MHz and 9.3 MHz), with green purple and red signals corresponding to the 6-coordinated Zn, 4-coordianted Zn and the sum of both contributions. The noted signal with asterisks indicates the spinning sidebands of the central transition.

  2xZnxGe4+xO14 (x = 0, 1) host only two cation species on the framework (B, C, D) sites, with different neutron scattering lengths (8.185(20) fm, 7.288(2) fm and 5.680(5) fm for Ge, Ga and

*:

  Fixed at 1 after its initial refined value converged to almost 1.

  (7) b a,b : constrained to refine to the same Biso values. * : Fixed at 1 after its initial refined value converged to almost 1.

Figure III. 16 .

 16 Figure III.16. NPD Rietveld refinements plots of a) Ca3Ga2Ge4O14 (x = 0) Rp= 3.04% Rwp= 3.83%, b) Ca3ZnGe5O14 (x = 1) Rp= 3.43% Rwp= 4.35%. Observed (red dot), calculated (black line), and difference (blue line) profiles are shown. The green tick marks correspond to allowed reflection positions.

Figure III. 17 .

 17 Figure III.17. Cationic 1a and 3f site coordinations and their nearby interatomic distances for both x = 0 and x = 1 compounds from NPD refined structures.

Figure III. 18 .

 18 Figure III.18. a), b)  2 evolution as a function of p1 (Ga occupancy on the 1a site for x = 0 compound), p2 (Zn occupancy on the 1a site for x = 1 compound). c), d) Rietveld fits (measured "black line", calculated "red line, difference "blue line" and indexation in green tick marks) zoomed view on the (001) and (100) for x = 0 and x = 1 compounds respectively for different fixed p1 and p2 values.

  Transmission electron microscopy measurements were conducted on powder samples deposited on a TEM amorphous holey carbon-coated copper grid. The powder sample was first finely ground and dispersed in ethanol, droplets from this mixture were then deposited on the grid mentioned above and let to dry. The sample's observation at the atomic scale in STEM-HAADF mode, each observed atom represents in reality a column of atoms (structure projection). To visualise the 2D projection of the Ca3GaZn0.5Ge4.5O14 (x = 0.5) crystal structure, the sample was oriented along the [001]* direction (see FigureIII.19a). This particular direction was chosen because it represents the stacking direction of the structure, with each column being composed of the same crystallographic site(Figure III.19b and Figure III.19c). The measured sample thickness (60 nm, representing 120 superimposed cells) by Electron Energy Loss Spectroscopy (EELS), was estimated to be unchanged over the whole imaged area (≈ 5 nm × 5 nm). Knowing that the acquired intensity in STEM-HAADF mode is proportional to the sample's thickness (e), density (ρ) and the mean atomic number (𝑍 ̅ ) of the observed crystallographic site "𝐼 ∝ 𝑒𝜌𝑍 𝑛 ", the acquired intensity in STEM-HAADF, is essentially due

Figure III. 19 .

 19 Figure III.19. a) Selected area electron diffraction (SAED) pattern of the Ca3GaZn0.5Ge4.5O14 (x = 0.5) sample oriented along the [001]* direction, with b) and c) showing simulated (using JEMS software) [53] and measured STEM-HAADF images respectively. The corresponding crystal structure projection is overlaid on the top-right corner of the image, where blue, green, pink and orange points represent the 3e, 1a, 3f and 2d crystallographic sites respectively. Due to the isoelectronicity of the three (Zn 2+ , Ga 3+ , Ge 4+ ) cations, it is not possible to distinguish between them by their STEM-HAADF intensities. Consequently, EDS maps at the atomic scale of the three cations were cumulated over different regions of the same grain for a total time of 40 minutes of tracking, due to the sample's deterioration under the beam after a certain amount of time. In Figure III.20 showing the atomic scale resolution acquired STEM-

Figure III. 20 .

 20 Figure III.20. a) Scheme of the trigonal P321 structure projected along [001], b) its corresponding atomic resolution STEM-HAADF image for the Ca3GaZn0.5Ge4.5O14 (x = 0.5) composition. Atomic-scale STEM-EDS maps of the cations c) Ca in blue, d) Ge in red, e) Ga in green (Wiener filtered image) and f) Zn in green (Wiener strong filtered image). The overlaid EDS maps of "Ca, Ga, Ge" and "Ca, Zn, Ge" are shown in g) and h) respectively. The crystallographic unit cell is outlined in white in panels (b) -(h). The orange rectangle overlaid on (b) is the region used for 1D profile fitting presented in Figure III.21.

  Figure III.20b, the marked area by a yellow rectangle was integrated to extract a 1D profile intensity "Wiener filtered EDS maps" (Figure III.21a). The width of the yellow rectangle was adjusted to maximise the signal, while taking care to minimise parasitic signals from the adjacent sites. A one-dimensional refinement approach was then proceeded on the data, in order to extract quantifications of each cation partial occupancy in the different crystallographic sites. As shown in Figure III.21b, the germanium map shows the best signal to noise ratio, thanks to its high abundance. It was thus first refined using two Gaussian contributions. The refined Gaussian peak positions from the Ge profile were then fixed for the Ga and Zn profile fitting (see Figure III.21b

Figure III. 21 .

 21 Figure III.21. a) STEM-HAADF intensity profile in grey and EDS profiles of Ca, Ge, Ga and Zn (in blue, red, dark green and light green respectively). The signal was integrated from the drawn orange rectangle in Figure III.20b. b) In black, EDS profiles of Ge, Ga and Zn extracted from the STEM-EDS raw maps. The signals are integrated through the yellow strip on two neighbouring 1a and 3f sites (Figure III.20b). The calculated signals decomposed in Gaussian curves (blue), difference in orange and the integrated areas (red for Ge, dark and light green for Ga and Zn respectively) under the calculated curves have been overlaid.

and

  Figure III.24.

Figure III. 22 .

 22 Figure III.22. Overlay contour map of Ca (red), Ga (black), Ge (green) and Zn (blue) extracted from STEM-EDS raw data after the mask application.

Figure III. 23 .

 23 Figure III.23. STEM-EDS 2D refinement plots of Ge, Ga and Zn from zone1, where the left column represents the data (after processing), middle column fitted data (fit in black contours) and the difference plots in the right column.

Figure III. 24 .

 24 Figure III.24. STEM-EDS 2D refinement plots of Ge, Ga and Zn from zone2, where the left column represents the data (after processing), middle column fitted data (fit in black contours) and the difference plots in the right column.

  were allowed to refine freely among Ge. See Figure III.25 and TableIII.11 for the refined plot and structural parameters.

Figure III. 25 .

 25 Figure III.25. NPD Rietveld refinements plot of Ca3GaZn0.5Ge4.5O14 (x = 0.5) Rp= 2.97% Rwp= 3.80%. Observed (red dot), calculated (black line), and difference (blue line) profiles are shown. The green tick marks correspond to allowed reflection positions.

  Errors were estimated by calculating standard deviation from the fitted areas of the 1D EDS profiles over the averaged 4 (1a, 3f sites) on the cell corners, shown in Figure III.20e, d and f. b Mean values from zone 1 and zone 2 refinements. See Table

  Chapter IV: New Oxide ion Conductors by Extending the Doping Range in La 1+x Ba 1-x Ga 3 O 7+x/2 (0.3 ≤ x ≤ 0.9) Melilites Development of new ceramics exhibiting high oxide ion conductivities at moderate temperatures is of interest for solid oxide fuel cells, electrocatalysers, and sensors[1]. In this context, as mentioned in Chapter I the LaAEGa3O7 melilites (AE* = Ca, Sr, Ba) are a wellknown structural family that exhibits excellent oxide ion conduction properties in the 500 -900°C temperature range[2]-[6]. As previously described in Chapter II, these melilites crystallise under the 𝑃4 ̅ 2 1 𝑚 space group (n°113) with a layered framework formed by edge sharing five-membered GaO4 tetrahedra pentagons, stacked along the c-axis. The A-site cations are positioned in the [GaO4]5 pentagons centre sandwiched between the framework layers.Conductivity properties of these melilite materials are mainly due to the ability of the host network to accommodate interstitial oxides by local expansion of the Ga coordination environment to GaO5[4]. Usually this is achieved by substitution of the alkali earth metal by an aliovalent cation, i.e lanthanum in the La1+xAE1-xGa3O7+x/2 solid solution. Charge transport then occurs by a cooperative two-dimensional[7] local migration involving rapid exchange of the interstitial oxide with those of the host framework[8],[9] by a knock-on mechanism. The maximum conductivity values depend strongly on two factors: (i) the material composition, increasing progressively with interstitial oxide (Oint) concentration (Figure IV.1a), (ii) the crystal structure of the host framework, as at high Oint concentrations a phase transition from the parent tetragonal melilite to an orthorhombic or pseudo-orthorhombic (triclinic) phases with partially-ordered interstitial oxides occurs. This has a limiting effect on ionic conductivity due to the increase of the energy barrier for oxide migration within certain directions. Further increases in Oint concentration lead to a decomposition of the phase, as shown in both La1+xCa1-xGa3O7+x/2 and La1+ySr1-yGa3O7+y/2: in both cases, the maximum conductivities were found for x = 0.64 and y= 0.54 compositions respectively, reaching 10 -1 S.cm -1 at 800°C. Interestingly, the Ca and Sr analogues adopts a pseudo-orthorhombic P1 cell at room temperature for doping amounts exceeding x = 0.54 and 0.6 respectively (Figure IV.1b). The high conductivity values reached by the Ca and Sr melilites at 800°C were found to be attainable under the tetragonal 𝑃4 ̅ 21m melilite polymorph[5],[10], as the disordered small tetragonal melilite cell is stabilised at the expense of the P1 polymorph for the Ca compound (this is also true for Sr melilite compositions stable under the orthorhombic polymorph at room temperature). In the Ba analogue La1+xBa1-xGa3O7+x/2, the melilite stability range was found to be much lower, as the maximum substitution amount was reported at x = 0.35 attainable by conventional solid-state reaction. Across this solid solution all compounds retained the small cell 𝑃4 ̅ 21m tetragonal melilite structure, and had comparable conductivity values as the Ca and Sr analogues at the same Oint concentration (x = 0.35) (see Figure IV.1b).

Figure IV. 1 .

 1 Figure IV.1. a) Conductivity at 800°C of the La1+xSr1-xGa3O7+x/2 solid-solution as a function of x, where the filled and hollow symbols represent the tetragonal and orthorhombic starting room temperature polymorphs. b) Arrhenius plots of the La1+xAE1-xGa3O7+x/2 melilites bulk conductivities at different x values with AE= Ca, Sr andBa. (a) panel was adapted from[10], (b) panel was adapted from[3],[5],[6].

  5 x = 1) with the maximum interstitial oxide (Oint) concentration possible in this solid solution was synthesised by direct crystallisation of the melt at high temperature [11]. La2Ga3O7.5 crystallises in the Ima2 symmetry and adopts an orthorhombic melilite structure with three distinct A-sites: La1, La2 and La3, arranged in the same way as the tetragonal polymorph (Figure IV.2a). Moreover, it is worth noting that the A-site channels can be divided into two types: La1 and La2/La3 hosting channels (Figure IV.2a and Figure IV.2b). The interstitial oxides (Oint) network of the La2Ga3O7.5 melilite is fully ordered into chains within the a direction over corner sharing [GaO4]5 pentagons (see Figure IV.2c

Figure IV. 2 .

 2 Figure IV.2. La2Ga3O7.5 crystal structure projection along (a) the c-axis, (b) the b-axis. Panel (c) shows a single [GaO4]n sheet projected along the c-axis evidencing the 1D chain-like ordered Oint network. With dark green, light green and red spheres corresponding to La, Ga and oxygen atoms.

Figure IV. 3 . 2 0. 3 ≤

 323 Figure IV.3. Stacked measured diffraction patterns by laboratory PXRD of the La1+xBa1-xGa3O7+x/2 compositions, with the insert showing a zoom of the main peak positioned in the 29-31 (2θ°) range. The green and orange tick marks corresonds to the 𝑃4 ̅ 2 1 𝑚 tetragonal and Ima2 orthorhombic melilites indexations.

Figure IV. 4 .

 4 Figure IV.4. Zoomed stacked diffraction patterns of the SPD measured La1+xBa1-xGa3O7+x/2 solid solution compositions on the 7.5°-10° (2θ) region. The bottom green and top orange tick marks represent the indexation of both P4 ̅2 1m and Ima2 melilite structures respectively. T and O stands for tetragonal and orthorhombic.

-xGa3O7+x/ 2 ( 0 . 3 ≤ 85 :

 20385 x ≤ 0.725): For these compositions, the tetragonal 𝑃4 ̅ 2 1 𝑚 cell was the only model used to describe the whole diffraction pattern. Moreover, for x = 0.3 and 0.675 the impurities structures were included in Rietveld the refinements to achieve the best possible fit. The total number of independently refined parameters reached 42 (zero shift, scale factor, 15 background terms, 6 profile parameters from a TCHZ profile function, axial divergence correction, 18 structural parameters) for x = 0.6, 0.65, 0.7 and 0.725 composition.On the other hand, for x = 0.3 and 0.675 compositions the total amount of refined parameters accounts 60 and 51 independently refined parameters respectively. These extra parameters come from the impurities cell and profile function parameters. These compositions were refined using both the tetragonal 𝑃4 ̅ 2 1 𝑚 and orthorhombic Ima2 melilite structures. The x = 0.75 composition refinement was constraint free, which led to 109 independently refined parameters (zero shift, 1*2 scale factor, 15 background terms, 6*2 profile parameters from a TCHZ profile function, axial divergence correction, 18+62 structural parameters). However, for x = 0.8 composition and due to the small amounts of the tetragonal melilite (2.32(6)% wt%) (see Figure IV.7), the metal oxide "M-O" distances were constrained to keep a minimum value of 1.7 Å and 2.5 Å for M= Ga, La/Ba respectively (111 independently refined parameters). The x = 0.85 composition on the other hand, contain only 1.14% (wt%) of the tetragonal melilite (Figure IV.7); to avoid non-physical refined values only the cell parameters of the 𝑃4 ̅ 2 1 𝑚 melilite were refined, while fixing the related structural parameters. Moreover, the refined profile showed a non-fitted peak broadening noticed on the measured diffraction pattern of this composition. A better refinement with considerably lower Rwp and GOF values (from Rwp= 12.6%, GOF= 1.97 to Rwp= 10.38%, GOF= 1.64) was secured by using Stephens peak broadening description of the main phase peak shapes, i.e. the orthorhombic melilite (98 independently refined parameters). La1.775Ba0.225Ga3O7.3875 (x = 0.775): The diffraction pattern of this composition was particularly challenging to refine due to unusual peak profiles, as displayed in Figure IV.5. To perform the best possible fit while keeping physically meaningful values/models, three approaches were attempted: (a) Stephens peak broadening description [14] which considers the space group symmetry and describes the sample strain and anisotropic crystallite size within the allowed hkl directions. This produced a relatively mediocre fit as seen in Figure IV.6a, and reliability factors of Rwp= 12.96% GOF= 2.28. (b) Spherical harmonics (eighth order) was used in second place to describe the anisotropic peak broadening; this allowed to achieve a better description of the measured profile (Figure IV.6b) with lower reliability factors of Rwp= 10.13% GOF = 1.78. Finally, a multi-cell approach was considered by using five orthorhombic and one tetragonal melilite cells, with only one profile function for all cells. The number of used cells was determined by having first a tetragonal cell and then orthorhombic cells were added one by one and refined, until an overlap of the Ima2 cells hkl peaks gave a near-continuous fit to the observed peaks. Four of the five Ima2 melilite cells parameters were constrained to refine with respect to a "reference" orthorhombic cell by the addition of a refinable shift parameter, defined in Table IV.2. In fact, by modelling different cells of the same compound it actually describes a possible composition gradient among the sample which could be easily induced by the direct crystallisation from the molten liquid synthesis procedure in the case of a not completely homogeneous melt. Moreover, this refinement strategy accomplished the best graphical fit (Figure IV.6c) and the lowest reliability factors (Rwp= 10.01% GOF= 1.07) over the three tested approaches and therefore was retained as the final description of the measured pattern. This led to a total of 125 independently refined parameters (zero shift, 1*6 scale factor, 18 background term, axial divergence correction, 6 profile parameters from a TCHZ profile function, 93 structural parameters).

Figure IV. 5 .

 5 Figure IV.5. SPD acquired pattern for the La1.775Ba0.225Ga3O7.3875 (x = 0.775) composition, with the insert showing a zoom on the 13.5°-17.2° (2) range. Green tick marks correspond to the tetragonal 𝑃4 ̅ 2 1 𝑚 melilite indexation.

Figure IV. 6 .

 6 Figure IV.6. Zoom on the 13.3° -14.9° (2θ) region from Rietveld refinements of the x = 0.775 compound using different strategies: (a) Stephens broadening description. (b) Spharical harmonic. (c) Multi-cells approach. In all panels red symbols, black and blue lines corresponds to Yobs, Ycalc and Yobs-Ycalc respectively. In (a) and (b) pannels green and orange tickmarks correspnds tp the 𝑃4 ̅ 2 1 𝑚 and Ima2 melilites respectively.

  described above led to satisfactory (in the same range) reliability factors, and are summarised in Table IV.1. Their related refined plots and structural parameters are shown in Figure IV.8, Figure IV.9 in the main text and from Figure A. 19 to Figure A. 22, and from Table A. 16 to Table A. 34 in the appendices. The extracted cell parameters and volumes (Figure IV.10a) exhibits a clear decreasing linear trend, which is consistent with the substitution of a larger Ba by a smaller La atom, i.e. ionic radii of 1.52 Å and 1.27 Å for Ba and La respectively [15]. Even though the overall volume trend shows a decline as x values increase (Figure IV.10a), one can notice an increasing trend of the a/c ratio for both tetragonal and orthorhombic melilites (Figure IV.10b), consistent with solid solution trend. Moreover, this is even supported by the a/b ratio of the orthorhombic cell, indicating and increasing trend (Figure IV.10c), consistent with the 1D ordering of the interstitial oxides along the a direction.

Figure IV. 9 .

 9 Figure IV.9. SPD data Rietveld refinement of the a) La1.75Ba0.25Ga3O7.375(x = 0.75) composition (Rwp= 9.11%, GOF= 1.51). b) La1.9Ba0.1Ga3O7.45(x = 0.9) composition (Rwp= 13.21%, GOF= 1.96). In both panels red, black and blue data corresponds to the measured, calculated and difference curves. In the (a) panel green and orange tick marks corresponds to the P4 ̅ 21m and Ima2 melilites. Where in panel (b) green and orange tick marks corresponds to Ima2 melilite an LaGaO3 perovskite.

Figure IV. 10 .

 10 Figure IV.10. a) Normalised cell parameters to the LaBaGa3O7 (x = 0) of both tetragonal and orthorhombic melilites extracted from Rietveld refined SPD data as a function of x (in the La1+xBa1-xGa3O7+x/2 solid solution). The large error bars in panel (a) for the x = 0.775 composition were drawn from the refined cell parameters distribution over the five orthorhombic melilite cells. b) and c) shows the a/c and a/b ratio of both P4 ̅ 21m and Ima2 melilites. In all three (a, b andc) panels the x = 0 and x = 1 compositions were taken from[11],[16].

Figure IV. 11 .

 11 Figure IV.11. a) Structural projection of the orthorhombic Ima2 melilite (x = 0.75 composition) along the aaxis, highlighting the La1-La1 and La3-La2 interatomic distances, which are shown in (b) as a function of x (concentration of Oint). c) Structural projection of one [GaO4]n sheet from the orthorhombic Ima2 melilite (x = 0.75 composition) along the c-axis with highlighted Ga5-Oint distance, which is shown in panel (d) as a function of x (concentration of Oint). The La2Ga3O7.5 x = 1 composition plotted in both (b) and (d) panels was taken from[11]. In (a) and (c) panels blue, dark green, light green and red spheres corresponds to Ba, La, Ga and oxygen atoms.

France, with a

  refined incident wavelength of λ= 1.5936(3) Å over the 0°-160° (2θ) angular range. IV.3.2.1. Room temperature NPD data analysis for La1+xBa1-xGa3O7+x/2 x = 0.3/ 0.6/ 0.7/ 0.8/ 0.9 compositions. Rietveld refinement of room temperature acquired data were carried out against both high intensity (HI)* and high resolution (HR)* data sets independently for all measured compositions. These refinements conditions are described in the following: La1+xBa1-xGa3O7+x/2 (x = 0.3, 0.6 and 0.7): These compositions were Rietveld refined using only the tetragonal melilite to describe the whole acquired neutron diffraction patterns.

  between SPD and NPD data refinements was made by comparing the refined cell parameters of the different structures (i.e. P4 ̅ 21m and Ima2), which indicated a good agreement between the two diffraction techniques (see Figure A. 23 in the appendices). Moreover, one can notice the further difference of refined weight fractions of both melilite polymorphs obtained from SPD and NPD refined data sets for the La1.8Ba0.2Ga3O7.4 (x = 0.8) composition (see Figure IV.7 and Figure IV.13). This can simply be explained by either: (i) the different synthesised sample for NPD experiments, which may have more tetragonal phase amounts due to the multiple combined beads to reach 3g of sample, compared to the SPD measured composition which needed only one bead. (ii) The broader pattern profile of neutron powder diffraction measurements making it difficult to refine accurate wt% fractions of the different present phases. Due to the low refined tetragonal melilite amount from thiscomposition (11% and 14.1% both in wt% from HI and HR data respectively), it will not be considered for the following structural analysis.

Figure IV. 13 .

 13 Figure IV.13. Refined wt% of both tetragonal and orthorhombic melilite polymorphs from neutron data as a function of substituted Ba by La, noted x from the La1+xBa1-xGa3O7+x/2 solid solution.

[ 5 ]

 5 (see Figure IV.14). This compound was found to feature a partial ordering of both A-site cations and interstitial oxides (Oint). Out of the eight accessible A-sites, four are fully occupied by La atoms, while the remaining four are mixed between La and Ca atoms with different occupancy rates. The interstitial oxides network on the other hand was assigned to occur among four of the six five-membered [GaO4]5 melilite network forming pentagons, with partially occupied sites in a 1D ordered chains (see Figure IV.14), showing a preference for Ca bearing channels. The 1D order feature of the Oint network in the La1+xCa1-xGa3O7+x/2 0.55 ≤ x ≤ 0.64 compounds exhibit two edge sharing Oint chains per unit, in comparison with the Ima2 orthorhombic melilite which shows fully 1D ordered Oint chains.

Figure IV. 14 .

 14 Figure IV.14. Crystal structure of the La1.64Ca0.36Ga3O7.32 (0 ≤ x ≤ 0.64) pseudo-orthorhombic P1 melilite [5], (a) projected along its stacking direction, with light blue, pink and orange coloured surfaces indicating Ca-free, Ca-rich, and Ca-poor channels. (b) Projection along the section of stacking direction with arrows indicating the described channels using the same colour coding. Blue, dark green, light green and red spheres corresponds to Ca, La, Ga and oxygen atoms.

Figure IV. 15 ,

 15 Figure IV.15, illustrating the relaxation of the Oint local environment in the La1.64Ca0.36Ga3O7.32 P1 melilite. In this case, static disorder of the Oint closest oxide is so great that its split site (namely O3a and O3b in Figure IV.15) shows a distance ranging from 0.49 Å to 0.67 Å between O3a and O3b. An examination of the refined tetragonal (P4 ̅ 21m) melilite across the different measured La1+xBa1-xGa3O7+x/2 x = 0.3, 0.6, 0.7 compositions, reveals first an increasing anisotropy of the anisotropic thermal parameters of the different structural atoms, as displayed in Figure IV.16a, Figure IV.16b, Figure IV.16c showing an expanding atomic displacement ellipsoid (plotted in 99% probability), indicating an increased static disorder of these atoms as more Ba is substituted by La and interstitial oxide concentration augment. Moreover, in Figure IV.16d illustrating the recalculated Biso values from the anisotropic thermal parameters (β11, β22, β33, β12, β13, β23) trend as a function of x (amount of substituted barium), it appears that for the La1.3Ba0.7Ga3O7.15 (x = 0.3) composition the thermal parameters are at their lowest values, which increase considerably to almost 3 Å 2 (for the O1 atom) as the tetragonal structure reaches

Figure IV. 15 .

 15 Figure IV.15. Local distortions of the interstitial oxide (Oint) environment in the La1.64Ca0.36Ga3O7.32 pseudo-orthorhombic P1 compound and how it affects the neighbouring channels. The Oint-Ox bond distances are shown to indicate the most affected oxide atoms. Ga is represented by light blue coloured spheres while the oxides are in green, purple and blue coloured spheres arranged from the closest to the furthest channel forming oxides. This figure was taken from [5].

Figure IV. 16 .

 16 Figure IV.16. a), b), c) Shows the refined P4 ̅ 21m structure of x = 0.3, 0.6 and 0.7 respectively projected along the c-axis and plotted in thermal ellipsoids in 99% probability. The blue arrows point the O1 atom which shows the strongest anisotropy. d) normalised plot of calculated isotropic displacement parameters for all structural atoms as a function of composition (x). e) plot of the Oint atom interatomic distances with the other structural atoms.

Figure IV. 17 .

 17 Figure IV.17. Ga-Oint, La-Oint and La-La interatomic distances obtained from neutron refined structures across the room temperature measured composition series (x values in La1+xBa1-xGa3O7+x/2). With T and O referring to tetragonal P4 ̅ 21m and orthorhombic Ima2 structures.

Figure IV. 18 .

 18 Figure IV.18. VT-PXRD measurements (20°C step size) of La1.9Ba0.1Ga3O7.45 (x =0.9) composition, evidencing the stability of the orthorhombic Ima2 melilite vs temperature. The yellow box shows the beginning of decomposition into LaGaO3 + LaBaGa11O20 + Ga2O3.

Figure IV. 19

 19 Figure IV.19. a) Stacked high temperature neutron powder diffraction patterns of the La1.9Ba0.1Ga3O7.45 (x = 0.9) composition measurement. A zoom on the 96° -100° (2θ) region is shown in (b) panel.

10 20 30

 30 40 50 60 70 80 90 100 110 120 130 140 150 96 97 98 99 100 intensity(a.u.)

  xGa3O7+x/2 0.55 ≤ x ≤ 0.64 solid solution, which adopts a pseudo-orthorhombic P1 cell at room temperature. At 700°C, this polymorph was found to be no longer stable, and transforms into the fully disordered P4 ̅ 21m melilite. The previously described SrREGa3O7 RE= [Er-Yb] melilite compositions in Chapter II, displayed similar behaviour, when crystallised from glass precursors, are stabilised under a P21212 polymorph due to the ordering between Sr and RE atoms. Eventually, at higher temperatures the fully disordered P4 ̅ 21m tetragonal melilite is stabilised at the expense of the ordered P21212 polymorph.Stability of the tetragonal (P𝟒̅ 21m) small-cell vs the orthorhombic (Ima2) superstructure melilites. Thermal stability of these La1+xBa1-xGa3O7+x/2 melilite compositions was studied by VT-PXRD measurements. Samples were heated from room temperature up to 1200°C using a 20°C step and measured over the 15° -40° (2θ) range with a measuring step of 0.016° and a measuring time of 0.7s/step. The obtained results are coupled to the discussed results above from SPD and NPD refinement data and are plotted in a phase-diagram like plot (Figure IV.20).

Figure IV. 20 .

 20 Figure IV.20. Phase-diagram like plot of the La1+xBa1-xGa3O7+x/2 solid solution studied compositions, evidencingthe polymorphs stability limits against x "amount of substituted barium" and temperature drown from VT-PXRD measurement. The transition temperatures from the mixed P4 ̅ 21m + Ima2 to fully P4 ̅ 21m in the 0.725 < x < 0.8 region were extrapolated from the measured x = 0.8 and 0.9 compositions. The x = 1 compound decomposition temperature was taken from[11].

  (i.e. BVS values around 2 for oxide). From the present La1+xBa1-xGa3O7+x/2 solid solution, as the La content increases, the Oint concentration also rises to keep charge compensation, which induces static disorder and distortions of its local environment. This is observed on the refined oxides ellipsoids directions (anisotropic displacement parameters), indicating a strong anharmonicity pointing toward adjacent [GaO4]n pentagons centre (see Figure IV.16a, Figure IV.16b, and Figure IV.16c). At a certain amount of Ba substitution for La (x = 0.9) the tetragonal cell is no longer capable of accommodating such amount of interstitial oxides in a disordered way while satisfying local bonding of the different Oint. Consequently, a structural transition occurs toward an orthorhombic melilite (S.G. Ima2) with ordered Oint network in a 1D corner sharing [GaO4]5 chains. With such ordering, the Oint local environment is better relaxed, hence causing less strain on the melilite [GaO4]5 infinite framework. AC Impedance measurements of La1+xBa1-xGa3O7+x/2 0.5 ≤ x ≤ 09 compositions.The synthesised beads of La1+xBa1-xGa3O7+x/2 (x = 0.6, 0.7, 0.8 and 0.9) compositions were coarsely polished until a thickness of 1 mm was reached, while making sure that two parallel faces are secured. The disks were coated with gold paste and then sintered at 600°C for 30 min to eliminate the organic components present in the coating paste and ensure the formation of electrodes. Impedance spectroscopy measurements were then proceeded by Alberto José Fernández-Carrión at the university of Guilin in China, using a Solartron 1260 frequency response analyser over the 10 -1 -10 7 Hz frequency range and between 300°C to 800 °C temperatures each 50°C and a heating step of 6°C/min.

Figure IV. 21

 21 Figure IV.21 shows complex impedance plots of La1.725Ba0.275Ga3O7.3625 (x = 0.725) composition (i.e. the tetragonal melilite with highest amount of interstitial oxides) at different temperatures. At 300°C the complex impedance plot comprises a partial semicircle with associated capacitances of 10 -12 F.cm -1 , indicative of bulk response[18], and a spike at lower frequencies with associated capacitance ranging from 10 -11 to 10 -8 F.cm -1 , gathering grain boundaries and electrode responses (Figure IV.21a and Figure IV.21b). Upon increasing temperature, the bulk semi-circle kept gradually getting smaller until it completely disappeared (at 350°C it is hardly discernible), while the electrode spike collapsed down, similar to other reported oxide conductors based on the melilite compounds[11] (Figure IV.21c). For T < 350°C the bulk resistance was extracted from the intercept of the fitted semi-circle at low frequencies. As of T ≥ 350°C, the bulk resistance was obtained from the data intercept at lower frequencies. The acquired data of La1+xBa1-xGa3O7+x/2 x = 0.5, 0.6, 0.7, 0.8, 0.9 compositions were analysed by the same process.

Figure IV. 21 .

 21 Figure IV.21. Complex impedance plots acquired on the La1.725Ba0.275Ga3O7.3625 (x = 0.725) at 300°C in (a) and (b) panels, and 750°C in (c) panel. with (b) showing a zoom of (a) at low frequency evidencing the bulk semicircle response.

Figure IV. 22 .

 22 Figure IV.22. a) Arrhenius plots of the measured La1+xBa1-xGa3O7+x/2 (0.5 ≤ x ≤ 0.9) compositions overlaid with La1.54Sr0.46Ga3O7.27 and La2Ga3O7.5 compounds conductivity for comparison. The related activation energies are shown in Table A. 67 from Chapter A.IV in the appendices. b) Extracted conductivities of the measured solid solution compositions at 500°C as a function of x (Oint concentration), the vertical dashed lines represent the stability limits of each polymorph.

[ 21 ]

 21 -[23]. To test the phase transition hypothesis, the x = 0.6 sample was taken as a representative sample and measured by VT-PXRD with a thermal protocol replicating the AC impedance heating measuring procedure. Measurements were conducted on a freshly synthesised La1.6Ba0.4Ga3O7.3 (x = 0.6) sample, between RT and 800°C using a 50°C step/scan. In Figure IV.23 showing the measurement results, no phase transition or decomposition was observed, yet the only difference that can be noticed is the slightly broader Bragg diffraction peaks between the initial pre-heating and post-heating room temperature measurements. This could suggest a disturbed sample microstructure due the heating protocol. To investigate this, two new beads were synthesised, one was heated on a conventional open atmosphere furnace (also by replicating the AC impedance heating measuring procedure) while the other one was left as-synthesised. The two beads were optically polished and observed by scanning electron microscope (SEM). In Figure IV.24 showing both acquired images, EDX confirmed the grains composition matching the nominal; moreover, it was not possible to quantify the grain boundary compositions due to their thin domains (< 1µm). The first obvious observation from the SEM acquired images could be the slightly different contrast between the bulk and grain boundaries, as the later ones appears darker, hence possessing a lighter composition: poor in La/Ba elements. One can also notice the smaller grains (and correspondingly more grain boundaries) detected on the post heat treatment sample vs the as-synthesised one.

Figure IV. 23 .

 23 Figure IV.23. VT-PXRD between RT and 800°C measurements of the La1.6Ba0.4Ga3O7.3 compound, using a step of 50°C/scan in the range of 14°-40°C (2θ) with a step of 0.016° and a measuring time of 1s/step. All measured diffraction patterns were indexed with the P4 ̅ 21m melilite cell.

Figure IV. 24 .

 24 Figure IV.24. SEM measurements on a) as-synthesised bead b) heat treated bead (replicating the AS-impedance measurement thermal protocol), in back scattered electron mode on beads of La1.6Ba0.4Ga3O7.3 composition. Both images are shown at the same enlargement scale.

[

  Ca, Sr] melilite could be investigated by alternative synthesis approaches as shown in this Chapter (i.e. direct crystallisation from an under-cooled melt), or by other methods allowing to secure metastable phases as glass crystallisation or sol-gel synthesis, which might help extending the tetragonal phase stability to higher doping concentrations. From this study and 133 Chapter V: Lanthanum Doping in the Ca 5 Ga 6 O 14 melilite-like Structures for New Oxide ion Conductors Introduction. Investigating compounds such as the melilites and melilite related structures for potential solid oxide fuel cell electrolyte materials operating at intermediate temperatures, is much of interest as stated in Chapters II and IV of this manuscript. In the CaO-Ga2O3 phase diagram two compositions were reported with a melilite-like framework, retaining similar [GaO4]n framework features [1], [2]: Ca5Ga6O14 and Ca3Ga4O9. The first one is described below while the latter one is described in the appendices Chapter A.V. The Ca5Ga6O14 structure crystallises in an orthorhombic cell (S.G. Cmc21 n°36). It adopts a melilite-related structure, formed by two melilite-type [GaO4]n sheets stacked along the c-axis with adjacent sheets related by a two-fold rotation about the c-axis (see Figure V.1). The structural calciums occupy three distinct sites accommodated between the layers,but only the Ca3 atoms are held in the melilite-like pentagonal channels centre, as due to the higher A/B cations ratio (4/5 vs 2/3 from the ABC3O7 melilite) and two-fold rotation between the framework sheets. The Ca1 and Ca2 atoms are displaced from their "ideal" melilite position to the edge of the framework-forming pentagonal channels (see Figure V.2).

Figure V. 1 .Figure V. 2 .

 12 Figure V.1. Ca5Ga6O14 crystal structure projection within the c-and b-axis shown in a) and b) respectively, with blue, green and red spheres representing calcium, gallium and oxygen atoms respectively. Panel c) indicates the two-fold rotation relation between [GaO4]n sheet 1 and 2 that leads to the melilite framework. Calciums were omitted for clarity.

V. 3 ,

 3 Ca substitution by La or Nd atoms shows the lowest energies. However, Nd indicates a slightly higher structure energy (∆𝐸 = 0.17𝑒𝑣 ). Therefore, La was chosen as a dopant element and the investigated solid solution was then LaxCa5-xGa6O14+x/2 0 ≤ x ≤ 5.

Figure V. 3 .

 3 Figure V.3. Calculated structures energies for each dopant in the Ca5Ga6O14 compound.

  Stoichiometric amounts of La2O3 (STREM chemicals, 99.9% purity), CaO (STREM chemicals, 99.95% purity) and Ga2O3 (STREM chemicals, 99.998% purity), were weighted according to the nominal composition. The precursors were mixed in an agate mortar using ethanol for a better homogeneity of the mixture. The resulting powder was allowed to dry at100°C in an open atmosphere laboratory oven for several minutes and pressed into pellets of 13 mm diameter. The pellet was placed in a platinum foil and fully covered with freshly made powder of the same composition; the covering powder acts as a "sacrificial powder", reducing Ga loss from the pellet sample during the heating process. The sample was fired at 1275°C for 48 hours in order to complete the synthesis[16]. The sacrificial powder was removed after the heating treatment by polishing the sample. Laboratory X-ray diffraction was used to check the formed phase of the different synthesised compositions. On the stacked diffraction patterns of the different synthesised compositions (Figure V.4), compositions for which 0 ≤ x ≤ 0.25 form phase pure samples that can be indexed with the Ca5Ga6O14 phase. For x > 0.25 (La0.25Ca4.75Ga6O14.125) compositions, additional Bragg peaks were noticed in the acquired diffraction patterns, and their intensities kept rising as x values increased. These peaks were indexed as stoichiometric LaCaGa3O7 melilite (S.G. P4 ̅ 21m n°113) (see Figure V.4). To extract the cell parameters trend and approximate weight % of the crystallised impurities (for x > 0.25 compositions), Rietveld refinements were carried out using Topas (V6)[17]. In Figure V.5a, the cell parameters show a clear linear trend as a decreases while b and c increase, which leads to a small overall unit cell volume enlargement from 1361.00(4) Å 3 (x = 0) to 1362.10(4) Å 3 (x = 0.25). In the 0.25 < x < 1 range, the cell parameters manifest a plateau, indicative of a LaxCa5-xGa6O14+x/2 solid solution limit at x = 0.25. This is supported by the growing amount of the LaCaGa3O7 secondary phase as the amount of lanthanum exceeds x = 0.25 (see Figure V.5b).

Figure V. 4 .

 4 Figure V.4. a) Stacked diffraction patterns of LaxCa5-xGa6O14+x/2 (0 ≤ x ≤ 1) samples synthesised by solid-state reaction, with their related indexations in green and blue representing the Ca5Ga6O14 and CaLaGa3O7 respectively. b) Zoom on the 26.5°-28.7° (2θ) showing the LaCaGa3O7 melilite impurity peak arising from compositions with x ≥ 0.3.

Figure V. 5 .

 5 Figure V.5. a) Normalised refined cell parameters of the LaxCa5-xGa6O14+x/2 (0 ≤ x ≤ 1) solid solution synthesised by solid-state reaction. b) extracted weight % of crystallised La-doped Ca5Ga6O14 and LaCaGa3O7 from the LaxCa5-xGa6O14+x/2 (0 ≤ x ≤ 1) compositions. Vertical dashed lines in both panels indicates the x dopant limits.

  Glass crystallisation attempts were unsuccessful as non-congruent crystallisation occurs from a 5CaO-3Ga2O3 glass precursor, leading to mixture between Ca5Ga6O14 and Ca3Ga4O9 crystalline phases. The x = 0.3 (La0.3Ca4.7Ga6O14.15) glass material was measured first by VT-PXRD from 750°C to 1200°C using a step of 50°C/scan. In fact, Figure V.6 indicates a phase pure crystallisation of this sample at 800°C, and a decomposition starting around 900°C into Ca3Ga4O9 + LaCaGa3O7. Nevertheless, hopes of increasing the concentration of La in the cell soon volatilised, since for the La0.3Ca4.7Ga6O14.15 (x = 0.3) ex-situ annealed glass sample at 800°C for 1 hour resulted in multi-phase crystallisation with both LaCaGa3O7 + Ca5Ga6O14 phases present in the measured diffraction pattern (Figure V.7). Even by trying to optimise the conditions by decreasing the annealing temperature and time, the same two phases were present.Moreover, taking a closer and more careful look to the VT-PXRD data at 800°C, the Bragg peaks appear much broader than the solid-state synthesised samples, which can mask other phases contribution in small wt%. Direct crystallisation from the melt either by slowly cooling the sample or by contact with the nozzle were successful in achieving phase pure compounds all the way to x = 0.25. However, for x = 0.3 compounds this approach led to the crystallisation of a two phase material, with both Ca5Ga6O14 and LaCaGa3O7 structures present (see Figure V.7).

Figure V. 6 .

 6 Figure V.6. VT-PXRD measurements of La0.3Ca4.7Ga6O14.15 (x = 0.3) glass compounds between 750°C and 1200°C. The different crystallised phases are indicated by green, orange and blue tick marks, corresponding to the Ca5Ga6O14, Ca3Ga4O9 and CaLaGa3O7 compounds respectively.

Figure V. 7 .

 7 Figure V.7. Acquired laboratory diffraction patterns of the La0.3Ca4.7Ga6O14.15 (x = 0.3) composition synthesised by glass crystallisation with an annealing treatment at 800°C for 1h (black line) and melt crystallised (red line) by slowly cooling the bead. The corresponding indexation are represented by green and blue tick marks. The insert shows an enlargement of the second CaLaGa3O7 melilite impurity peak indicated by a blue arrow.

  The synthesised LaxCa5-xGa6O14+x/2 x = 0 and x = 0.25 samples purities were checked by laboratory PXRD as they were both fully indexed with the Ca5Ga6O14 structure. The samples were then subject of a composition verification by electron microprobe analysis. First, freshly synthesised samples in the form of pellets were coarsely polished to remove the covering sintered sacrificial powder. An optical quality polishing was then applied, and finally a conducting carbon layer was deposited on the freshly polished surface. As shown in Figure V.8a and Figure V.8b, imaging in backscattered electron (BSE) mode, a clear contrast between black and grey domains can be noticed. Here, the black regions represent holes / porosity in the sample and can also be induced from grain detachment during the polishing process. Moreover, the measured atomic percentage of Ca, Ga and La in both LaxCa5-xGa6O14+x/2 x = 0 and x = 0.25 compounds are in good agreement with the theoretical nominal values (Figure V.8c and Figure V.8d): Ca5.07(4)Ga5.94(3)O14 measured vs Ca5Ga6O14 nominal for x = 0, and La0.25(1)Ca4.80(3)Ga6.0(3)O14.125 measured vs La0.25Ca4.75Ga6O14.125 nominal for x = 0.25.

Figure V. 8 .

 8 Figure V.8. a), b) SEM imaging in backscattered electron (BSE) mode of both LaxCa5-xGa6O14+x/2 x = 0 and x = 0.25 samples respectively. c) and d) microprobe measured Ca, Ga and La content in both x = 0 and x = 0.25 compositions.SPD data analysis.To first locate the La atom positions in the doped Ca5Ga6O14 structure, synchrotron X-ray powder diffraction (SPD) measurements were conducted on both LaxCa5-xGa6O14+x/2 x = 0 and x = 0.25 in Soleil synchrotron at the CRISTAL beamline, with an incident wavelength of λ = 0.67153 Å. The powders were first independently diluted in amorphous SiO2 powder according to a 1:3 wt% ratio to reduce beam absorption, filled in 0.3mm diameter quartz capillaries then measured.

3. 58 to

 58 Rwp= 1.83%, GOF= 2.88. Refined La occupancies displayed its distribution over only Ca1 and Ca3 channels, as the Ca2 occupancy converged to 0.998(3). A third and final Rietveld refinement was conducted with fixed Ca2 occupancy at 1, while freely refining the La content in Ca1 and Ca3 sites (89 refined parameter). Comparing the A-sites refined occupancies [0.990(3)Ca1/0.010(3)La1 -1Ca2/0La2 -0.756(4)Ca3/0.244(4)La3], the disorder between Ca and La elements occurs mainly on Ca3 channels. Considering the refinement errors, Ca1 is effectively a single cation site holding only Ca atoms. See Figure V.9b for refined plot and TableV.2 for refined structural parameters. Calculating the atomic % of both La and Ca from the identified site occupancies by the Rietveld method against x = 0.25 SPD data, resulted in 1.051(5)% for La and 18.850(5)% for Ca, which is consistent with the nominal composition (0.995% La, 18.905% Ca). From these refinement results, the near-absence of CaO or other Ca-rich secondary phases and the microprobe analysis confirming the nominal composition stoichiometry, the hypothesis of charge compensation on the La-doped introduction of cation vacancies can be ruled out, which leave the second one: introduction of interstitial oxides, to be studied.* the OccXn notation means occupation of atom X in site number n

Figure V. 9 .

 9 Figure V.9. Final Rietveld refined SPD data of a) Ca5Ga6O14 (x = 0) (Rwp= 2.06% GOF= 3.23), and b) La0.25Ca4.75Ga6O14.125 (x = 0.25) (Rwp= 1.67% GOF= 2.63). c) and d) shows a zoom on the (002) peak which exhibits the first biggest misfit.

V. 3 . 1 .

 31 Figure V.1a and Figure V.1b for the structural projection along this two directions respectively, and Figure V.11a and Figure V.12a for the STEM-HAADF acquired images). Along these orientations, the visualised structure is a 2D projection where each observed atom actually represents a column of atoms, with heaviest (Z ̅ ) or denser atomic columns appearing brighter. A first observation of the STEM-HAADF images along the [001], which allows to compare the Ca1, Ca2 and Ca3 spots intensities, show more intense Ca3 spots (indicated by orange arrows in Figure V.11a) compared to the almost invisible Ca1 and Ca2 spots (indicated by red arrows in Figure V.11a). Knowing that the Ca1/Ca2 and Ca3 atom columns have the same electron density, this informs us of heavier atoms present in the Ca3 sites, consistent with the refined La occupancies on that site. The plotted Z profile from both directions indicates a higher intensity for Ca3 channels (Figure V.11b and Figure V.12b), which could be the consequence of more La introduced in the Ca3 sites as opposed to Ca1/Ca2 sites, supporting the previous analysis and results. However, this could also be the result of channelling affects arising from nearby Ca1/Ca2 sites with small Ca3-cation bond lengths. The latter explanation is more relevant for the [010] direction as the distances of Ca3-cation (first neighbours) are much more longer along the [001]: d(Ca3-cation)min= 2.028(3) Å vs 1.709(5) Å in the 2D projection along the [001] and [010] respectively. To complete this analysis, Energy dispersive X-ray (EDX) mapping at the atomic scale was performed along the [001] direction to better illustrate the La dispersion over the different calcium sites. However, due to the sample degradation under the beam and poor orientation regions (disoriented nanodomains), the best maps were acquired over 20 min of tracking and changing zones (Figure V.11c). In this figure, it can be seen that the La signal is focused mainly on the Ca3 sites. Moreover, electron energy loss spectroscopy (EELS) was performed along the [010] direction, as shown in Figure V.13. It appears that La signal is more present in the Ca3 channels with no strong evidence of being also held in the Ca1/Ca2 channels.Both these results from EDX atomic mapping and EELS profiles are consistent with the refined La disorder from SPD data, as most of the La goes to the Ca3 sites.

Figure V. 10 .

 10 Figure V.10. a) HRSTEM image of a La0.25Ca4.75Ga6O14.125 (x = 0.25) oriented crystal along the [001] direction, evidencing the low nanodomains disorientations. b) Selected area electron diffraction (SAED) pattern of a grain oriented along the [001] direction and showing peak streaks indicative of low disoriented nanodomains organisation.

Figure V. 11 .

 11 Figure V.11. a) High resolution STEM-HAADF image of La0.25Ca4.75Ga6O14 (x = 0.25) sample oriented along the [001] (see Figure V.1a for its related crystal structure projection). The crystal related SAED is shown on the top right insert while the top left insert shows an overlay of the structure. b) the drawn Z profile from the integrated area highlighted by yellow rectangle in (a). c) STEM-EDX map of La overlaid with the calcium network, with light and dark blue spheres representing Ca/Ca2 and Ca3 atoms respectively. In panel (a) orange and red arrows indicate the Ca3 and Ca1/Ca2 sites respectively, while in panel (c) only orange arrows are shown to indicate Ca3 positions.

Figure V. 12 .

 12 Figure V.12. a) High resolution STEM-HAADF image of La0.25Ca4.75Ga6O14 (x = 0.25) sample oriented along the [010] (see Figure V.13b for its related crystal structure projection). The crystal related SAED is shown on the top right insert while the top left insert shows an overlay of the structure. Orange and red arrows indicate the Ca3 and Ca1/Ca2 sites. b) the drawn Z profile from the integrated area highlighted by yellow rectangle in (a).

Figure V. 13 .

 13 Figure V.13. a) Structural projection of the La0.25Ca4.75Ga6O14.125 compound along the [010] direction. b) EELS map of Ca, Ga and La of a crystal oriented along the [010]. c) the extracted profiles of each element from two different regions in (b) and shown in (a).

Figure V. 14 .

 14 Figure V.14. Final Rietveld refined NPD (HR) data of a) Ca5Ga6O14 (x = 0) (Rwp= 3.58% GOF= 0.68), and b) La0.25Ca4.75Ga6O14.125 (x = 0.25) (Rwp= 3.21% GOF= 0.60). Green tick marks correspond to the Ca5Ga6O14 and La0.25Ca4.75Ga6O14.125 structures panels (a) and (b) respectively, while the orange tick marks represent the CaO impurity quantified at ⁓0.08(6)% for x = 0 and ⁓0.71(9)% for x = 0.25 materials, both in weight%.

V

  .15b), signifying an internal disturbance caused by the cationic disorder or triggered by the residence of an interstitial oxide. Additionally, comparing the distances of this channel pentagon centroid to the nearest oxides (Figure V.16a and Figure V.16c), it reveals a small positional displacement of the O2 atom towards the outside the channel, while the others remainalmost the same within the plotted 3×σ error, hence enlarging these channels to potentially accommodate an interstitial oxide. This behaviour is consistent with the one observed in the anion ordered La2Ga3O7.5 and La1.64Ca0.36Ga3O7.32 melilites, where the Oint containing channels shows a displacement of their forming oxides toward the centroids of neighbouring [GaO4]5 pentagons to satisfy the local bonding of the interstitial oxides[8],[22],[28], as shown in Figure V.16b and Figure V.16d. Even though this displacement is weak in our La0.25Ca4.75Ga6O14.125 (x = 0.25) compared to the La2Ga3O7.5 shown in the same figure, it can be linked to its much lower Oint content.

Figure V. 15 .

 15 Figure V.15. a) Comparison between NPD (HR) refined oxygens displacement parameters against both x = 0 and x = 0.25 materials. b) highlighted O2, O8 and O9 positions inside the Ca5Ga6O14 cell.

Figure V. 16 .

 16 Figure V.16. a) Structural projection of the Ca3 channels pentagons along the c-axis in the Ca5Ga6O14 compound. b) Overlay between of one [GaO4]5 framework pentagonal channels from the LaCaGa3O7 melilite (grey atoms) and the Oint containing channel from the La2Ga3O7.5 melilite (coloured atoms), with purple arrows indicating the displacement direction of the channels forming oxides. In both panels green and red spheres represent gallium and oxygen atoms. c) and d) panels shows the determined distances from the channels centroids to the labelled oxides from (a) and (b) respectively, with errors plotted in 3×σ.

Interstitial oxide position determination

  by Fourier difference map and maximum entropy method (MEM) calculations from NPD data.

  Figure V.17a, from the NPD (HR) refined data, almost no Fourier peak can be distinguished as the maximum positive nuclear density is at the same level as the maximum negative density (see also Figure A. 35a and Figure A. 35c in the appendices Chapter A.V). In contrast with the NPD (HI) refined data, from their Fourier difference map (Figure V.17b) a very small intensity Fourier peak can be identified in the Ca3 channels by the GaO sheets level at the (x = 1/2, y= 0.025, z=0.51) position, typical of an interstitial oxide "Oint" as positioned in the melilite structures[8]-[10], [22] (see also Figure A. 35b and Figure A. 35d in the appendices Chapter A.V). An oxygen atom was placed at this position and freely refined its y, z coordinates and site occupancy while fixing its x coordinate to 1/2 (mirror plane) and defining its Biso as a mean value of the structural oxygens Biso values. Refinements with this additional oxide did not improve the overall fit and the same reliability factors were retained. Even though a stable refinement was obtained, the barely distinguishable weak intensity of the Fourier peak from the noise (see positive to negative nuclear density intensity in Figure A. 35c and Figure A. 35d) implies further investigations in confirming the interstitial oxide existence in that position.

Figure V. 17 .

 17 Figure V.17. a), b) Fourier difference map section at z= 0.51 centred at the Ca3 channels from La0.25Ca4.75Ga6O14.125 NPD (HR) and NPD (HI) refined data respectively.

3 . 2 ,

 32 Figure V.20a and Figure V.20b). This observation is consistent with the detected trend on the relaxed structures containing the Oint in the Ca3 channels, indicating lower structure energies vs the Ca1/Ca2 Oint containing channels structures (see Figure V.19b). In contrast with previously reported melilites containing interstitial oxides, Config542 manifests an Oint positioning in the Ca3 [GaO4]5 pentagons centre, directly between two lanthanum atoms (see Figure V.20c). Config538 on the other hand manifests a slight shift of the Oint from the La-La axis centre in the mirror plane (see Figure V.20d). Calculated bond valence sum (BVS) of the interstitial oxide in both configurations revealed to be 1.66 in config542 and 1.78 in config538,these results indicate that the Oint is better suited in config538 as this its calculated charge is closer to the theoretical value of 2. However, it is not completely impossible for an oxide to sit in an under-bonded site if the overall structure energy is lower than other where the oxide atom is occupying a less under-bonded site, which the case for confige542 exhibiting the lowest structure energy. Moreover, comparing our maximum La-doped (x = 0.25) RT-NPD refined model to both predicted configurations by DFT, one can notice a huge increase of the O3-Ga1-O2 angle, varying from 100.0(4)° (our L0.25Ca4.75Ga6O14.125 RT-NPD refined structure) to 140.24° and 113.20° for config538 and config542 respectively (Figure V.21a and Figure V.21b), pushing the O2 atom from its initial position (Figure V.22). This actually indicates the caused local distortion of the Ca3 channels when an interstitial oxide in present on that site, similar to the reported La2Ga3O7.5 with a notable increase of the equivalent angles in

Figure V. 19 .

 19 Figure V.19. a) Calculated energies for the 554 DFT relaxed structures, with the insert indicating the lowest energy structures. b) Energies of the relaxed structures highlighted by a dashed rectangle in (a) plotted in Oint containing channels.

Figure V. 20 .

 20 Figure V.20. Crystal structure projection of an [GaO4]n infinite sheet from the two energetically favourable predicted structures of La-doped Ca5Ga6O14 compound, with a) and b) corresponding to configuration538 and configuration542 respectively. c) and d) zoomed view of the Ca3 channel showing the local environments of the Oint and its shift between the two predicted configurations. Green and red spheres represent gallium and oxygen atoms, while the interstitial oxides are highlighted in orange in both c) and d) panels.

Figure V. 21 .

 21 Figure V.21. Local distortion of the O3-Ga1-O2 angle of: a) LaxCa5-xGa6O14+x/2 x = 0, 0.25, b) both predictedconfig538 and config542 structures, c) LaCaGa3O7[43] and La2Ga3O7.5[22] for comparison.

Figure V. 22 .

 22 Figure V.22. Overlay of the La0.25Ca4.75Ga6O14.125 NPD refined structure (coloured atoms) with both predicted config538 (grey atoms) and config542 (grey atoms) in a) and b) panels respectively. The purple arrows indicate the oxides displacement directions.

  is needed to ensure an optimised charge transport within the sample. The initially sintered pellets of LaxCa5-xGa6O14+x/2 x = 0 and 0.25 compositions were polished to get rid of the sacrificial powder first. The pellets were then subject to a density measurement by Archimedes law (as described in the appendices Chapter A.I section A.I.6.1). The pellets were found to be 67% dense. In fact, this low density is not surprising considering the observed amount of porosity in the acquired SEM (BSE mode) images (shown in section V.3.1 Figure V.8).

Figure V. 24 .

 24 Figure V.24. a), b) Complex impedance plots at different temperatures for Ca5Ga6O14 (x = 0) and La0.25Ca4.75Ga6O14.125 (x = 0.25) compounds respectively.c) Arrhenius plots of the total conductivity (dashed lines) of compounds from this work, compared to the other melilite compounds from[9],[22] and Chapter IV of this thesis.

  5), while the latter one with lower Oint concentrations adopts a two-dimensional (2D) Oint network covering their whole underlying framework over the ab-plane (see Figure V.25). These types Oint distribution facilitate the oxides mobility as the charge carrier can hop between neighbouring channels in the structure. This was previously explained in Chapter IV. In contrast with our final model of the La0.25Ca4.75Ga6O14.125 compound, defined by combining SPD, NPD, MEM and DFT prediction, the underlying Oint distribution can be described as 0D confined network (Figure V.25c) in which the Oint is hosted in isolated Ca3 channels, inhibiting charge transport within the ab-plane due to the need for these oxides to migrate via energetically unfavourable neighbouring Ca1/Ca2 channels. Moreover, for similar Oint concentration per formula unit in the Sr-based melilites, i.e. La1.12Sr0.88Ga3O7.06, this sample exhibit a conductivity value 1.5×10 -4 S.cm -1 at 800°C which is one order of magnitude higher than the La0.25Ca4.75Ga6O14.125 (x = 0.25) studied material at the same temperature. This could indicate that with higher Oint concentration (i.e. higher doping amount) the conductivity of this material might increase as in the Sr-based malilites.

Figure V. 25 .

 25 Figure V.25. Different interstitial oxide ordering in the mellite family, with a) fully disordered forming a 2D network from [10], b) 1D ordered in a chain-like dispersion from [22], c) 0D confined Oint dispersion from the DFT predicted config542 (this work).With green and red spheres representing gallium and oxygene atoms. The interstitial oxide are coloured in blue and highlited by an orange transparent circle.

  authors explained this inhomogeneity by possible Ca conduction mechanisms operating. This could suggest possible cationic conduction in our synthesised LaxCa5-xGa6O14+x/2 (x = 0) and (x = 0.25) samples on top of the oxide ion one. Even though the authors showed that for the fully Al substituted in Ca12Al14-xGaxO33 solid solution (x = 14) crystalline phase sees all its Ca sites are fully occupied, with Ga sites are partially occupied by Rietveld refinements against lab

Figure A. 1 .

 1 Figure A. 1. Aerodynamic levitation coupled to two CO2 lasers montage. A.I.2. Characterisation techniques of the synthesised samples. A.I.2.1. Differential scanning calorimetry (DSC) thermal analysis.Differential scanning calorimetry (DSC) measurements for the present work were conducted on a Setaram MULTI HTC 1600 apparatus, which contains two chambers dedicated to a sample and a reference, operating at high temperatures all the way to 1600°C under argon gas flow.

Figure A. 2 .

 2 Figure A. 2. X-ray diffraction principle is shown in a) while b) indicates an example of a measured diffraction pattern of a multiphased sample.In-situ variable temperatures powder X-ray diffraction (VT-PXRD) was performed using a Bruker D8 Advance laboratory diffractometer (also Cu Kα radiation, Bragg-Brentano geometry) equipped with a Vantec detector and an Anton Paar HTK1200N furnace for measurements up 1200°C, or with an Anton Paar HTK1600N for measurements up to 1600°C.

Figure A. 3 .

 3 Figure A. 3. a) Synchrotron accelerator scheme. b) comparison between laboratory and synchrotron X-ray sources.

"

  Deduction = Hypothesises & measurements" pr(Sc|DI) = pr(Sc|I) × pr(D|ScI) Posterior = Prior × Likelihood pr(Sc|I) ∝ 𝑒 𝛼𝑆 pr(D|ScI) ∝ 𝑒 -

  )} is hence maximised by the maximisation of the Shannon entropy term 𝑆 and the minimization of the likelihood term (𝜒 term or 𝐹-constraints), which depends on the agreement between the experimentally observed 𝐹 𝑜𝑏𝑠 and the MEM calculated 𝐹 𝑀𝐸𝑀 obtained by Fourier transform of the MEM trial density at the considered iteration cycle of the calculations. The entropy 𝑆 measures the total amount of uncertainty represented by this distribution, after all relevant information has been taken into account: 𝑆 = -𝑘 ∑ 𝜌 𝑛 ln (𝜌 𝑛 ) 𝑁 𝑛=1

2 𝑖-

 2 weighted profile: 𝑅 𝑤𝑝 = 100. √ ∑ 𝑊 𝑖 (𝑌 𝑜𝑏𝑠 𝑖 -𝑌 𝑐𝑎𝑙𝑐 𝑖 ) Bragg residue: 𝑅 𝐵𝑟𝑎𝑔𝑔 = 100. ∑ |𝐼 𝑜𝑏𝑠 𝑘 -𝐼 𝑐𝑎𝑙𝑐 𝑘 | 𝑘 ∑ 𝐼 𝑜𝑏𝑠 𝑘 𝑘 (Equation A.5) with 𝐼 𝑜𝑏𝑠 𝑘 and 𝐼 𝑐𝑙𝑎𝑐 𝑘 being the observed and calculated intensities of the k th Bragg reflexion. -Experimental statistic factor: 𝑅 𝑒𝑥𝑝 = √ (N-P+C) ∑ 𝑊 𝑖 𝑌 𝑜𝑏𝑠 𝑖 2 𝑖 (Equation A.6) with N, P and C represent the number of used measured points, number of refined parameters and used constraints respectively.-Goodness of fit (GOF): 𝜒 2 = (

Figure A. 5 ,

 5 Figure A. 5, the generated homogeneous electrons beam is focused on a spot of the sample allowing the scanning of its surface. Arising signals can be analysed in three different modes:

Figure A. 5 .

 5 Figure A. 5. Scheme of an SEM components.

A.I. 5 . 2 . 8 )Figure A. 7 .

 5287 Figure A. 7. Complex impedance curves of a polycrystalline sample in the ideal case.

Figure VI. 1 .

 1 Figure VI.1. Ca2CoSi2O7 structure projection within the c-axis showing the B-site ordering, with Ca in blue, Co in orange and Si in light purple and oxides in red.

Figure A. 10 .

 10 Figure A. 10. Rietveld refinement of SrLuGa3O7 ordered melilite (Rp= 6.87% Rwp= 9.18%) (SPD data). Observed (black dot), calculated (red line), and difference (blue line) profiles are shown. The set of green vertical lines corresponds to reflection positions. Table A. 1 Final refined structural parameters obtained from SPD data collected at room temperature on the SrLuGa3O7 superstructure melilite (P21212 space group, a = 23.6710(2) Å, b = 7.91556(8) Å and c = 5.20516(4) Å). Note that the oxide x, y, z coordinates were subjected to soft restraints to keep them close to the corresponding values from SrYbGa3O7 (see Chapter II section II.4.1).

Figure A. 11 .

 11 Figure A. 11. Rietveld refinement of a) SrTmGa3O7 ordered melilite (Rp= 5.28% Rwp= 7.06%) (SPD data) and b) SrTmGa3O7 disordered melilite (SPD data, Rp= 6.36% Rwp= 8.32%). Observed (black dot), calculated (red line), and difference (blue line) profiles are shown. The set of green vertical lines corresponds to reflection positions.

Figure A. 12 .

 12 Figure A. 12. Rietveld refinement of a) SrErGa3O7 ordered melilite (Rp= 6.70% Rwp= 8.60%) (SPD data) and b) SrErGa3O7 disordered melilite (SPD data, Rp= 6.78% Rwp= 8.75 %). Observed (black dot), calculated (red line), and difference (blue line) profiles are shown. The set of green vertical lines corresponds to reflection positions.

Figure A. 13 .

 13 Figure A. 13. Rietveld refinement of a) SrHoGa3O7 ordered melilite (SPD data, Rp= 4.85% Rwp= 6.30%) and b) SrHoGa3O7 disordered melilite (lab data, Rp= 1.41% Rwp= 2.08%). Observed (black dot), calculated (red line), and difference (blue line) profiles are shown. The set of green vertical lines corresponds to reflection positions.

Figure A. 14 .

 14 Figure A. 14. Rietveld refinement of a) SrDyGa3O7 ordered melilite (lab data, Rp= 1.66% Rwp= 2.21%) and b) SrDyGa3O7 disordered melilite (lab data, Rp= 2.62% Rwp= 3.35%). Observed (black dot), calculated (red line), and difference (blue line) profiles are shown. The set of green vertical lines corresponds to reflection positions.

Figure A. 15 .

 15 Figure A. 15. Rietveld refinement of a) Ca3Ga1.5Zn0.25Ge4.25O14 (x = 0.25) (SPD data, Rp= 8.465% Rwp= 10.907%) and b) Ca3GaZn0.5Ge4.5O14 (x = 0.5) (SPD data, Rp= 7.617% Rwp= 9.506%). Observed (red dot), calculated (black line), and difference (blue line) profiles are shown. The set of green vertical lines corresponds to reflection positions.

Figure A. 16 .Figure A. 17 .Figure A. 18 .

 161718 Figure A. 16. Rietveld refinement of Ca3Ga0.5Zn0.75Ge4.75O14 (x = 0.75) (SPD data, Rp= 8.465% Rwp= 10.907%). Observed (red dot), calculated (black line), and difference (blue line) profiles are shown. The set of green vertical lines corresponds to reflection positions.

Figure A. 19 .Figure A. 20 .Figure A. 21 .

 192021 Figure A. 19. SPD data Rietveld refinement of the a) La1.3Ba0.7Ga3O7.15(x = 0.3) composition (Rwp= 10.91%, GOF= 1.51). b) La1.65Ba0.35Ga3O7.325 (x = 0.65) composition (Rwp= 7.12%, GOF= 1.27). In both panels red, black and blue data corresponds to the measured, calculated and difference curves, with green tick marks corresponding to the P4 ̅ 21m tetragonal melilite. In the (a) panel pink and purple tick marks corresponds to LaGaO3 perovskite and LaBa2Ga11O20 phase.

Figure A. 22 .

 22 Figure A. 22. SPD data Rietveld refinement of the a) La1.8Ba0.2Ga3O7.4 (x = 0.8) composition (Rwp= 8.98%, GOF= 1.35). b) La1.85Ba0.15Ga3O7.425 (x = 0.85) composition (Rwp= 10.37%, GOF= 1.64). In both panels red, black and blue data corresponds to the measured, calculated and difference curves, with green and orange tick marks corresponding to the P4 ̅ 21m and Ima2 melilites. Pink tick marks in panel (a) represents the La1.3Ba0.7Ga3O7.15 (x = 0.3) impurity indexation.

Figure A. 28 .

 28 Figure A. 28. Room temperature NPD HI data Rietveld refinement of the La1.9Ba0.1Ga3O7.45 (x = 0.9) composition.

Figure A. 34 .

 34 Figure A. 34. Final Rietveld refined NPD (HR) data of a) Ca5Ga6O14 (x = 0) (Rwp= 3.03% GOF= 1.00), and b) La0.25Ca4.75Ga6O14.125 (x = 0.25) (Rwp= 2.76% GOF= 0.90). Green tick marks correspond to the Ca5Ga6O14 and La0.25Ca4.75Ga6O14.125 structures panels (a) and (b) respectively, while the orange tick marks represent the CaO impurity quantified at ⁓0.19(6)% for x = 0 and ⁓0.69(9)% for x = 0.25 materials, both in weight%.

Figure A. 35 .

 35 Figure A. 35. a) and b) Fourier difference map section at z= 0.51 centered at the Ca3 channels from La0.25Ca4.75Ga6O14.125 NPD (HR) and NPD (HI) refined data respectively. One [GaO4]n sheet is overlayed in both a) and b) panels with dark grey and light grey spheres corresponding to Ga and O atoms. c) and d), 3Dprojection of the Fourier difference maps shown in a) and b) respectively.

(

  synthèses, structures…) et physiques (caractérisation des propriétés macroscopiques). La compréhension des liens entre ces deux aspects est importante pour le développement de nouveaux matériaux aux performances accrues. De récents travaux de recherche ont démontré la possibilité de prédire la structure cristalline ainsi que les propriétés physiques d'une composition chimique donnée par calculs DFT [1-4]. L'obstacle majeur rencontré après la prédiction du matériau (structure et/ou propriétés) est la synthèse de ce dernier, parfois impossible par des voies de synthèses classiques. En chimie du solide, la méthode de synthèse des matériaux inorganiques la plus répondue et la réaction à l'état solide. Cette voie de synthèse est simple à opérer, elle nécessite un fin broyage et un mélange homogène des réactifs. Pour mettre en oeuvre la réaction de ces derniers, des températures élevées (900°C ≤ T ≤ 1700°C) et de longs temps de chauffage sont requis. Dans certains cas, plusieurs traitements thermiques consécutifs avec broyages intermédiaires sont nécessaires pour une réaction complète. Ceci s'explique par l'énergie et le temps demandés par la migration des atomes au sein d'un grain d'un des précurseurs vers les joints de grains pour former de nouvelles liaisons et créer le nouveau composé. Par ailleurs, les hautes températures utilisées lors de la réaction amènent aux produits les plus stables thermodynamiquement [5], il est donc difficile d'atteindre des phases intermédiaires hors-équilibre. La Figure I.1 du chapitre I montre un comparatif de plusieurs voies de synthèse permettant de stabiliser des phases hors-équilibre et indiquant les avantages et les inconvénients de chacune d'entre elles. Au cours de cette thèse, les voies de synthèses assistées par fusion ont été utilisées, notamment une approche unique déployée au laboratoire CEMHTI : la lévitation aérodynamique couplée au chauffage laser (CO2). Cette technique consiste à préparer un mélange homogène par broyage manuel des poudres de précurseurs, puis à presser la poudre sous forme de pastille. La pastille est ensuite cassée en petits morceaux de 30 mg qui sont déposés sur une buse conique. Deux lasers CO2 dirigés par un jeu de miroirs (depuis le haut et le bas) chauffent l'échantillon qui lévite à l'aide d'un jet de gaz. La puissance des lasers est augmentée progressivement jusqu'à ce que l'échantillon atteigne l'état fondu, il est alors maintenu pendant quelques secondes dans cet état puis les lasers sont coupés, ce qui permet de refroidir très rapidement l'échantillon et possiblement de figer l'état désordonné du liquide fondu à l'état solide, formant ainsi un verre. Le verre étant un état métastable, la cristallisation peut être induite par un traitement thermique adéquat à des températures relativement basses (T ≤ 900°C), ce qui permet de stabiliser des phases cristallines intermédiaires hors-équilibre (Figure I.2 et Figure I.4 du chapitre I). Le suivi d'une telle procédure de synthèse a par exemple permis la découverte de la nouvelle phase cristalline BaAl4O7 avec une cristallisation contrôlée de deux nouveaux polymorphes α ou β [6]. Il est important de noter que cette nouvelle phase cristalline n'est pas accessible par réaction en phase solide. De plus, ce composé cristallisé en « bulk » a été répertorié comme la première céramique transparente synthétisée par cristallisation complète d'un verre massif [6]. Ces travaux ont motivé de nombreuses recherches sur les nouveaux matériaux transparents obtenus par cristallisation complète et congruente du verre pour des applications optiques, photoniques, énergétiques, etc (plusieurs exemples sont cités dans le chapitre I de ce manuscrit).

9 )

 9 Figure II.1). Cette mise en ordre est possible grâce à une certaine flexibilité du sous-réseau en couche de la mélilite formé par des tétraèdres d'oxyde de gallium (GaO4), où chaque GaO4 est lié par trois ou quatre de ses sommets. Dans ce travail de thèse, la synthèse de cette nouvelle phase a été réalisée avec succès pour deux autres terres rares RE = [Dy, Lu] par cristallisation à partir d'un précurseur vitreux de même composition, préalablement synthétisé par lévitation aérodynamique. L'étude thermique de ces composés par calorimétrie différentielle à balayage a permis de mettre en évidence les températures de transition vitreuses (Tg), cristallisation (Tc) mais aussi de transition de phase (P4 ̅ 21m → P21212). Grâce à cette étude, un traitement thermique différent du premier a été appliqué à de nouveaux échantillons vitreux et a permis de stabiliser la phase parent P4 ̅ 21m de la mélilite pour la série RE = [Dy-Yb / Y], non répertoriée précédemment pour l'ytterbium. La structure parent et la surstructure ordonnée de ces matériaux ont été finement étudiées par affinement Rietveld sur des données de diffraction des rayons x par rayonnement synchrotron et par microscopie électronique en transmission (STEM-HAADF et STEM-EDX). L'affinement Rietveld a mis en évidence la complexité de la mise en ordre des composés à l'Ho et à l'Er, pour lesquels les trois sites sont mixtes entre la terre rare et le strontium. Cependant, l'observation par MET du SrYGa3O7 à l'échelle atomique a montré la coexistence des deux polymorphes de la mélilite (P4 ̅ 21m + P21212) au sein du même grain (chapitre II, Figure II.11), ce qui expliquerait les occupations mixtes affinées par la méthode Rietveld. Un diagramme de stabilité entre les deux polymorphes de la mélilite a été tracé en combinant les résultats de la

L

  'intérêt porté au composé Ca5Ga6O14 est dû à sa structure cristalline de type mélilite. Ce composé cristallise dans une maille orthorhombique (groupe d'espace Cmc21) avec une structure en couche formée par deux feuillets [GaO4]n de type mélilite empilés de façon antiparallèle selon l'axe c. Cette différence d'empilement induit des contraints de liaisons sur les cations calcium des sites A ; par conséquent ces derniers sont décalés de leurs position ''idéale'' dans la maille vers les bords des pentagones [GaO4]5 sur la projection selon l'axe c (Figure V.1 et V.2, Chapitre V). La substitution du Ca ou du Ga par un cation aliovalent a été d'abord sondée par calculs DFT. Ces calculs ont déterminé que le lanthane est l'élément le plus favorable énergétiquement pour la stabilisation de la structure dopée. La synthèse de la solution solide LaxCa5-xGa6O14+x/2 a ainsi été étudiée par différents procédés : réaction à l'état solide, cristallisation à partir d'un verre ou du liquide surfondu et par méthode sol-gel. Parmi cette panoplie de méthodes, la synthèse par réaction solide s'est avérée la plus appropriée avec une substitution maximum de x = 0.25 et des taux de cristallinité améliorés. Une première analyse par DRX synchrotron a démontré que le désordre chimique entre La et Ca ne se localise que sur le site Ca3. Ce résultat s'explique par la structure locale du site Ca3 qui représente le plus de similarités avec la structure mélilite parent (canaux ouverts avec positionnement du Ca au centre). D'autres analyses par cartographie STEM-EDX du lanthane ainsi que l'analyse par méthode Rietveld de diffractogrammes neutrons ont confirmé ce résultat sur le désordre chimique entre La et Ca. Pour conserver la neutralité de charge de la composition après dopage, l'introduction de lacunes cationiques ou d'ions oxydes interstitiels est impérative. Des analyses par microsonde de Castaing et affinement des taux d'occupation des cations Ca et Ga sur les diffractogrammes rayons X synchrotron et neutron de la phase dopé (x = 0.25) n'ont pas indiqué un déficit en Ca ou en Ga, ce qui nous permet d'écarter la première hypothèse. L'hypothèse de l'introduction d'oxygènes interstitiels a été étudiée par carte de Fourier différence et par méthode de maximum entropie sur les diffractogrammes neutrons. Une perturbation de la structure locale du site Ca3 peut être clairement visualisée à travers les paramètres thermiques affinés des oxydes, mais aussi à travers la densité nucléaire reconstruite par calculs MEM. Par ailleurs, étant donné le faible taux de dopage, une augmentation de seulement 0.89% de la quantité d'oxygène est attendue, ce qui rend la localisation de ces derniers très difficile. La structure du composé dopé a finalement été prédite par calculs DFT indiquant la structure la plus énergétiquement stable. Ces calculs ont mis en évidence la présence d'oxydes interstitiels dans les canaux des sites Ca3 au niveau des feuillets [GaO4]n, totalement en accord avec les résultats obtenus sur la perturbation de la structure locale du site Ca3.

  d'abord la composition puis en effectuant une trempe avec des vitesses de refroidissement élevées (⁓ 300°C/s) tout en faisant léviter l'échantillon. Cette lévitation d'échantillons permet d'éviter la présence d'impuretés mais aussi de centres de nucléation qui induiraient une cristallisation hétérogène lors du refroidissement. Le verre obtenu est ensuite cristallisé par un traitement thermique adéquat (préalablement étudié par DSC et diffraction des rayons X in situ à des températures variables). L'utilisation de la lévitation aérodynamique comme outil de synthèse a permis aussi d'opérer la cristallisation des échantillons directement à partir du liquide surfondu, atteignant ainsi des nouvelles phases hors-équilibre. La cristallisation du verre a permis d'élargir la famille des mélilites (P4 ̅ 21m) avec des petites terres rares RE = Yb, mais aussi la famille des mélilites (P21212) a d'autres terres rares RE = Dy, Lu. La structure cristalline de ces deux polymorphes ainsi que leur stabilité thermique ont été étudiés, permettant le tracé d'un ''diagramme de phase'' indiquant le domaine de stabilité de chacun d'eux (chapitre II). Cette méthode de synthèse originale a permis aussi la synthèse de la nouvelle solution solide Ca3Ga2-2xZnxGe4+xO14 (0 ≤ x ≤ 1) cristallisant sous une symétrie P321 de la structure langasite (chapitre III). Le composé Ca3Ga2Ge4O14 (x = 0) a été aussi synthétisé par cristallisation directe du liquide surfondu avec des taux de cristallinité largement supérieur a ceux obtenues par cristallisation du verre. Cette deuxième technique de synthèse s'est révélé être le seul moyen de repousser les limites des dopants dans la solution solide La1+xBa1-xGa3O7+x/2 (0.35 ≤ x < 1), établie a x = 0.35 dans la littérature. Cette famille de compositions cristallise dans la famille des mélilites sous différent polymorphes : P4 ̅ 21m pour 0 ≤ x ≤ 0.725 et Ima2 pour 0.9 ≤ x. De ce fait, nous avons réussi à stabiliser à température ambiante la mélilite tétragonale P4 ̅ 21m avec la plus haute concentration en oxygènes interstitiels (i.e. La1.725Ba0.275Ga3O7.3625 x = 0.725).

Figure 1 .

 1 Figure 1. (a) Synchrotron powder diffraction data of the SrYbGa 3 O 7 melilite phase indexed with the P4̅ 2 1 m melilite substructure (blue marks) and in the 3 × 1 × 1 P2 1 2 1 2 superstructure (red marks). (b) [0-11]* and [001]* Selected Area Electron Diffraction patterns of the SrTmGa 3 O 7 melilite phase synthesized by full crystallization from glass. The indexations of the tetragonal melilite substructure (a = 7.9 Å × c = 5.2 Å, P4̅ 2 1 m) and the 3 × 1 × 1 superstructure (a = 23.7 Å × b = 7.9 Å × c = 5.2 Å, P2 1 2 1 2) are shown in blue and red, respectively. The arrows point to the reflections assigned to double diffraction.

Figure 2 .

 2 Figure 2. Combined Rietveld refinement of SPD (a) and NPD (b) data on cation-ordered SrYbGa 3 O 7 melilite at room temperature (R p = 3.772%, R wp = 4.427%). Observed (red points), calculated (black line), and difference (blue line) profiles are shown. The green tick marks correspond to allowed reflection positions.

3. 3 .

 3 Atomic-Scale Imaging of the 3 × 1 × 1 Superstructure (RE = Yb). The Rietveld refinements of SrYbGa 3 O 7 provide an average structural model describing the superstructure with three distinct crystallographic A sites (one fully occupied by Yb, one fully occupied by Sr, and one shared equally by Sr and Yb), but it may not provide an accurate picture of the local Yb/Sr distribution on the nanometer scale.

Figure 3 .

 3 Figure 3. [001] projections of (a) the cation-ordered 3 × 1 × 1 melilite superstructure of SrYbGa 3 O 7 , with GaO 4 tetrahedra in blue, Sr in green, and Yb in red. (b) The parent melilite structure of SrLaGa 3 O 7 , with the disordered Sr/La site in black/white. (c-e) Histograms showing the distribution of refined A-O distances in SrYbGa 3 O 7 for Yb (red), Sr/Yb (patterned green/red), and Sr (green) sites. Each histogram is overlaid with the published A-O distances of the undistorted SrLaGa 3 O 7 parent phase (patterned black/white bars).

Figure 4 .

 4 Figure 4. (a) Atomic scale STEM-HAADF micrograph of the SrYbGa 3 O 7 superstructure sample oriented along the [001] zone axis. The hexagonal ABA′ tiling, from the discussion in section 4.1,i s overlaid to highlight the superstructure (Ga, Yb1/Sr1, Yb2, and Sr3 atoms are respectively represented in blue, red, green/red, and green). The green framed inset corresponds to a STEM-HAADF simulated image by JEMS software. (b) Experimental profile corresponding to the red framed box area. (c) Distribution of the calculated atomic number (Z) from the measured peak volumes for each crystallographic site (Yb1/Sr1, Yb2, and Sr3).

3 . 4 .× 1 ×

 341 Thermal Stability and Structural Phase Diagram Across the Series RE =T b -Lu, Y. The occurrence of the 3 1 superstructure as a function of composition (RE = Tb-Lu, Y) and temperature were mapped by a combination of in situ high-temperature PXRD and thermal analysis by DSC.

Figure 5 .

 5 Figure 5. Atomic-scale STEM-EDS elemental maps of the cations (a) Yb (red), (b) Sr (green), (c) Ga (blue), and (d) the overlaid EDS maps showing the mixed sites (50:50 Yb1/Sr1) in red/green highlighted by yellow arrows. (e) SrYbGa 3 O 7 superstructure projection of the cationic sites along the [001] axis. Ga atoms are drawn in blue, Sr3 sites in green, Yb2 sites in red, and the mixed sites (50/50 Yb1/Sr1) in red/green. (f) STEM-HAADF image of the SrYbGa 3 O 7 superstructure along the [001] zone axis. On all the images, the yellow arrows highlight the mixed Yb1/Sr1 sites (50/50 average occupancy).

Figure 6 .

 6 Figure 6. Variable temperature powder X-ray diffraction (VT-PXRD) on SrREGa 3 O 7 (RE = Tb-Lu, Y) on heating and cooling, starting from the precursor glasses. Peaks representing the initial melilite (substructure) crystallization, the 3 × 1 × 1 structural ordering (superstructure), and the onset of decomposition are indicated, respectively, by triangle, diamond, and square symbols. Note that the maximum intensities of the decomposition peaks are between 1 and 3% (Tb, Dy, Ho, Er, Y) or 5 and 8% (Tm, Yb) of the most-intense melilite peak, while Lu decomposed substantially (∼50%). Peaks labeled † arise from the alumina sample holder. The precursor glass for RE = Lu contained a small amount of crystallized melilite, indicated by ‡.

3 . 5 .

 35 Structural Trends Across the Series RE =D y -Lu, Y. The structural model derived for SrYbGa 3 O 7 was used as a template for Rietveld refinement of the 3 × 1 × 1 superstructure polymorphs of RE = Ho, Er, Tm, and Lu

Figure 7 .

 7 Figure 7. Differential scanning calorimetry (DSC) measurements of SrREGa 3 O 7 (RE =T b -Lu, Y) glass composition, where T g ,T c , and T o are glass transition, crystallization, and ordering temperatures, respectively. (a) Heating plots using a 10 °C/min heating rate from room temperature to 925 °C. (b) Cooling plots using a 10 °C/min cooling rate from 925 °C to room temperature.

Figure 8 .

 8 Figure 8. SrREGa 3 O 7 phase diagram showing the maximum extent of the 3 × 1 × 1 superstructure domain, as a function of temperature and A-site ionic radius ratio. The points for RE =T b -Lu, Y are drawn from DSC and VT-PXRD results (this work), while the region RE = La-Gd is drawn from the literature. 6

Figure 9 .

 9 Figure 9. Near infrared emission band of the SrErGa 3 O 7 glass and ordered and disordered ceramics powdered samples, under excitation at 520 nm (Xe lamp source). Data were collected under strictly the same conditions.

Figure 10 .

 10 Figure 10. Long-range structural ordering in SrYbGa 3 O 7 . (a) The experimentally observed arrangement of RE2 sites on a pseudohexagonal sublattice which maximizes their separation. (b) The experimentally observed structure viewed as a hexagonal tiling with two tile types in a striped ABA′ arrangement. (c) The tiles A, B, and C can be combined to produce the hypothetical half-ordered AA′ (=BC) structure, the hypothetical fully ordered BB structure, and the disordered CC structure (parent melilite). The fractional population of each site is shown next to each structure. Note that BB contains pairs of edge-sharing RE2 sites (black outline), while AA′ contains a low population of RE2 sites (1/4). The intergrowth of AA′ and BB fragments to form ABA′ eliminates RE2-RE2 edge-sharing by reducing the population of RE2 sites to an intermediate value (1/3).

Figure 11 .

 11 Figure 11. Phase diagram indicating the different structural orderings reported for the (AE,RE)Ga 3 O 7 melilite family, according to the ionic radii of their A site cations. The parent structure and 5D-modulated structure regions have been compiled from the literature.6,8,12 Note that the parent structure region for AE = Ca, marked with an asterisk, was reported prior to the discovery of structural modulation in CaLaGa 3 O 7 and CaNdGa 3 O 7 .

Figure S1 .

 S1 Figure S1. Laboratory X-ray powder diffraction data of SrREGa3O7 (RE = Tb-Lu, Y) glass samples synthesized by aerodynamic levitation coupled to laser heating (ADL).

Figure S2 .

 S2 Figure S2.In situ X-ray powder diffraction data of the nominal SrYbGa3O7 composition recorded from 500°C up to 1500 °C (no phase modification occurs between room temperature and 500°C). The different colors correspond to the indexation of SrCO3 (black), Yb2O3 (blue), Ga2O3 (green), SrGa2O4 (pink) and Yb3Ga5O12 (purple). From room temperature to 900°C only the SrCO3, Yb2O3 and Ga2O3 precursors are present. At 900°C SrCO3 reacts with Ga2O3 to form SrGa2O4. At 1250°C Yb2O3 and residual Ga2O3 react to form the Yb3Ga5O12 garnet and the other crystalline phases melt from 1350°C.

Figure S3 .

 S3 Figure S3. (a) Photograph of the SrREGa3O7 polished glass and ceramic materials (from Boyer et al., J. Mater. Chem. C, 2016, 4, 3238). (b) Bright field TEM micrograph of the SrYbGa3O7 transparent ceramic showing a wide grain size distribution and the absence of residual glass, porosity or secondary phase.

Figure S4 .

 S4 Figure S4.[001]* Selected Area Electron Diffraction pattern of disordered SrTmGa3O7 melilite parent synthesized by rapid quenching from the high-temperature disordered domain. The indexation of the classic tetragonal melilite structure (a=7.9 Å x c = 5.2 Å, P-421m) is reported and the arrows point the reflections assigned to double diffraction.

Figure S5 .

 S5 Figure S5. Post-DSC PXRD data of SrREGa3O7, where black and dark blue tick marks correspond to the P21212 3x1x1 ordered superstructure (exhibited by RE = Dy -Lu, Y) and the P-421m disordered structure (exhibited by SrTbGa3O7 only) respectively.

Figure S6 .

 S6 Figure S6. Glass, ordered and disordered melilite SrREGa3O7 (RE =Tb -Lu, Y) domains of stability on (a) heating and (b) cooling at rates of 10°C min -1 , drawn from DSC results (Figure 7, main manuscript) and PXRD measurements performed post-DSC (Figure S5).

Figure S7 .Figure S8 .Figure S9 .

 S7S8S9 Figure S7. Rietveld refinement of a) disordered SrYbGa3O7 (laboratory PXRD data, Rp = 2.87% Rwp = 3.83%) and b) disordered SrTmGa3O7 (SPD data, Rp = 6.36% Rwp = 8.32%). Observed (black dot), calculated (red line), and difference (blue line) profiles are shown. The set of green vertical lines corresponds to reflection positions.

Figure S10 .

 S10 Figure S10. Rietveld refinement of a) SrTmGa3O7 (Rp = 5.28% Rwp = 7.06%) and b) SrErGa3O7 (Rp = 6.70% Rwp = 8.60%) ordered melilites (SPD data). Observed (black dot), calculated (red line), and difference (blue line) profiles are shown. The set of green vertical lines corresponds to reflection positions.

Figure S11 .

 S11 Figure S11. Rietveld refinement of a) SrHoGa3O7 (Rp = 4.85% Rwp = 6.30%) and b) SrLuGa3O7 (Rp = 6.87% Rwp = 9.18%) ordered melilites (SPD data). Observed (black dot), calculated (red line), and difference (blue line) profiles are shown. The set of green vertical lines corresponds to reflection positions.

Figure S12 .

 S12 Figure S12. Rietveld refinement of SrDyGa3O7 ordered melilite (laboratory data, Rp = 1.66% Rwp = 2.21%). Observed (black dot), calculated (red line), and difference (blue line) profiles are shown. The set of green vertical lines corresponds to reflection positions.

Figure S13 .

 S13 Figure S13. [001]* HRTEM image and associated FFTs of the SrYGa3O7 melilite parent synthesized by full crystallization from glass. Disordered classic tetragonal P-421m melilite structure and ordered 3x1x1 P21212 melilite supercell coexist like close neighboring nanodomains.

Figure S14 .

 S14 Figure S14. Evolution of the unit cell volume across the SrREGa3O7 (RE = Dy -Lu) series. RE = Dy was chosen as V0. The cell volume for SrLaGa3O7 is added for comparison.

Figure S15 .Figure S16 .

 S15S16 Figure S15. Optical transmission windows of the SrHoGa3O7 (a), SrErGa3O7 (b), SrTmGa3O7 (c), and SrYbGa3O7 (d) glass and ceramic melilites, recorded by UV-visible-NIR and FTIR transmission spectroscopies and normalized for 1 mm thickness 27 .

Figure S17 .

 S17 Figure S17. Emission photoluminescence spectra recorded on polished bulk SrErGa3O7 glass and ceramic melilites, under 520 nm excitation wavelength (from Xe lamp). Data were collected in the strictly same conditions.

  Stabilization of the Trigonal Langasite Structure in Ca 3 Ga 2-2x Zn x Ge 4+x O 14 (0 ≤ x ≤ 1) with Partial Ordering of Three Isoelectronic Cations Characterized by a Multitechnique Approach 1. INTRODUCTION

Figure 1 .

 1 Figure 1. Crystal structure projection of the A 3 BC 3 D 2 O 14 langasite structure family along the (a) c-axis and (b) b-axis, showing both the P321 cell (straight black lines) and C2 cell (dashed black lines).

Figure 2 .

 2 Figure 2. (a) Variable temperature PXRD measurements on the Ca 3 ZnGe 5 O 14 x = 1 glass composition showing its crystallization upon heating (0.5 °C/min heating rates), where * and † represent the CaZnGe 2 O 6 and Ca 2 ZnGe 2 O 7 impurities, respectively. Green tick marks represent the P321 Ca 3 ZnGe 5 O 14 indexation. (b) DSC measurements of Ca 3 Ga 2-2x Zn x Ge 4+x O 14 x = 0 (black), 0.25 (red), 0.5 (blue), 0.75 (green), and 1 (purple) samples, using a 10 °C/min rates upon heating.

3. 2 .

 2 Structure Evolution from 0 ≤ x ≤ 1b y Synchrotron XRD. The reported Ca 3 ZnGe 5 O 14 monoclinic langasite structure (SG. C2, a = 13.938(5) Å, b = 7.941(3) Å, c = 5.0560(

Figure 3 .

 3 Figure 3. (a) Synchrotron powder diffraction data from Ca 3 Ga 2-2x Zn x Ge 4+x O 14 x = 0 (black), 0.25 (red), 0.5 (blue), 0.75 (green), and 1 (purple), highlighting the systematic shift of the (100), (001), and (101)/(21̅ 0) peaks due to the Ga 3+ substitution by Zn 2+ and Ge 4+ . Dark blue tick marks correspond to Ca 3 Ga 2 Ge 4 O 14 (space group P321). (b) SPD pattern of glass-crystallized Ca 3 ZnGe 5 O 14 (purple) compared with a simulated pattern of the previously reported monoclinic C2s t r u c t u r e 14 (dark yellow), with their respective cell indexations (dark yellow and purple tick marks). (c) Normalized refined cell parameters (from Rietveld analysis) of the P321 langasite structure across the solid solution series to the parent Ca 3 Ga 2 Ge 4 O 14 cell parameters.

Figure 4 .

 4 Figure 4. NPD Rietveld refinements plots of (a) Ca 3 Ga 2 Ge 4 O 14 (x = 0), R p = 3.04%, R wp = 3.83%; (b) Ca 3 ZnGe 5 O 14 (x = 1), R p = 3.43%, R wp = 4.35%. Observed (red dot), calculated (black line), and difference (blue line) profiles are shown. The green tick marks correspond to allowed reflection positions.

Table 1 .a

 1 Refined Structural Parameters Obtained from NPD Data Collected at Room Temperature on Ca 3 Ga 2 Ge 4 O 14 (P321 Space Group, a = 8.0712(2) Å and c = 4.9680(2) Å) Constrained to refine to the same B iso values. b Fixed at 1 after its initial refined value converged to almost 1.

(7) aa

  Constrained to refine to the same B iso values. b Fixed at 1 after its initial refined value converged to almost 1.

Figure 5 .

 5 Figure 5. (a) Selected area electron diffraction (SAED) pattern of the Ca 3 GaZn 0.5 Ge 4.5 O 14 (x = 0.5) sample oriented along the [001]* direction, with (b) and (c) showing simulated (using JEMS software)32 and measured STEM-HAADF images, respectively. The corresponding crystal structure projection is overlaid on the top-right corner of the image, where blue, green, pink and orange points represent the 3e, 1a, 3f, and 2d crystallographic sites, respectively.

Figure 8 .

 8 Figure 8. STEM-EDS 2D refinement plots of Ge, Ga, and Zn from zone1, where the left column represents the data (after processing), the middle column fitted data (fit in black contours) and the difference plots in the right column.

Figure 9 .

 9 Figure 9. NPD Rietveld refinements plot of Ca 3 GaZn 0.5 Ge 4.5 O 14 (x = 0.5) R p = 2.97% R wp = 3.80%. Observed (red dot), calculated (black line), and difference (blue line) profiles are shown. The green tick marks correspond to allowed reflection positions.

Figure 10 .

 10 Figure 10. Refined M-O distances from SPD and NPD (hollow circles and filled squares, respectively) for compositions 0 ≤ x ≤ 1. (a) B-O3 (black), C-O2 (blue), and C-O3 (red) distances and (b) their corresponding polyhedral volumes BO 6 (1a, orange) and CO 4 (3f, green). (c) Cationic 1a and 3f site coordination and their nearby interatomic distances for both x = 0 and x = 1 compounds from NPD refinements.

Figure I. 1 .

 1 Figure I.1. In-situ powder X-ray diffraction (VT-PXRD) data of a CaCO 3 -Ga 2 O 3 -GeO 2 mixture, with respect of Ca 3 Ga 2 Ge 4 O 14 nominal composition, between room temperature and 1200°C. a) and b) inserts show the indexed diffraction patterns at room temperature and 1200°C, with the different color tickmarks corresponding to, CaCO 3 (black), Ga 2 O 3 (blue), GeO 2 (red), Ca 3 Ga 2 Ge 4 O 14 (green) and CaGeO 3 (orange).

Figure II. 1 .

 1 Figure II.1. 71 Ga NMR spectra acquired on sample of composition Ca 3 Ga 2 Ge 4 O 14 (x=0) by a MAS spin echo (green) and a QPASS (blue) experiments, showing the two coordination types of Ga in the sample.

1 Figure S1 .

 1S1 Figure S1. Variable temperature powder X-ray diffraction (VT-PXRD) measurements of, a) glass of composition Ca 3 Ga 2 Ge 4 O 14 (x=0), b) glass of a slightly deviated composition from Ca 3 Ga 2 Ge 4 O 14 (x=0) with an excess of 2.17% (%wt) of GeO2 added in the nominal composition. Green tickmarks represent the Ca 3 Ga 2 Ge 4 O 14 indexation.

Figure S2 .

 S2 Figure S2. Laboratory X-ray powder diffraction data of Ca 3 Ga 2-x Zn x Ge 4+x O 14 (x=0, 0.25, 0.5, 0.75, 1) glass samples synthesized by aerodynamic levitation coupled to laser heating (ADL).

12

 12

Figure S3 .

 S3 Figure S3. Crystallized Ca 3 Ga 2 Ge 4 O 14 (x=0) sample from a) glass at 820°C in an open atmosphere furnace, b) molten liquid on the ADL montage, by turning the lasers off while the droplet is touching the nozzle. Green tick marks represent Ca 3 Ga 2 Ge 4 O 14 indexation. c) the extracted FWHM's for each peak from a) and b).

Figure S6 .

 S6 Figure S6. SPD data of Ca 3 Ga 2-2x Zn x Ge 4+x O 14 x=0 (black), 0.25 (red), 0.5 (blue), 0.75 (green) and 1 (purple) compositions, with dark blue tickmarks corresponding to Ca 3 Ga 2 Ge 4 O 14 indexation.

Figure S7 .

 S7 Figure S7. Overlay between Rietveld refined C2 (black atoms) and P321 (green atoms) structures for the Ca 3 ZnGe 5 O 14 (x=1) composition against SPD data, along the c-axis.

Figure S9 .

 S9 Figure S9. Rietveld refinement of a) Ca 3 GaZn 0.5 Ge 4.5 O 14 (x=0.5) (SPD data, R p = 7.617% R wp = 9.506%) and b) Ca 3 Ga 0.5 Zn 0.75 Ge 4.75 O 14 (x=0.75) (SPD data, R p = 8.465% R wp = 10.907%). Observed (red dot), calculated (black line), and difference (blue line) profiles are shown. The set of green vertical lines corresponds to reflection positions.

Figure S10

 S10 Figure S10 Rietveld refinement of Ca 3 ZnGe 5 O 14 (x=1) SPD data against the hexagonal P321 cell, a) without strain (R p = 7.18% R wp = 8.93%), b) modelled strain (R p = 7.02% R wp = 8.75%). Observed (red dot), calculated (black line), and difference (blue line) profiles are shown. The set of green vertical lines corresponds to reflection positions.

Figure S11 .

 S11 Figure S11. Rietveld refinement of Ca 3 ZnGe 5 O 14 (x=1) SPD data against the monoclinic C2 structure, a) without strain (R p = 7.20% R wp = 8.93%), b) modelled strain (R p = 5.14% R wp = 6.68%). Observed (red dot), calculated (black line), and difference (blue line) profiles are shown. The set of green vertical lines corresponds to reflection positions.

Figure S12 .FigureFigure S14 .

 S12S14 Figure S12. Cell parameters evolution of the Ca 3 ZnGe 5 O 14 sample vs temperature.

Figure S15 .

 S15 Figure S15. Overlay contour map of Ca (red), Ga (black), Ge (green) and Zn (blue) extracted from STEM-EDS raw data after the mask application.

Figure S16 .

 S16 Figure S16. STEM-EDS 2D refinement plots of Ge, Ga and Zn from zone2 (zone 1 is shown in Figure 8 of the main text). The sample composition is Ca 3 GaZn 0.5 Ge 4.5 O 14 .

xGa6O14+x/ 2

 2 solid solutions. The La1+xBa1-xGa3O7+x/2 series was synthesised by direct crystallisation of their under-cooled melts. The series retained its parent tetragonal structure up to La1.725Ba0.275Ga3O7.3625 (x= 0.725), which is the highest interstitial oxide concentration ever observed in this polymorph. Despite its lower carrier concentration, tetragonal La1.6Ba0.4Ga3O7.15 (x= 0.6) member was found to exhibit the highest conductivity values at 500°C, matching the best known melilite conductors La1.64Ca0.36Ga3O7.32 and La1.54Sr0.46Ga3O7.27. In contrast, the LaxCa5-xGa6O14+x/2 series revealed a much lower substitution limit of x= 0.25 attained by solid-state reaction, with a 100x enhancement in conductivity upon La doping. The low substitution rate posed major challenges for the structural characterisation of these compositions, which were addressed by combining maximum-entropy analysis of neutron diffractograms with DFT-based structure prediction. Keywords: Crystallisation from glass / under-cooled melt at high temperatures, New metastable materials, Out of equilibrium materials, Structural analysis by Rietveld refinement, Atomic resolution transmission electronic microscopy.CEMHTI-CNRS UPR30791D Avenue de la Recherche Scientifique 45071 Orléans Cedex 2

  1.1.2). The samples melted around 1650°C, were held for several seconds at that temperature and then subsequently quenched by turning the lasers off (estimated cooling rates of 300°C/s); hence, achieving glass samples in the form of spherical beads. The amorphous state of the beads was confirmed by laboratory PXRD (see FigureII.3), and only SrLuGa3O7 showed a very small amount of crystallised melilite, distinct to what Marina Boyer reported in her PhD, as she obtained mainly crystalline beads at this composition[35].

Table II .1. Powder diffraction measurement conditions of the different synthesised melilite compositions.

 II

	RE		Dy, Y		Ho	Er
	Polymorph	Ordered	Disordered	Ordered	Disordered	Ordered	Disordered
	Technique	Lab	Lab	SPD	Lab	SPD	SPD
	Wavelength(Å) 1.5406	1.5406	0.414225	1.5406	0.414225	0.457874
	RE		Tm		Yb	Lu
	Polymorph	Ordered	Disordered	Ordered	Disordered	Ordered	Disordered
	Technique	SPD	SPD	SPD	Lab	SPD	--
	Wavelength(Å) 0.414225	0.414225	0.414225	1.5406	0.457874	--

Table II .2. Final Rietveld refinements relibility factors for all SrREGa3O7 RE= [Dy -Lu] compositions measured under both melilite polymorphs, except Lu.

 II

	RE	Dy		Ho		Er
	melilite P4 ̅ 21m	P21212	P4 ̅ 21m	P21212	P4 ̅ 21m	P21212
	Rp	2.62%	1.66%	1.41%	4.85%	6.72%	6.70%
	Rwp	3.35%	2.21%	2.08%	6.30%	8.71 %	8.60%
	GOF	1.19	1.73	5.16*	1.11	1.22	1.32
	RE	Tm		Yb		Lu
	melilite P4 ̅ 21m	P21212	P4 ̅ 21m	P21212	P21212
	Rp	6.36%	5.28%	2.87%	4.09	6.87%
	Rwp	8.32%	7.06%	3.83%	5.36	9.18%
	GOF	1.26	1.06	1.64	0.96	1.65

*high GOF values are due to over counted data (i.e. Rexp= 0.40%)

Table II .3. Summarised refined occupancies of all SrREGa3O7 RE= [Dy -Lu] compositions.

 II

	RE	melilite Occupancy A-site1	Occupancies A-site2	Occupancies A-site3
	Dy	P21212 0.50(1)Dy/0.50(1)Sr	0.90(1)Dy/0.10(1)Sr	0.10(1)Dy/0.90(1)Sr
	Ho P21212 0.499(2)Ho/0.501(2)Sr 0.924(2)Ho/0.076(2)Sr 0.076(3)Ho/0.924(3)Sr
	Er	P21212 0.504(3)Er/0.496(3)Sr	0.863(3)Er/0.137(3)Sr	0.132(4)Er/0.868(4)Sr
	Tm P21212 0.5Tm/0.5Sr	1Tm	1Sr
	Yb	P21212 0.5Yb/0.5Sr	1Yb	1Sr
	Lu	P21212 0.520(4)Lu/0.480(4)Sr 0.891(3)Lu/0.109(3)Sr 0.045(2)Sr/0.455(2)Lu ×2 a
	a : the ×2 means two sites with the same occupancies (split site model).

Table II .4. Final refined structural parameters obtained from SPD data collected at room temperature on the SrYbGa3O7 superstructure melilite (P21212 space group, a = 23.70181(6) Å, b = 7.92117(3) Å and c = 5.21167(1) Å).

 II

	Atom	Site	x	y	z	Occ	Biso
	Yb1/Sr1 4c	0.71965(3) 0.35610(7)	0.50561(11) 0.5/0.5	0.47(3) a
	Yb2	4c	0.61899(2) 0.69067(6)	0.45533(9)	1	0.77(2) a
	Sr3	4c	0.05797(4) 0.33969(11) 0.50854(18) 1	0.66(5) a
	Ga1	4c	0.94935(4) 0.35511(13) 0.9867(2)	1	0.31(2)
	Ga2	2a	0	0	-0.0245(4)	1	0.39(3)
	Ga3	4c	0.82689(5) 0.52010(13) 1.0016(3)	1	0.28(2)
	Ga4	4c	0.71054(4) 0.66505(13) 0.9532(2)	1	0.34(2)
	Ga5	4c	0.11862(5) 0.12302(12) 0.03042(19) 1	0.38(2)
	O1	4c	-0.0427(2) 0.1575(9)	-0.2062(12) 1	0.82(4) b
	O2	4c	0.8850(3)	0.4297(8)	0.8111(11)	1	0.82(4) b
	O3	4c	0.7083(2)	0.6649(9)	0.2992(10)	1	0.82(4) b
	O4	4c	0.9412(3)	0.3542(8)	0.3226(11)	1	0.82(4) b
	O5	4c	0.1275(3)	0.1117(7)	-0.3145(9)	1	0.82(4) b
	O6	2b	0	0.5	0.8478(16)	1	0.82(4) b
	O7	4c	0.7711(3)	0.5734(8)	0.7784(14)	1	0.82(4) b
	O8	4c	-0.0464(2) -0.1451(8)	0.1539(11)	1	0.82(4) b
	O9	4c	0.7966(3)	0.3709(9)	0.2280(14)	1	0.82(4) b
	O10	4c	0.8481(2)	0.7003(8)	0.2033(11)	1	0.82(4) b
	O11	4c	0.6527(3)	0.5512(8)	0.7981(10)	1	0.82(4) b

a Calculated from anisotropic refined values b Constrained to refine to the same value

Table II .5. Refined anisotropic thermal parameters from SPD data of the A-sites cations in the SrYbGa3O7 superstructure melilite compound.

 II

		B11	B22	B33	B12	B13	B23
	Yb1/Sr1	0.00024(1) 0.00233(9) 0.0027(3) 0.00025(3) 0.00024(5)	-0.0003(1)
	Yb2	0.00034(1) 0.00513(9) 0.0023(2) 0.00096(2) 0.00050(3)	0.0028(1)
	Sr3	0.00055(2) 0.0017(2)	0.0028(4) 0.00073(4) -0.00026(8)	0.0003(3)

Table II .6. Final refined structural parameter of SrYbGa3O7 disordered melilite (P𝟒 ̅ 21m space group, a= 7.91986(9) Å, and c = 5.21070(7) Å).

 II

	Atom	Site	x	y	z	Occ	Biso
	Yb1/Sr1 Ga1 Ga2	4e 2a 4e	0.33863(9) 0 0.14503(15)	0.16137(9) 0 0.35497(15)	0.5123(4) 0 0.9698(5)	0.5/0.5 1 1	2.78(4) 2.00(7) 2.28(6)
	O1	2c	0.5	0	0.179(2)	1	3.97(2) a
	O2	4e	0.1438(9)	0.3562(9)	0.2990(14)	1	3.97(2) a
	O3	8f	0.0932(7)	0.1615(8)	0.7782(15)	1	3.97(2) a
	a Constrained to refine to the same value

  The calculated average partial occupancies of the Sr and RE from the refined weight% of each of the two polymorphs falls in the same range as the initial refined ones using only the P21212 model to describe the whole pattern (see TableII.7).

5 for RE1/Sr1 site1, 1/0 for RE2/Sr2 site2 and 0/1 for RE3/Sr3 site3 (Rp= 9.32% Rwp= 11.37% for Er and Rp= 7.56% Rwp= 9.17% for Ho). It resulted in a 60.6(2) wt% / 39.4(2) wt% for Er and 89.48(4) wt% / 10.52(4) wt% for Ho mixed ordered / disordered melilites respectively.

Table II .7. Comparison between calculated and refined occupancies of Ho and Er melilites.

 II Calculated from the refined wt% of each polymorph from the both ideally ordered + disordered melilites refonements. 2 From Table A. 4 "Er" and Table A. 6 "Ho".

			Refinement of both ordered/disorder 1	Refined 2	Refinement of both ordered/disorder 1	Refined 2
	site	RE	Ho	Ho	Er	Er
	RE2/Sr2 0.947(1)/0.053(1)	0.924(2)/0.076(2)	0.803(3)/0.197(3)	0.863(3)/0.137(3)
	Sr3/RE3 0.947(1)/0.053(1)	0.924(3)/0.076(3)	0.803(3)/0.197(3)	0.868(4)/0.132(4)
	1

Table III .1. Refined structural parameters obtained from SPD data collected at room temperature on Ca3Ga2Ge4O14 (x = 0) (P321 space group, a= 8.072032(6) Å and c= 4.966435(5) Å) sample.

 III

	Atom	Position	x	y	z	Occ	Biso
	Ca Ga1/Ge1 Ga2/Ge2 Ge3 O1 O2 O3	3e 1a 3f 2d 2d 6g 6g	0.42012(7) 0 0.76255(3) 1/3 1/3 0.4652(2) 0.2144(2)	0 0 0 2/3 2/3 0.3154(2) 0.0795(2)	0 0 0.5 0.53090(8) 0.1914(4) 0.3180(2) 0.7626(3)	1 0.4/0.6* 0.47/0.53* 1 1 1 1	0.96(1) 0.608(7) 0.679(5) 0.593(6) 1.21(2) a 1.21(2) a 1.21(2) a
	*Fixed occupancy from

Table III .2. Refined structural parameters obtained from SPD data collected at room temperature on Ca3ZnGe5O14 (x = 1) (P321 space group, a= 8.02916(2) Å and c= 5.014362(17) Å) sample. Modelled strain.

 III Site was set to be fully occupied without refining each atom occupancy a : constrained to refine to the same Biso values.

	Atom	Position	x	y	z	Occ	Biso
	Ca Zn1/Ge1 Zn2/Ge2 Ge3 O1 O2 O3	3e 1a 3f 2d 2d 6g 6g	0.41841(8) 0 0.76499(4) 1/3 1/3 0.4671(2) 0.22055(19) 0.0773(2) 0 0 0 2/3 2/3 0.3189(2)	0 0 0.5 0.52849(11) 1 1 0.5/0.5* 0.17/0.83* 1.154(7) 1.16(1) 1.48(1) 1.009(9) 0.1919(6) 1 1.95(3) a 0.3233(3) 1 1.95(3) a 0.7504(3) 1 1.95(3) a

*

  Cell parameters evolution of the Ca3ZnGe5O14 sample vs temperatures on heating.

	trigonal polymorph and a possible monoclinic phase transition at high temperatures, VT-
	PXRD measurement were conducted on a previously glass crystallised sample from room
	temperature to 850°C (sample's decomposition temperature from VT-PXRD). The extracted
	cell parameters from the measured patterns vs T(°C) by Pawley refinements, shows a linear
	trend and no slope change was noticed until the sample decomposition. This trend was further
	confirmed by the a/c ratio which showed a monotonic decreasing tendency (see Figure III.13),
	with no appearance of C2 peaks on their related diffraction patterns. Therefore, the glass
	crystallised Ca3ZnGe5O14 (x =1) sample was assumed to retain its trigonal polymorph until it
	decomposes, with no apparent C2 phase transition.
								5.05
		8.1			a			0.6244
		8.09			c a/c			5.045	0.6242
		8.08						5.04	0.624
	a(Å)	8.06 8.07						5.03 5.035 c(Å)	0.6236 0.6238	a/c
		8.05						5.025	0.6234
								0.6232
		8.04						5.02	0.623
		8.03
		100	200	300	400	500	600	700
					T(°C)

Figure III.13.

Table III.3. Refined structural parameters obtained from NPD data collected at room temperature on Ca3Ga2Ge4O14 (P321 space group, a= 8.0712(2) Å and c= 4.9680(2) Å).

	Atom	Position x	y	z	Occ	Biso
	Ca Ga1/Ge1 Ga2/Ge2 Ge3 O1 O2 O3	3e 1a 3f 2d 2d 6g 6g	0.4183(7) 0 0.7635(4) 1/3 1/3 0.4616(5) 0.2174(4)	0 0 0 2/3 2/3 0.3144(4) 0.0793(4)	0 0 1/2 0.5273(9) 0.1843(11) 0.3113(6) 0.7667(6)	1 0.51(8)/0.49(8) 0.50(3)/0.50(3) 1 * 1 1 1	0.91(10) 0.92(5) a 0.92(5) a 0.92(5) a 1.18(4) b 1.18(4) b 1.18(4) b
	a,b : constrained to refine to the same Biso values.

Table III .4. Refined structural parameters obtained from NPD data collected at room temperature on Ca3ZnGe5O14 (P321 space group, a= 8.0308(3) Å and c= 5.0164(4) Å).

 III

	Atom	Position x	y	z	Occ	Biso
	Ca Zn1/Ge1 Zn2/Ge2 Ge3 O1 O2 O3	3e 1a 3f 2d 2d 6g 6g	0.4198(8) 0 0.7674(5) 1/3 1/3 0.4617(7) 0.2227(6)	0 0 0 2/3 2/3 0.3173(5) 0.0785(6)	0 0 1/2 0.5295(12) 0.1854(17) 0.3139(10) 0.7585(10)	1 0.52(4)/0.48(4) 0.16(1)/0.84(1) 1 * 1 1 1	1.18(13) 1.09(8) a 1.09(8) a 1.09(8) a 2.17(7) b 2.17(7) b 2.17

Table III .5. Comparison between the refined occupancies of Ga and Ge in the 1a, 3f and 2d sites from this work and Dudka's work [12] on the Ca3Ga2Ge4O14 (x = 0) compound.

 III

			This Work			Dudka et. al. [11]
	Site Atom	1a	3f	2d	1a	3f	2d
	Ga	0.51(8) 0.50(3) 0	0.2	0.6	0
	Ge	0.49(8) 0.50(3) 1	0.8	0.4	1

Table III .6. Cation oxide interatomic distances and bond valence sums calculated for all Ga and Ge sites of Ca3Ga2Ge4O14.

 III

	site	bond	length (Å)	site	bond	length (Å)	site	bond	length (Å)
	B(1a)	Ga1/Ge1-O3 x6 1.926(3) *BVS (Ga) 3.53(2) *BVS (Ge) 3.71(2)	C(3f)	Ga2/Ge2-O3 x2 1.787(4) Ga2/Ge2-O2 x2 1.853(5) *BVS (Ga) 3.37(2) *BVS (Ge) 3.49(2)	D(2d)	Ge3-O1 x1 1.704(7) Ge3-O2 x3 1.776(4) *BVS (Ga) 3.72(3) *BVS (Ge) 3.91(3)
	*Calculated with a distance cut-off at 3Å

Table III .7. Cation oxide interatomic distances and bond valence sums calculated for all Zn and Ge sites of Ca3ZnGe5O14.

 III

	site	bond	length (Å)	site	bond	length (Å)	site	bond	length (Å)
	B(1a)	Zn1/Ge1-O3 x6 1.984(6) *BVS (Zn) 2.74(2) *BVS (Ge) 3.17(2)	C(3f)	Zn2/Ge2-O3 x2 1.767(6) Zn2/Ge2-O2 x2 1.862(6) *BVS (Zn) 3.06(2) *BVS (Ge) 3.58(2)	D(2d)	Ge3-O1 x1 1.73(1) Ge3-O2 x3 1.770(6) *BVS (Zn) 3.29(3) *BVS (Ge) 3.89(4)
	*Calculated with a distance cut-off at 3Å

Table III

 III

	.8) a significant decrease representing 6.4% of
	the polyhedral volume can be spotted due to the shorter M-O bonds, consistent with a partial
	occupancy of the smaller Ge 4+ . As for the 3f site (notted Ge1 and Ge3 tetra sites in Table III.8)
	a slight increase of the tetrahedral volume can be noticed, also coherent with the refined partial
	occupancy of the bigger cations Zn 2+ . The 2d sites (notted Ge2 tetra site in Table III.8) on the
	other hand shows almost no polyhedral volume change, confirming their full occupancy by
	Ge 4+ cations in both structures.

Table III .8. Comparison between the reported C2 [2] and NPD refined P321 M-O bond of the Ca3ZnGe5O14 (x = 1) composition.

 III

		Reported C2	Refined P321
	Bond lengths (Å) V (Å 3 )	Zn1-O1* x2 Zn1-O4* x2 Zn1-O6* x2 Zn1* octa site 10.77(2) 2.10(1) 2.008(9) 1.992(8)	1.985(2) 1.985(2) 1.985(2) 10.08(2)
	Bond lengths (Å) V (Å 3 )	Ge1-O6* x1 Ge1-O2* x1 Ge1-O1* x1 Ge1-O7* x1 Ge1* tetra site 2.74(2) 1.731(8) 1.830(7) 1.718(10) 1.830(7)	1.740(1) 1.862(6) 1.740(1) 1.862(6) 2.86(2)
	Bond lengths (Å) V (Å 3 )	Ge3-O4* x2 Ge3-O3* x2 Ge3* tetra site 2.77(2) 1.749(9) 1.852(7)	1.862(6) 1.767(6) 2.86(2)
	Bond lengths (Å) V (Å 3 )	Ge2-O7* x1 Ge2-O5* x1 Ge2-O3* x1 Ge2-O2* x1 Ge2* tetra site 2.71(2) 1.768(6) 1.714(8) 1.767(7) 1.769(7)	1.770(7) 1.727(11) 1.770(7) 1.770(7) 2.74(2)
	*M-O atoms notation taken from C2 model, see Table III.9 for the P321 analogue atoms.

Table III .9. Atomic Wyckoff positions in the hexagonal P321 structure and their images in the monoclinic C2 cell.

 III

	Origin in P321	Analogue in C2
	Atom	Wyk. Pos.	Atom	Wyk. Pos.
	Ca1 Ge1/Zn1 Ge2/Zn2 Ge3 O1 O2 O3	3f 1a 3f 2d 2d 6g 6g	Ca1 Ca2 Zn1 Ge1 Ge3 Ge2 O5 O2 O3 O7 O1 O4 O6	2a 4c 2a 4c 4c 2b 4c 4c 4c 4c 4c 4c 4c
				82

Cationic disorder characterisation between Ga, Ge and Zn in the intermediate composition Ca3GaZn0.5Ge4.5O14 (x = 0.5).

Table III .11. Refined structural parameters obtained from NPD data collected at room temperature on Ca3GaZn0.5Ge4.5O14 (x = 0.5) (P321 space group, a= 8.0460(2) Å and c= 4.9994(2) Å) sample.

 III Constrained to refine to the same Biso values.

	Atom	Position x	y	z	Occ	Biso
	Ca Ga1/Ge1/Zn1 1a 3e Ga2/Ge2/Zn2 3f Ge3 2d O1 2d O2 6g O3 6g	0.4198(7) 0 0 0 0.7648(4) 0 1/3 2/3 1/3 2/3 0.4629(5) 0.3175(4) 0.3120(7) 0 0 1/2 0.5283(9) 0.1874(13) 1 1 0.25(2)/0.531(15)/0.22(3) 0.250(8)/0.656(5)/0.094(10) 0.98(6) a 1.12(11) 0.98(6) a 1 0.98(6) a 1.66(5) b 1 1.66(5) b 0.2208(5) 0.0788(4) 0.7631(7) 1 1.66(5) b
	a,b :

Table III .12. Refined occupancies for Zn, Ga and Ge on the 1a, 3f and 2d sites, extracted from NPD data and STEM-EDS maps.

 III

		Site Atom	1a	3f	2d
		Zn	0.22(3)	0.094(10)	0
	NPD Refinement	Ga	0.25(2)	0.250(8)	0
		Ge	0.531(15)	0.656(5)	1
		Zn	0.23(10) a	0.09(4) a	0
	1D Refinement	Ga	0.28(8) a	0.24(3) a	0
		Ge	0.57(5) a	0.64(2) a	1
	2D Refinement

Table IV .1. Summary of all compositions Rietveld refinements, including: reliability factors, cell parameters, weight fractions, and impurities weight fractions.

 IV Cell parameter of the Ima2 cell with the highest wt% b combined wt% of all Ima2 cells

	x	Rwp	GOF structure	a (Å)	b (Å)	c (Å)	wt%	impurities wt%
	0.3	10.91% 1.51 P4 ̅ 21m	8.12688(2)	= a	5.35114(1)	99.47	0.53
	0.6	8.16%	1.20 P4 ̅ 21m	8.08849(1)	= a	5.29991(1)	100	-
	0.65	7.12%	1.27 P4 ̅ 21m	8.08170(1)	= a	5.291514(8) 100	-
	0.675 7.81%	1.33 P4 ̅ 21m	8.07836(2)	= a	5.28703(1)	99.84	0.16
	0.7	10.41% 1.49 P4 ̅ 21m	8.07489(2)	= a	5.28269(1)	100	-
	0.725 11.78% 2.12 P4 ̅ 21m	8.07235(2)	= a	5.27953(2)	100	-
	0.75	9.11%	1.51	P4 ̅ 21m Ima2	8.06891(2) 11.43139(6)	= a 11.39361(5)	5.27513(2) 10.55194(4) 23.94 76.06	-
	0.775 10.01% 1.07	P4 ̅ 21m Ima2	8.06246(4) 11.43791(8) a 11.36654(8) a 10.5397(1) a 84.82 b = a 5.26941(5) 15.18	-
	0.8	8.98%	1.35	P4 ̅ 21m Ima2	8.06223(7) 11.45216(8)	= a 11.35246(7)	5.2685(1) 10.53719(5) 97.59 2.32	0.09
	0.85	10.37% 1.64	P4 ̅ 21m Ima2	8.0560(1) 11.46897(5)	= a 11.31829(4)	5.2614(2) 10.52236(3) 98.86 1.14	-
	0.9	13.21% 1.96 Ima2	11.47630(2)	11.2955(2)	10.50930(2) 99.98	0.08

a

Table IV .2. Cell parameters refinement strategy for the different defined orthorhombic and tetragonal cells.

 IV

	parameter Orthorhombic cell 1 (Ima2)	Orthorhombic cell 2 (Ima2)	Orthorhombic cell 3 (Ima2)	Orthorhombic cell 4 (Ima2)	Orthorhombic cell 5 (Ima2)	tetragonal cell (P4 ̅ 21m)
	a b c wt%	a1: freely refined b1: freely refined c1: freely refined 20.3(2)%	a1+shifta b1+shiftb c1+shiftc 21.1(2)%		a1+2*shifta b1+2*shiftb c1+2*shiftc 19.5(2)%		a1+3*shifta b1+3*shiftb c1+3*shiftc 11.8(2)%	a1+4*shifta b1+4*shiftb c1+4*shiftc 12.1(2)%	a6: freely refined a6: freely refined c6: freely refined 15.2(1)%
					wt% Tetra melilite	wt% Ortho melilite
			100
				90
				80
				70
				60
			%wt	50
				40
				30
				20
				10
				0
				0.3	0.4	0.5	0.6	x	0.7	0.8	0.9	1
					Yobs Ycalc		Yobs-Ycalc Bragg indexation
		Intesity(a.u.)
					30		31		32	33	34	35
		0		10		20	2(°)	30	40	50
										109

Figure IV.7. Extracted weight% of both tetragonal and orthorhombic melilites from the performed Rietveld refinements against SPD measured La1+xBa1-xGa3O7+x/2 (0.3 ≤ x ≤ 0.9) compositions. Figure IV.8. SPD data Rietveld refinement of the La1.6Ba0.4Ga3O7.3 (x = 0.6) composition (Rwp= 8.16%, GOF= 1.20). Where red, black, blue and green data represents the aquired, simulated, difference and model indexation (P4 ̅ 21m) data respectively.

  , scale factor, 11 background term, 6 profile parameters from a TCHZ profile function, axial divergence correction, 39 structural parameters) for each composition.Reliability factors, refined plots and structural parameters of the procedures described above are shown in TableIV.4, Figure IV.12 and Table IV.3 in the main text, and Figure A. 24 to Figure A. 28 and Table A. 35 to Table A. 52 respectively, in the appendices Chapter A.IV.

	La1.8Ba0.2Ga3O7.4 (x = 0.8): From previously measured SPD data, this composition
	exhibited a mixture between both P4 ̅ 21m and Ima2 melilite compounds. Hence, Rietveld
	refinements of neutron data were carried out using both structures. First the overall composition
	was constrained to not move too far from the nominal using a penalty function. Moreover,
	unlike the previously described x = 0.3 -0.7 compositions refinements, all the thermal
	parameters were refined as isotropic for both structures. After a first Rietveld run (until
	convergence was reached), the refined occupancies of La/Ba from the tetragonal structure
	yielded very high errors (i.e. occupancies of 0.8(9)La/0.1(9)Ba). This can be explained by the
	refine to the same value, to avoid negative refined thermal parameters. This approach generated
	87 independently refined parameter (zero shift, scale factor, 11 background term, 6 profile
	parameters from a TCHZ profile function, axial divergence correction, 67 structural
	parameters).

* See Chapter A.I section A.I.2.2.3 in the appendices for the definition of these data sets which come from the same measured 2D data. shiftrelatively low amount of tetragonal melilite (i.e. 14% for the HI data; 11% for the HR data, both in wt%). The A-site cations occupancies were then fixed to the nominal values for the tetragonal melilite only, while refining those from the orthorhombic polymorph. This provided the same fit to the data with unchanged reliability factors and weight fractions between the two melilite structures. Additionally, in the final Rietveld refinement, gallium atom isotropic thermal parameters were constrained to refine to a common value applied to both structures; the same restraint was applied to the oxygen atoms. By proceeding with such a refinement plan, the total amount of independently refined parameters was minimised to 98 (zero shift, 1*2 scale factor, 11 background term, 6*2 profile parameters from a TCHZ profile function, axial divergence correction, 55 + 16 structural parameters).

La1.9Ba0.1Ga3O7.45 (x = 0.9): In the SPD refinement of La1.9Ba0.1Ga3O7.45, only the orthorhombic (Ima2) melilite was found to be present in this composition diffraction pattern, with no strong evidence of the tetragonal (P4 ̅ 21m) melilite. Consequently, Rietveld refinements of the room temperature data were carried out using only the orthorhombic model. Here again, the only constraints applied to the system were the use of the penalty function to constrain the overall composition close to the nominal value (La/Ba and Oint occupancies refined). Moreover, in the final Rietveld refinement, thermal parameters of all gallium atoms were constrained to Figure IV.12. Room temperature NPD HR data Rietveld refinement of the La1.9Ba0.1Ga3O7.45 (x = 0.9) composition (Rwp= 4.84%, GOF= 2.02).

Table IV .3 Final NPD HR refinement of La1.9Ba0

 IV

	Atom	x	y	z	Occ	Biso
	La1/Ba1	-0.5862(2)	0.2504(8)	0.4858(4)	0.968(6)/0.028(10) 0.38(8)
	La2/Ba2	0.75	0.0870(6)	-0.0090(7)	0.894(18)/0.11(3)	0.3(2)
	La3/Ba3	0.75	0.4166(7)	-0.0364(7)	0.971(18)/0.04(3)	0.6(2)
	Ga1	-0.8857(3)	-0.2425(6)	0.2192(4)	1	0.43(4) a
	Ga2	0	0	0.2373(10)	1	0.43(4) a
	Ga3	0.5	0.5	0.2394(10)	1	0.43(4) a
	Ga4	0.75	-0.1067(7)	-0.2467(8)	1	0.43(4) a
	Ga5	0.25	0.0956(7)	0.2498(8)	1	0.43(4) a
	O1	-0.8870(4)	-0.2483(9)	-0.1078(5)	1	0.57(8)
	O2	-0.4760(7)	0.3659(6)	0.1444(8)	1	0.86(14)
	O3	-0.5396(6)	-0.3778(6)	-0.3728(8)	1	0.61(13)
	O4	-0.1258(6)	-0.0362(6)	-0.1581(8)	1	1.23(13)
	O5	-0.8907(6)	0.0614(6)	0.3481(7)	1	0.87(13)
	O6	0.75	0.2845(7)	0.1345(10)	1	1.47(18)
	O7	0.75	-0.1223(10) 0.0758(10)	1	0.8(2)
	O8	0.25	0.2487(12)	0.3279(7)	1	0.55(10)
	O9	0.25	0.1080(11)	0.5833(10)	1	0.61(19)
	O10	0.25	-0.0872(8)	0.2297(10)	0.878(17)	1

.1Ga3O7.45 (x = 0.9) composition structural parameters (S.G. Ima2, a= 11.46923(16) Å, b= 11.29077(17) Å, c= 10.50358(18) Å).

a Constrained to refine to the same value.

Table IV .4. Summary of the obtained reliability factors and weight fractions from the performed Rietveld refinements against NPD acquired data.

 IV 3.2.1, the overall composition was constrained to not move too far from the nominal values (La/Ba and Oint amounts). All gallium atoms isotropic displacement parameters were constrained to refine to the same value.

	x	T(°C)	Data set	Rwp	GOF	polymorph wt%
	This led to 87 independently refined parameters (zero shift, scale factor, 11 background term, 6 profile parameters from a TCHZ profile function, axial divergence correction, 67 structural parameters). 0.3 RT HI 3.15% 2,44 P4 ̅ 21m 100 HR 3.58% 1.57 100 P4 ̅ 21m 0.6 RT HI 2.73% 2.11 P4 ̅ 21m 100 HR 3.19% 1.39 100 P4 ̅ 21m 0.7 RT HI 2.88% 2.23 P4 ̅ 21m 100 HR 3.27% 1.43 P4 ̅ 21m 100 0.8 RT HI 3.67% P4 ̅ 21m 14.12 2.91 Ima2 85.88 HR 4.67% P4 ̅ 21m 11 2.08 Ima2 89
		RT	HI HR	3.77% 4.84%	2.79 2.02	Ima2 Ima2	100 100
		525	HI HR	3.11% 3.89	2.56 1.81	Ima2 Ima2	100 100
	0.9	720	HI HR	2.47% 3.20%	2.04 1.49	Ima2 P4 ̅ 21m Ima2 P4 ̅ 21m	64.17 35.83 65.89 34.11
		770 820	HI HR HI HR	2.90% 3.50% 2.87% 3.50%	2.37 1.61 2.34 1.61	Ima2 P4 ̅ 21m Ima2 P4 ̅ 21m P4 ̅ 21m P4 ̅ 21m	46.65 53.35 44.25 55.75 100 100

La1.9Ba0.1Ga3O7.45 (x = 0.9) at 720°C and 770°C: Final Rietveld refinements at these temperatures were performed using both tetragonal and orthorhombic cells to achieve the best possible description of the measured diffraction patterns. Both structures were subjected to their own individual compositional constrains. This yielded to a total of 118 refined parameters (zero shift, 1*2 scale factor, 11 background term, 6*2 profile parameters from a TCHZ profile function, axial divergence correction, 71 + 20 structural parameters). La1.9Ba0.1Ga3O7.45 (x = 0.9) at 820°C: The final measured temperature (820°C) neutron data was refined using only the P4 ̅ 21m melilite as a starting model. The overall composition was constrained by a penalty function (La/Ba and Oint amounts as described before). By operating a Rietveld refinement with the described conditions, the total number of independently refined parameters was 58 (zero shift, scale factor, 11 background term, 6 profile parameters from a TCHZ profile function, axial divergence correction, 38 structural parameters).

Rietveld refinements are summarised in Table

IV

.4. Refined plots and structural parameters of the procedures described above are shown in Figure A. 29 to Figure A. 32 and

Table A. 53 to Table A. 63 respectively, in the appendices Chapter A.IV. 123

Table V .1. Refined structural parameters obtained from SPD data collected at room temperature on Ca5Ga6O14. (x = 0) (Cmc21 space group, a= 11.47246(14) Å, b= 11.29197(14) Å and c= 10.50904(14) Å) sample.

 V

	Atom	Wyck x	y	z	Occ	Biso
	Ca1 Ca2 Ca3 Ga1 Ga2 Ga3 Ga4 O1 O2 O3 O4 O5 O6 O7 O8 O9	8b 8b 4a 8b 4a 4a 8b 8b 4a 8b 8b 4a 8b 4a 8b 4a	0.1581(2) 0.3570(2) 0 0.35656(9) 0 0 0.24473(12) 0.2842(6) 0 0.2665(7) 0.3722(7) 0 0.3415(5) 0 0.1285(6) 0	0.1023(2) 0.31652(19) 0.5248(3) 0.14580(12) 0.30107(15) -0.00041(15) 0.4644(3) 0.25 0.2004(3) 0.2448(4) 0.5088(3) 0.4422(3) 0.40228(10) 0.4764(3) 0.2793(6) 0.5855(7) 0.6104(8) 0.5776(9) 0.0277(5) 0.5955(7) 0.4361(6) 0.3773(7) 0.1437(9) 0.3805(9) 0.1463(6) 0.3408(7) 0.0080(8) 0.6334(11) 0.3726(6) 0.3621(7) 0.2944(8) 0.6167(10)	1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1	0.44(5) 0.54(5) 0.35(8) 0.27(3) 0.33(4) 0.51(4) 0.30(2) 0.13(5) a 0.13(5) a 0.13(5) a 0.13(5) a 0.13(5) a 0.13(5) a 0.13(5) a 0.13(5) a 0.13(5) a
	a Constrained to refine to a common value

Table V .2. Refined structural parameters obtained from SPD data collected at room temperature on La0.25Ca4.75Ga6O14.125 (x = 0.25) (Cmc21 space group, a= 11.47670(8) Å, b= 11.29646(11) Å and c= 10.51206(10) Å) sample.

 V

	Atom	Wyck x	y	z	Occ	Biso
	Ca1/La1 8b Ca2 8b Ca3/La3 4a Ga1 8b Ga2 4a Ga3 4a Ga4 8b O1 8b O2 4a O3 8b O4 8b O5 4a O6 8b O7 4a O8 8b O9 4a	0.1614(3) 0.3559(3) 0 0.35621(9) 0 0 0.24453(12) 0.40138(10) 0.4767(3) 0.1031(2) 0.25 0.3218(2) 0.2001(4) 0.5223(2) 0.2412(3) 0.14654(12) 0.5097(3) 0.29818(16) 0.4415(3) 0.00029(15) 0.4649(3) 0.2814(6) 0.2810(6) 0.5849(8) 0 0.6236(8) 0.5781(10) 0.2725(7) 0.0238(5) 0.5988(8) 0.3692(7) 0.4370(6) 0.3835(8) 0 0.1399(10) 0.3683(10) 0.3457(6) 0.1476(7) 0.3462(8) 0 0.0091(9) 0.6331(12) 0.1242(6) 0.3707(7) 0.3572(7) 0 0.2982(8) 0.6112(11)	0.990(3)/0.010(3) 1.52(8) 1 1.16(6) 0.756(4)/0.244(4) 0.90(8) 1 0.38(3) 1 0.36(4) 1 0.37(4) 1 0.31(2) 1 0.37(5) a 1 0.37(5) a 1 0.37(5) a 1 0.37(5) a 1 0.37(5) a 1 0.37(5) 1 0.37(5) a 1 0.37(5) a 1 0.37(5) a
	a Constrained to refine to a common value

  Table V.3 and Table A.70 in the appendices Chapter A.V. On the other extreme of the solid solution, the x = 0.25 composition, a first analysis of the refined structural parameters indicates a lower La content from both data sets (see Table A. 74). In comparison with the La content obtained from SPD data, this difference can be explained by the bigger scattering contrast between Ca and La atoms on X-ray diffraction (ZCa= 20 vs ZLa= 57) compared to neutron diffraction (Ca bc= 4.10(2) fm vs La bc= 8.24(4) fm) [27]. Refinement of NPD data were run, this time with the La content being subject of constraints, refining to values close to the nominal composition by the use of a penalty function (see Figure V.14b and Figure A. 34b in the appendices Chapter A.V for refined plot andTable V.4 and Table A. 71 in the appendices Chapter A.V for refined structural parameters) (see also Table A. 74).

Table V .3. Final Refined structural parameters obtained from NPD (HR) data collected at room temperature on

 V

	Atom	Wyck x	y	z	Occ	Biso
	Ca1 Ca2 Ca3 Ga1 Ga2 Ga3 Ga4 O1 O2 O3 O4 O5 O6 O7 O8 O9	8b 8b 4a 8b 4a 4a 8b 8b 4a 8b 8b 4a 8b 4a 8b 4a	0.1585(4) 0.3576(4) 0 0.3557(2) 0 0 0.2449(2) 0.2850(3) 0 0.2678(3) 0.3730(3) 0 0.3396(2) 0 0.1271(3) 0	0.1018(3) 0.3159(3) 0.5248(5) 0.1466(2) 0.2992(3) -0.0008(3) 0.4023(2) 0.2776(3) 0.6163(4) 0.0272(3) 0.4352(3) 0.1455(4) 0.1495(3) 0.0083(4) 0.3733(3) 0.2987(4)	0.25 0.2033(6) 0.2455(7) 0.5102(5) 0.4429(5) 0.4667(5) 0.4789(5) 0.5858(5) 0.5752(6) 0.5942(6) 0.3817(6) 0.3831(6) 0.3384(5) 0.6393(7) 0.3667(6) 0.6154(6)	1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1	0.55(6) 0.59(7) 0.77(11) 0.14(4) 0.15(6) 0.32(7) 0.11(4) 0.47(5) 0.74(8) 0.56(6) 0.34(5) 0.45(7) 0.32(5) 0.67(8) 0.71(6) 0.51(9)

Ca5Ga6O14 (x = 0) (Cmc21 space group, a= 11.50417(11) Å, b= 11.27557(10) Å and c= 10.48616(10) Å) sample.

Table V .4. Final Refined structural parameters obtained from NPD (HR) data collected at room temperature on La0.25Ca4.75Ga6O14.125 (x = 0) (Cmc21 space group, a= 11.47246(14) Å, b= 11.29197(14) Å and c= 10.50904(14) Å) sample. La content was constrained to refine near the nominal value, which led a refined composition of: La0.27(6)Ca4.73(6)Ga6O14. Note that the composition is not charge balanced due to the interstitial oxide not added to the structure.

 V

	Atom	Wyck x	y	z	Occ	Biso
	Ca1/La1 8b Ca2 8b Ca3/La3 4a Ga1 8b Ga2 4a Ga3 4a Ga4 8b O1 8b O2 4a O3 8b O4 8b O5 4a O6 8b O7 4a O8 8b O9 4a	0.1576(5) 0.3562(5) 0 0.3562(2) 0 0 0.2432(3) 0.2839(3) 0 0.2725(3) 0.3726(4) 0 0.3405(3) 0 0.1267(4) 0	0.1014(5) 0.3170(5) 0.5220(6) 0.1470(3) 0.2975(4) 0.0003(4) 0.4020(3) 0.2778(3) 0.6239(6) 0.0247(3) 0.4350(3) 0.1461(5) 0.1482(4) 0.0095(6) 0.3718(4) 0.3015(5)	0.25 0.2042(8) 0.2426(8) 0.5112(6) 0.4437(7) 0.4685(7) 0.4799(6) 0.5848(7) 0.5750(8) 0.5955(7) 0.3824(7) 0.3820(7) 0.3397(7) 0.6393(8) 0.3658(7) 0.6135(9)	0.96(2)/0.04(2) 1 0.81(3)/0.19(3) 1 1 1 1 1 1 1 1 1 1 1 1 1	1.93(14) 1.78(10) 0.88(15) 0.23(5) 0.59(8) 0.39(8) 0.33(5) 0.68(6) 1.99(12) 0.76(7) 0.79(8) 0.48(9) 0.54(7) 0.98(11) 1.30(9) 1.16(12)

Table A . 2. Final refined structural parameters obtained from SPD data collected at room temperature on the SrTmGa3O7 superstructure melilite (P21212 space group, a = 23.74405(8) Å, b = 7.92635(3) Å and c = 5.21619(2) Å).

 A

	Atom	Site	x	y	z	Occ	Biso
	Tm1/ Sr1 4c	0.21996(3)	0.14458(8)	0.49507(13)	0.5/0.5	0.472(12)
	Tm2	4c	0.38119(2)	0.31222(6)	0.45491(10)	1	0.545(10)
	Sr3	4c	0.05781(4)	0.33948(13)	0.5090(2)	1	0.68(2)
	Ga1	4c	0.44927(5)	0.14431(16)	0.0101(3)	1	0.40(2)
	Ga2	2a	0	0	0.9800(4)	1	0.38(3)
	Ga3	4c	0.17290(6)	0.48152(15)	0.9992(3)	1	0.28(2)
	Ga4	4c	0.28920(5)	0.33617(15)	0.9518(2)	1	0.23(2)
	Ga5	4c	0.11827(6)	0.12410(14)	0.0312(2)	1	0.34(2)
	O1	4c	0.4575(3)	0.3414(10)	0.2031(14)	1	1.02(4) a
	O2	4c	0.3860(3)	0.0699(9)	0.1978(14)	1	1.02(4) a
	O3	4c	0.2907(3)	0.3382(10)	0.3003(12)	1	1.02(4) a
	O4	4c	0.4439(3)	0.1450(10)	0.6755(13)	1	1.02(4) a
	O5	4c	0.1282(3)	0.1206(9)	0.6855(11)	1	1.02(4) a
	O6	2b	0.5	0	0.1570(18)	1	1.02(4) a
	O7	4c	0.2258(3)	0.4230(10)	0.7708(17)	1	1.02(4) a
	O8	4c	0.0482(3)	0.1424(10)	0.1656(14)	1	1.02(4) a
	O9	4c	0.2982(3)	0.1308(10)	0.7806(17)	1	1.02(4) a
	O10	4c	0.1519(3)	0.3020(10)	0.1986(14)	1	1.02(4) a
	O11	4c	0.3467(3)	0.4558(10)	0.7984(12)	1	1.02(4) a
	a Constrained to refine to the same value

Table A . 3. Final refined structural parameters of the SrTmGa3O7 disordered melilite (P𝟒 ̅ 21m space group, a = b = 7.92455(3) Å, and c = 5.21558(2) Å).

 A

	Atom	Site	x	y	z	Occ	Biso
	Tm1/Sr1	4e	0.33812(3)	0.16188(3)	0.51362(10)	0.5/0.5	1.783(8)
	Ga1	2a	0	0	0		1.08(2)
	Ga2	4e	0.14401(4)	0.35599(4)	0.96889(14)		1.07(1)
	O1	2c	0.5	0	0.1854(11)		3.31(5) a
	O2	4e	0.1418(3)	0.3582(3)	0.3109(6)		3.31(5) a
	O3	8f	0.0956(3)	0.1603(3)	0.7952(6)		3.31(5) a

a Constrained to refine to the same value

Table A . 4. Final refined structural parameters obtained from SPD data collected at room temperature on the SrErGa3O7 superstructure melilite (P21212 space group, a = 23.7790

 A

	Atom	Site	x	y	z	Occ	Biso
	Er1/ Sr1	4c	2.400(12)	2.400(12)	2.400(12)	0.504(3)/0.496(3) 0.64(2)
	Er2/ Sr2	4c	2.431(12)	2.431(12)	2.431(12)	0.863(3)/0.137(3) 0.449(17)
	Sr3/Er3	4c	0.05550(6) 0.33884(18)	0.5025(3)	0.868(4)/0.132(4) 0.90(3)
	Ga1	4c	0.44958(8) 0.1445(2)	0.0139(3)	1	0.32(3)
	Ga2	2a	0	0	0.9854(7)	1	0.35(4)
	Ga3	4c	0.17125(8) 0.4862(2)	0.0016(6)	1	0.27(3)
	Ga4	4c	0.28803(7) 0.3416(2)	0.9573(3)	1	0.26(3)
	Ga5	4c	0.11858(9) 0.1279(2)	0.0331(3)	1	0.29(3)
	O1	4c	0.4580(5)	0.3503(15)	0.195(2)	1	0.88(6) a
	O2	4c	0.3834(5)	0.0776(13)	0.206(2)	1	0.88(6) a
	O3	4c	0.2903(4)	0.3408(14)	0.3119(17) 1	0.88(6) a
	O4	4c	0.4425(5)	0.1491(15)	0.6797(18) 1	0.88(6) a
	O5	4c	0.1279(6)	0.1195(13)	0.6936(15) 1	0.88(6) a
	O6	2b	0.5	0	0.152(2)	1	0.88(6) a
	O7	4c	0.2276(5)	0.4305(14)	0.768(2)	1	0.88(6) a
	O8	4c	0.0489(5)	0.1335(14)	0.170(2)	1	0.88(6) a
	O9	4c	0.2989(5)	0.1465(15)	0.785(2)	1	0.88(6) a
	O10	4c	0.1491(5)	0.3086(14)	0.195(2)	1	0.88(6) a
	O11	4c	0.3441(5)	0.4570(13)	0.7905(16) 1	0.88(6) a
	a Constrained to refine to the same value

(1) Å, b = 7.93013(4) Å and c = 5.22786(2) Å).

Table A . 5. Final refined structural parameters of the SrErGa3O7 disordered melilite (P𝟒 ̅ 21m space group, a = b = 7.93227(2) Å, and c = 5.22367(2) Å).

 A

	Atom	Site	x	y	z	Occ	Biso
	Er1/Sr1	4e	0.33837(2)	0.16163(2)	0.51404(8)	0.5/0.5	1.670(6)
	Ga1	2a	0	0	0		1.09(1)
	Ga2	4e	0.14408(4)	0.35592(4)	0.96875(12)		1.06(1)
	O1	2c	0.5	0	0.1852(9)		3.18(5) a
	O2	4e	0.1414(3)	0.3586(3)	0.3095(5)		3.18(5) a
	O3	8f	0.0944(3)	0.1603(3)	0.7932(5)		3.18(5) a

a Constrained to refine to the same value

Table A . 6. Final refined structural parameters obtained from SPD data collected at room temperature on the SrHoGa3O7 superstructure melilite (P21212 space group, a = 23.8034(1) Å, b = 7.93800(4) Å and c = 5.23828(2) Å).

 A

	Atom	Site	x	y	z	Occ	Biso
	Ho1/ Sr1	4c	0.21976(4)	0.14841(10)	0.49652(14) 0.499(2)/0.501(2) 0.63(2)
	Ho2/Sr2	4c	0.38174(3)	0.31544(8)	0.45774(11) 0.924(2)/0.076(2) 0.57(1)
	Sr3/ Ho3	4c	0.05660(5)	0.33980(16)	0.5059(2)	0.924(3)/0.076(3) 1.15(3)
	Ga1	4c	0.44942(6)	0.14477(19)	0.0122(3)	1	0.57(3)
	Ga2	2a	0	0	0.9842(5)	1	0.61(4)
	Ga3	4c	0.17200(6)	0.48408(18)	0.0028(4)	1	0.46(2)
	Ga4	4c	0.28820(6)	0.33958(18)	0.9549(3)	1	0.41(3)
	Ga5	4c	0.11873(7)	0.12693(18)	0.0329(2)	1	0.40(2)
	O1	4c	0.4568(4)	0.3471(12)	0.2000(17)	1	1.05(4) a
	O2	4c	0.3862(4)	0.0749(11)	0.1940(17)	1	1.05(4) a
	O3	4c	0.2893(4)	0.3454(12)	0.3003(12)	1	1.05(4) a
	O4	4c	0.4412(4)	0.1512(12)	0.6774(13)	1	1.05(4) a
	O5	4c	0.1263(5)	0.1161(11)	0.6915(11)	1	1.05(4) a
	O6	2b	0.5	0	0.1534(19)	1	1.05(4) a
	O7	4c	0.2258(4)	0.4286(11)	0.7706(18)	1	1.05(4) a
	O8	4c	0.0489(4)	0.1336(11)	0.1682(16)	1	1.05(4) a
	O9	4c	0.2975(4)	0.1355(12)	0.7869(19)	1	1.05(4) a
	O10	4c	0.1509(4)	0.3098(12)	0.2047(16)	1	1.05(4) a
	O11	4c	0.3455(4)	0.4564(10)	0.7999(12)	1	1.05(4) a

a Constrained to refine to the same value

Table A . 7. Final refined structural parameters of the SrHoGa3O7 disordered melilite

 A

	Atom	Site	x	y	Z	Occ	Biso
	Ho1/Sr1	4e	0.33867(5)	0.16133(5)	0.51151(14)	0.5/0.5	1.06(2)
	Ga1	2a	0	0	0		0.61(3)
	Ga2	4e	0.14444(7)	0.35556(7)	0.96831(17)		0.77(2)
	O1	2c	0.5	0	0.1757(10)		2.27(6) a
	O2	4e	0.1422(4)	0.3578(4)	0.3186(6)		2.27(6) a
	O3	8f	0.0940(4)	0.1626(4)	0.7916(6)		2.27(6) a
	a Constrained to refine to the same value

(P𝟒 ̅ 21m space group, a = b = 7.93999(2) Å, and c = 5.23060(2) Å).

Table A . 8. Final refined structural parameters obtained from lab XRPD data collected at room temperature on the SrDyGa3O7 superstructure melilite (P21212 space group, a = 23.8404(3) Å, b = 7.9510(1) Å and c = 5.24314(2) Å).

 A

	Atom	Site	x	y	z	Occ	Biso
	Dy1/Sr1	4c	0.2210(2)	0.1475(5)	0.4976(6)	0.50(1)/0.50(1)	1.3(1)
	Dy2/Sr2	4c	0.38229(17) 0.3203(4)	0.4609(5)	0.90(1)/0.10(1)	0.92(9)
	Sr3/Dy3	4c	0.0558(2)	0.3372(7)	0.5076(7)	0.90(1)/0.10(1)	1.4(1)
	Ga1	4c	0.0558(2)	0.3372(7)	0.5076(7)	1	0.8(2)
	Ga2	2a	0.4501(3)	0.1441(9)	0.0111(10)	1	1.6(2)
	Ga3	4c	0	0	0.998(2)	1	0.2(1)
	Ga4	4c	0.1710(3)	0.4826(8)	0.9962(18)	1	0.8(2)
	Ga5	4c	0.2873(3)	0.3374(9)	0.9535(11)	1	0.7(2)
	O1	4c	0.1182(3)	0.1274(9)	0.0322(8)	1	0.3(2) a
	O2	4c	0.4541(12)	0.330(4)	0.226(5)	1	0.3(2) a
	O3	4c	0.3927(12)	0.077(3)	0.175(5)	1	0.3(2) a
	O4	4c	0.2888(14)	0.360(4)	0.295(3)	1	0.3(2) a
	O5	4c	0.4417(11)	0.150(4)	0.650(4)	1	0.3(2) a
	O6	2b	0.1217(15)	0.120(4)	0.672(4)	1	0.3(2) a
	O7	4c	0.5	0	0.146(5)	1	0.3(2) a
	O8	4c	0.2226(14)	0.433(4)	0.805(6)	1	0.3(2) a
	O9	4c	0.0510(10)	0.126(4)	0.149(4)	1	0.3(2) a
	O10	4c	0.3051(12)	0.116(3)	0.730(5)	1	0.3(2) a
	O11	4c	0.1451(12)	0.312(3)	0.261(4)	1	0.3(2) a
	a Constrained to refine to the same value

Table A . 9. Final refined structural parameters of the SrDyGa3O7 disordered melilite (P𝟒 ̅ 21m space group, a = b = 7.95008(6) Å, and c = 5.23788(4) Å).

 A

	Atom	Site	x	y	Z	Occ	Biso
	Ho1/Sr1	4e	0.33874(10)	0.16126(10)	0.5121(3)	0.5/0.5	1.82(4)
	Ga1	2a	0	0	0	1	1.36(7)
	Ga2	4e	0.14504(15)	0.35496(15)	0.9688(4)	1	1.45(6)
	O1	2c	0.5	0	0.187(2)	1	2.25(1) a
	O2	4e	0.1433(8)	0.3567(8)	0.3153(13)	1	2.25(1) a
	O3	8f	0.0893(7)	0.1610(8)	0.7873(15)	1	2.25(1) a
	a Constrained to refine to the same value

201

Chapter A.III: Supplementary information for Chapter III.

Table A . 10. Refined structural parameters obtained from SPD data collected at room temperature on Ca3Ga1.5Zn0.25Ge4.25O14 (x = 0.25) (P321 space group, a= 8.05847(2) Å and c= 4.986577(14) Å) sample.

 A Site was put to be fully occupied without refining each atom occupancy a : constrained to refine to the same Biso values.

	Atom	Position	x	y	z	Occ	Biso
	Ca Ga1/Ge1/Zn1 1a 3e Ga2/Ge2/Zn2 3f Ge3 2d O1 2d O2 6g O3 6g	0.41970(8) 0 0.76349(4) 1/3 1/3 0.4649(2) 0.2165(2)	0 0 0 2/3 2/3 0.3170(2) 0.0759(2)	0 0 0.5 0.53149(10) 0.1913(5) 0.3183(3) 0.7588(3)	1 1* 1* 1 1 1 1	1.02(1) 1.04(1) 0.90(1) 0.76(1) 1.40(3) a 1.40(3) a 1.40(3) a

*

Table A . 11. Refined structural parameters obtained from SPD data collected at room temperature on Ca3GaZn0.5Ge4.5O14 (x = 0.5) (P321 space group, a= 8.041920(12) Å and c= 4.999015(8) Å) sample.

 A

	Atom	Position	x	y	z	Occ	Biso
	Ca Ga1/Ge1/Zn1 1a 3e Ga2/Ge2/Zn2 3f Ge3 2d O1 2d O2 6g O3 6g	0.41956(8) 0 0.76427(4) 1/3 1/3 0.4650(2) 0.21624(19)	0 0 0 2/3 2/3 0.3164(2) 0.0756(2)	0 0 0.5 0.52968(9) 0.1867(5) 0.3208(3) 0.7547(3)	1 1* 1* 1 1 1 1	1.00(1) 1.15(1) 1.006(6) 0.844(7) 1.72(2) a 1.72(2) a 1.72(2) a

*Site was put to be fully occupied without refining each atom occupancy a : constrained to refine to the same Biso values.

Table A . 12. Refined structural parameters obtained from SPD data collected at room temperature on Ca3Ga0.5Zn0.75Ge4.75O14 (x = 0.75) (P321 space group, a= 8.03574(2) Å and c= 5.009068(17) Å) sample.

 A

	Atom	Position	x	y	z	Occ	Biso
	Ca Ga1/Ge1/Zn1 1a 3e Ga2/Ge2/Zn2 3f Ge3 2d O1 2d O2 6g O3 6g	0.41827(11) 0 0.76488(6) 1/3 1/3 0.4676(3) 0.2203(2)	0 0 0 2/3 2/3 0.3187(3) 0.0763(3)	0 0 0.5 0.52939(14) 0.1880(7) 0.3224(4) 0.7527(4)	1 1* 1* 1 1 1 1	0.92(2) 1.26(2) 0.971(1) 0.79(1) 1.26(4) a 1.26(4) a 1.26(

Table A . 13. Refined structural parameters obtained from SPD data collected at room temperature on Ca3ZnGe5O14 (P321 space group, a= 8.02916(2) Å and c= 5.014362(17) Å) sample. No strain modelled.

 A Site was put to be fully occupied without refining each atom occupancy a : constrained to refine to the same Biso values.

	Atom	Position	x	y	z	Occ	Biso
	Ca Zn1/Ge1 Zn2/Ge2 Ge3 O1 O2 O3	3e 1a 3f 2d 2d 6g 6g	0.41846(8) 0 0.76506(4) 1/3 1/3 0.4676(2) 0.22065(19)	0 0 0 2/3 2/3 0.3195(2) 0.0772(2)	0 0 0.5 0.52816(11) 0.1926(5) 0.3230(3) 0.7502(3)	1 1* 1* 1 1 1 1	1.15(1) 1.47 (1) 1.126(7) 0.999(8) 1.91(3) a 1.91(3) a 1.91(3) a

*

Table A . 14. Refined structural parameters obtained from SPD data collected at room temperature on Ca3ZnGe5O14 (C2 space group, a= 13.91669(9) Å, b= 8.02315(5) Å, c= 5.01415(2) Å and β= 90.0759(4) °) sample. No strain modelled.

 A

	Atom	Position	x	y	z	Occ	Biso
	Ca1 Ca2 Zn1 Ge1 Ge2 Ge3 O1 O2 O3 O4 O5 O6 O7	2a 4c 1a 4c 2b 4c 4c 4c 4c 4c 4c 4c 4c	0.5 0.2917(2) 0.11841(10) 0.33313(10) 0.5 0.5 0.1177(4) 0.1611(6) 0.4249(5) 0.4317(5) 0.3341(6) 0.0234(4) 0.2304(5)	0.7623(5) 0.3948(4) 0.56943(16) 0.6860(2) 0.41986(18) 0.1858(3) 0.6953(9) 0.3732(11) 0.5748(11) 0.3296(9) 0.6729(11) 0.4947(8) 0.5907(10)	0 0.0006(7) 0.4969(4) 0.47222(13) 0.5 0 0.7829(10) 0.680(2) 0.3031(15) 0.7441(13) 0.8088(6) 0.2834(13) 0.3407(17)		1.44(8) 1.02(4) 1.39(3) 0.96(1) 0.92(4) 1.00(1) 1.21(4) a 1.21(4) a 1.21(4) a 1.21(4) a 1.21(4) a 1.21(4) a 1.21(4) a
	a : constrained to refine to the same Biso values.

Table A . 15. Refined structural parameters obtained from SPD data collected at room temperature on Ca3ZnGe5O14 (C2 space group, a= 13.90286(11) Å, b= 8.03170(7) Å, c= 5.014276(16) Å and β= 89.9544(10) °) sample. Modelled strain.

 A

	Atom	Position	x	y	z	Occ	Biso
	Ca1 Ca2 Zn1 Ge1 Ge2 Ge3 O1 O2 O3 O4 O5 O6 O7	2a 4c 1a 4c 2b 4c 4c 4c 4c 4c 4c 4c 4c	0.5 0.2903(2) 0.11569(10) 0.33367(13) 0.5 0.5 0.1017(4) 0.1562(6) 0.4298(6) 0.4377(4) 0.3344(7) 0.0451(5) 0.2364(6)	0.7601(4) 0.3895(5) 0.55532(16) 0.6757(3) 0.4145(2) 0.1800(4) 0.7363(7) 0.3734(13) 0.5696(13) 0.3391(9) 0.679(2) 0.4900(9) 0.5876(13)	0 0.0005(8) 0.5034(4) 0.47220(10) 0.5 0 0.7201(10) 0.674(2) 0.3262(18) 0.7873(9) 0.8071(4) 0.2636(13) 0.3066(17)		0.45(6) 1.55(4) 1.25(3) 0.980(7) 1.07(5) 0.97(1) 1.46(3) a 1.46(3) a 1.46(3) a 1.46(3) a 1.46(3) a 1.46(3) a 1.46(3) a

a : constrained to refine to the same Biso values.

Table A . 16. Final refined La1.3Ba0.7Ga3O7.15 (x = 0.3) composition structural parameters (S.G. P𝟒 ̅ 21m, a= b= 8.12688(2) Å, c= 5.35114(1) Å).

 A

	Atom	x	y	z	Occ	Biso
	La1/Ba1	0.33616(2) 0.16384(2) 0.50816(7)	0.65/0.35	0.402(4)
	Ga1	0	0	0	1	0.204(10)
	Ga2	0.14217(4) 0.35783(4) -0.03032(11)	1	0.542(9)
	O1	0.5	0	0.1901(8)	1	0.77(3)
	O2	0.1388(3)	0.3612(3)	0.3131(5)	1	0.77(3)
	O3	0.0847(3)	0.1636(3)	0.7935(4)	1	0.77(3)
	O4	0.358(3)	0.142(3)	0.056(7)	0.075	0.77(3)

Table A .

 A

	17. Final refined La1.6Ba0.4Ga3O7.3 (x = 0.6) composition structural parameters (S.G. P𝟒 ̅ 21m, a=
	b= 8.08170(1) Å, c= 5.291514(8) Å).
	Atom	x	y	z	Occ	Biso
	La1/Ba1	0.335860(18) 0.164140(18) 0.50785(7)	0.8/0.2	0.761(4)
	Ga1	0	0	0	1	0.492(9)
	Ga2	0.14197(3)	0.35803(3)	-0.03021(10)	1	0.982(9)
	O1	0.5	0	0.1871(7)	1	1.43(3)
	O2	0.1387(2)	0.3613(2)	0.3127(4)	1	1.43(3)
	O3	0.0825(2)	0.1624(2)	0.7924(3)	1	1.43(3)
	O4	0.3436(12)	0.1564(12)	0.018(4)	0.15	1.43(3)

Table A . 18. Final refined La1.65Ba0.35Ga3O7.325 (x = 0.65) composition structural parameters

 A

	Atom	x	y	z	Occ	Biso
	La1/Ba1	0.335690(17) 0.164310(17) 0.50756(6)	0.825/0.175 1.007(4)
	Ga1	0	0	0	1	0.678(9)
	Ga2	0.14199(3)	0.35801(3)	-0.03164(10)	1	1.261(8)
	O1	0.5	0	0.1941(6)	1	1.54(3)
	O2	0.13590(19)	0.36410(19)	0.3137(4)	1	1.54(3)
	O3	0.08324(18)	0.1644(2)	0.7920(3)	1	1.54(3)
	O4	0.3442(10)	0.1558(10)	-0.003(3)	0.1625	1.54(3)

(S.G. P𝟒 ̅ 21m, a= b= 8.08849(1) Å, c= 5.29991(1) Å).

Table A . 19. Final refined La1.675Ba0.325Ga3O7.3375 (x = 0.675) composition structural parameters (S.G. P𝟒 ̅ 21m, a= b= 8.07836(2) Å, c= 5.28703(1) Å).

 A

	Atom	x	y	z	Occ	Biso
	La1/Ba1	0.335820(19) 0.164180(19) 0.50797(7)	0.8375/0.1675 1.213(4)
	Ga1	0	0	0	1	0.872(10)
	Ga2	0.14215(3)	0.35785(3)	-0.03170(11)	1	1.393(10)
	O1	0.5	0	0.1914(7)	1	2.06(3)
	O2	0.1372(2)	0.3628(2)	0.3055(4)	1	2.06(3)
	O3	0.0837(2)	0.1639(2)	0.7928(3)	1	2.06(3)
	O4	0.3501(11)	0.1499(11)	0.032(3)	0.16875	2.06(3)

Table A . 20. Final refined

 A

		La1.7Ba0.3Ga3O7.35 (x = 0.7) composition structural parameters (S.G. P𝟒 ̅ 21m,
	a= b= 8.07489(2) Å, c= 5.28269(1) Å).
	Atom	x	y	z	Occ	Biso
	La1/Ba1	0.33549(2)	0.16451(2)	0.50774(10)	0.85/0.15	0.737(5)
	Ga1	0	0	0	1	0.413(12)
	Ga2	0.14219(4)	0.35781(4)	-0.03048(14)	1	0.934(12)
	O1	0.5	0	0.1840(10)	1	1.48(4)
	O2	0.1346(3)	0.3654(3)	0.3130(6)	1	1.48(4)
	O3	0.0834(3)	0.1635(3)	0.7883(5)	1	1.48(4)
	O4	0.33549(2)	0.16451(2)	0.003(5)	0.175	1.48(4)

Table A . 21. Final refined La1.725Ba0.275Ga3O7.3625 (x = 0.725) composition structural parameters

 A

	Atom	x	y	z	Occ	Biso
	La1/Ba1	0.33569(3)	0.16431(3)	0.50894(10)	0.8675/0.1375 1.107(6)
	Ga1	0	0	0	1	0.766(15)
	Ga2	0.14221(5)	0.35779(5)	-0.03121(16)	1	1.363(14)
	O1	0.5	0	0.1950(11)	1	2.29(5)
	O2	0.1345(3)	0.3655(3)	0.3009(7)	1	2.29(5)
	O3	0.0855(3)	0.1641(3)	0.7894(6)	1	2.29(5)
	O4	0.3481(8)	0.1519(8)	0.0582(18)	0.3625	2.29(5)

(S.G. P𝟒 ̅ 21m, a= b= 8.07235(2) Å, c= 5.27953(2) Å).

Table A . 22. Final refined La1.75Ba0.25Ga3O7.375 (x = 0.75) composition structural parameters

 A

	Atom	x	y	z	Occ	Biso
	La1/Ba1	0.33515(8)	0.16485(8)	0.4990(3)	0.875/0.125 1.38(3)
	Ga1	0	0	0	1	0.90(5)
	Ga2	0.14206(13) 0.35794(13) -0.0270(6)	1	1.63(4)
	O1	0.5	0	0.185(3)	1	0.77(11)
	O2	0.1368(8)	0.3632(8)	0.3262(18)	1	0.77(11)
	O3	0.0836(7)	0.1640(9)	0.7983(16)	1	0.77(11)
	O4	0.33515(8)	0.16485(8)	-0.000(11)	0.25	0.77(11)

(S.G. P𝟒 ̅ 21𝒎, 𝒂= 𝒃= 8.06891(2) Å, 𝒄= 5.27513(2) Å).

Table A . 23. Final refined La1.75Ba0.25Ga3O7.375 (x = 0.75) composition structural parameters (S.G. Ima2, a= 11.43139(6) Å, b= 11.39361(5) Å, c= 10.55194(4) Å).

 A

	Atom	x	y	z	Occ	Biso
	La1/Ba1	-0.58610(6)	0.2493(2)	0.48475(13) 0.9167/0.0833 a 0.714(18)
	La2/Ba2	0.75	0.0852(2)	-0.0276(3)	0.8334/0.1667 a 0.98(7)
	La3/Ba3	0.75	0.4144(3)	-0.0263(3)	0.8333/0.1667 1.28(8)
	Ga1	-0.88855(11) -0.2494(5)	0.2123(3)	1	1.08(4)
	Ga2	0	0	0.2218(5)	1	0.11(11)
	Ga3	0.5	0.5	0.2340(6)	1	1.17(14)
	Ga4	0.75	-0.1053(8)	-0.2572(6)	1	1.59(16)
	Ga5	0.25	0.1038(7)	0.2475(5)	1	0.54(13)
	O1	-0.8893(8)	-0.244(2)	-0.1230(11) 1	1.57(8)
	O2	-0.4777(11)	0.3618(12)	0.1243(15)	1	1.57(8)
	O3	-0.5508(11)	-0.3804(12) -0.3788(17) 1	1.57(8)
	O4	-0.1306(12)	-0.0368(13) -0.1710(17) 1	1.57(8)
	O5	-0.8936(12)	0.0530(13)	0.3445(15)	1	1.57(8)
	O6	0.75	0.2768(13)	0.1348(17)	1	1.57(8)
	O7	0.75	-0.122(3)	0.074(3)	1	1.57(8)
	O8	0.25	0.251(4)	0.3308(15)	1	1.57(8)
	O9	0.25	0.120(3)	0.577(3)	1	1.57(8)
	O10	0.25	-0.0955(13) 0.227(3)	0.75 a	1.57(8)

a Fixed to the nominal composition

Table A . 24. Final refined La1.775Ba0.225Ga3O7.3875 (x = 0.775) composition cell 1 structural parameters (S.G. Ima2, a= 11.45837(7) Å, b= 11.34648(7) Å, c= 10.53977(9) Å).

 A

	Atom Atom	x x	y y	z z	Occ Occ	Biso Biso
	La1/Ba1 La1/Ba1	-0.58686(8) -0.58686(8)	0.24858(19) 0.4817(6) 0.24858(19) 0.4817(6)	0.8875/0.075 a 0.8875/0.075 a	0.38443 b 0.38443 b
	La2/Ba2 La2/Ba2	0.75 0.75	0.0849(3) 0.0849(3)	-0.0264(7) -0.0264(7)	0.8875/0.15 a 0.8875/0.15 a	0.45365 b 0.45365 b
	La3/Ba3 La3/Ba3	0.75 0.75	0.4158(3) 0.4158(3)	-0.0344(7) -0.0344(7)	0.8875/0.15 a 0.8875/0.15 a	0.77528 b 0.77528 b
	Ga1 Ga1	-0.88671(15) -0.2535(3) -0.88671(15) -0.2535(3)	0.2113(7) 0.2113(7)	1 1	0.89918 b 0.89918 b
	Ga2 Ga2	0 0	0 0	0.2299(8) 0.2299(8)	1 1	0.31456 b 0.31456 b
	Ga3 Ga3	0.5 0.5	0.5 0.5	0.2358(7) 0.2358(7)	1 1	0.01001 b 0.01001 b
	Ga4 Ga4	0.75 0.75	-0.1045(4) -0.1045(4)	-0.2569(8) -0.2569(8)	1 1	1.07162 b 1.07162 b
	Ga5 Ga5	0.25 0.25	0.0998(4) 0.0998(4)	0.2391(8) 0.2391(8)	1 1	0.33539 b 0.33539 b
	O1 O1	-0.88723 b -0.88723 b	-0.26809 b -0.26809 b	-0.11788 b -0.11788 b	1 1	0.3209 b 0.3209 b
	O2 O2	-0.48405 b -0.48405 b	0.36824 b 0.36824 b	0.12209 b 0.12209 b	1 1	0.3209 b 0.3209 b
	O3 O3	-0.55204 b -0.55204 b	-0.36768 b -0.36768 b	-0.37826 b -0.37826 b	1 1	0.3209 b 0.3209 b
	O4 O4	-0.13731 b -0.13731 b	-0.03781 b -0.03781 b	-0.17337 b -0.17337 b	1 1	0.3209 b 0.3209 b
	O5 O5	-0.89494 b -0.89494 b	0.05828 b 0.05828 b	0.34768 b 0.34768 b	1 1	0.3209 b 0.3209 b
	O6 O6	0.75 0.75	0.27628 b 0.27628 b	0.13621 b 0.13621 b	1 1	0.3209 b 0.3209 b
	O7 O7	0.75 0.75	-0.13585 b -0.13585 b	0.07166 b 0.07166 b	1 1	0.3209 b 0.3209 b
	O8 O8	0.25 0.25	0.2346 b 0.2346 b	0.33203 b 0.33203 b	1 1	0.3209 b 0.3209 b
	O9 O9	0.25 0.25	0.1051 b 0.1051 b	0.57471 b 0.57471 b	1 1	0.3209 b 0.3209 b
	O10 O10	0.25 0.25	-0.10097 b -0.10097 b	0.228 b 0.228 b	0.775 a 0.775 a	0.3209 b 0.3209 b
	a Fixed to the nominal composition
	b Fixed from the Stephens refinement approach

a Fixed to the nominal composition b Fixed from the Stephens refinement approach

Table A . 26. Final refined La1.775Ba0.225Ga3O7.3875 (x = 0.775) composition cell 3 structural parameters (S.G. Ima2, a= 11.41747(9) Å, b= 11.3866(1) Å, c= 10.5396(1) Å).

 A

	Atom	x	y	z	Occ	Biso
	La1/Ba1	-0.58686(8)	0.24858(19) 0.4817(6)	0.8875/0.075 a	0.38443 b
	La2/Ba2	0.75	0.0849(3)	-0.0264(7)	0.8875/0.15 a	0.45365 b
	La3/Ba3	0.75	0.4158(3)	-0.0344(7)	0.8875/0.15 a	0.77528 b
	Ga1	-0.88671(15) -0.2535(3)	0.2113(7)	1	0.89918 b
	Ga2	0	0	0.2299(8)	1	0.31456 b
	Ga3	0.5	0.5	0.2358(7)	1	0.01001 b
	Ga4	0.75	-0.1045(4)	-0.2569(8)	1	1.07162 b
	Ga5	0.25	0.0998(4)	0.2391(8)	1	0.33539 b
	O1	-0.88723 b	-0.26809 b	-0.11788 b	1	0.3209 b
	O2	-0.48405 b	0.36824 b	0.12209 b	1	0.3209 b
	O3	-0.55204 b	-0.36768 b	-0.37826 b	1	0.3209 b
	O4	-0.13731 b	-0.03781 b	-0.17337 b	1	0.3209 b
	O5	-0.89494 b	0.05828 b	0.34768 b	1	0.3209 b
	O6	0.75	0.27628 b	0.13621 b	1	0.3209 b
	O7	0.75	-0.13585 b	0.07166 b	1	0.3209 b
	O8	0.25	0.2346 b	0.33203 b	1	0.3209 b
	O9	0.25	0.1051 b	0.57471 b	1	0.3209 b
	O10	0.25	-0.10097 b	0.228 b	0.775 a	0.3209 b

a Fixed to the nominal composition b Fixed from the Stephens refinement approach

Table A . 27. Final refined La1.775Ba0.225Ga3O7.3875 (x = 0.775) composition cell 4 structural parameters (S.G. Ima2, a= 11.3970(1) Å, b= 11.4064(1) Å, c= 10.5396(2) Å).

 A

	Atom	x	y	z	Occ	Biso
	La1/Ba1	-0.58686(8)	0.24858(19) 0.4817(6)	0.8875/0.075 a	0.38443 b
	La2/Ba2	0.75	0.0849(3)	-0.0264(7)	0.8875/0.15 a	0.45365 b
	La3/Ba3	0.75	0.4158(3)	-0.0344(7)	0.8875/0.15 a	0.77528 b
	Ga1	-0.88671(15) -0.2535(3)	0.2113(7)	1	0.89918 b
	Ga2	0	0	0.2299(8)	1	0.31456 b
	Ga3	0.5	0.5	0.2358(7)	1	0.01001 b
	Ga4	0.75	-0.1045(4)	-0.2569(8)	1	1.07162 b
	Ga5	0.25	0.0998(4)	0.2391(8)	1	0.33539 b
	O1	-0.88723 b	-0.26809 b	-0.11788 b	1	0.3209 b
	O2	-0.48405 b	0.36824 b	0.12209 b	1	0.3209 b
	O3	-0.55204 b	-0.36768 b	-0.37826 b	1	0.3209 b
	O4	-0.13731 b	-0.03781 b	-0.17337 b	1	0.3209 b
	O5	-0.89494 b	0.05828 b	0.34768 b	1	0.3209 b
	O6	0.75	0.27628 b	0.13621 b	1	0.3209 b
	O7	0.75	-0.13585 b	0.07166 b	1	0.3209 b
	O8	0.25	0.2346 b	0.33203 b	1	0.3209 b
	O9	0.25	0.1051 b	0.57471 b	1	0.3209 b
	O10	0.25	-0.10097 b	0.228 b	0.775 a	0.3209 b

a Fixed to the nominal composition b Fixed from the Stephens refinement approach

Table A . 28. Final refined La1.775Ba0.225Ga3O7.3875 (x = 0.775) composition cell 5 structural parameters (S.G. Ima2, a= 11.3561(2) Å, b= 11.4468(2) Å, c= 10.5394(2) Å).

 A

	Atom	x	y	z	Occ	Biso
	La1/Ba1	-0.58686(8)	0.24858(19) 0.4817(6)	0.8875/0.075 a	0.38443 b
	La2/Ba2	0.75	0.0849(3)	-0.0264(7)	0.8875/0.15 a	0.45365 b
	La3/Ba3	0.75	0.4158(3)	-0.0344(7)	0.8875/0.15 a	0.77528 b
	Ga1	-0.88671(15) -0.2535(3)	0.2113(7)	1	0.89918 b
	Ga2	0	0	0.2299(8)	1	0.31456 b
	Ga3	0.5	0.5	0.2358(7)	1	0.01001 b
	Ga4	0.75	-0.1045(4)	-0.2569(8)	1	1.07162 b
	Ga5	0.25	0.0998(4)	0.2391(8)	1	0.33539 b
	O1	-0.88723 b	-0.26809 b	-0.11788 b	1	0.3209 b
	O2	-0.48405 b	0.36824 b	0.12209 b	1	0.3209 b
	O3	-0.55204 b	-0.36768 b	-0.37826 b	1	0.3209 b
	O4	-0.13731 b	-0.03781 b	-0.17337 b	1	0.3209 b
	O5	-0.89494 b	0.05828 b	0.34768 b	1	0.3209 b
	O6	0.75	0.27628 b	0.13621 b	1	0.3209 b
	O7	0.75	-0.13585 b	0.07166 b	1	0.3209 b
	O8	0.25	0.2346 b	0.33203 b	1	0.3209 b
	O9	0.25	0.1051 b	0.57471 b	1	0.3209 b
	O10	0.25	-0.10097 b	0.228 b	0.775 a	0.3209 b

a Fixed to the nominal composition b Fixed from the Stephens refinement approach

Table A . 29. Final refined La1.775Ba0.225Ga3O7.3875 (x = 0.775) composition cell 6 structural parameters

 A

	Atom	x	Y	z	Occ	Biso
	La1/Ba1	0.33499(17) 0.16501(17) 0.4851(5)	0.8875/0.1125 a 1.38348 b
	Ga1	0	0	0	1	0.9019 b
	Ga2	0.1410(3)	0.3590(3)	-0.0298(11)	1	1.62865 b
	O1	0.5	0	0.18535 b	1	0.76567 b
	O2	0.13683 b	0.36317 b	0.32623 b	1	0.76567 b
	O3	0.08361 b	0.16396 b	0.79828 b	1	0.76567 b
	O4	0.33499 b	0.16501 b	-0.00039 b	0.19375 a	0.76567 b
	a Fixed to the nominal composition

(S.G. P𝟒 ̅ 21m, a= b= 8.06246(4) Å, c= 5.26941(5) Å). b Fixed from the Stephens refinement approach

Table A . 30. Final refined La1.8Ba0.2Ga3O7.4 (x = 0.8) composition structural parameters (S.G. Ima2, a= 11.45216(8) Å, b= 11.35246(7) Å, c= 10.53719(5) Å).

 A

	Atom	x	y	z	Occ	Biso
	La1/Ba1	-0.58647(5)	0.2493(3)	0.48233(11)	0.933/0.066 a	0.290(14)
	La2/Ba2	0.75	0.0850(3)	-0.01863(18) 0.866/0.133 a	0.94(8)
	La3/Ba3	0.75	0.4153(3)	-0.03299(18) 0.866/0.133 a	0.29(6)
	Ga1	-0.88777(10) -0.2517(3)	0.2135(2)	1	0.66(3)
	Ga2	0	0	0.2317(7)	1	-0.15(6)
	Ga3	0.5	0.5	0.2330(8)	1	0.74(8)
	Ga4	0.75	-0.1068(4)	-0.2549(5)	1	0.77(11)
	Ga5	0.25	0.0998(4)	0.2433(5)	1	0.27(9)
	O1	-0.8866(6)	-0.2613(12) -0.1143(8)	1	0.25(7) b
	O2	-0.4814(9)	0.3655(9)	0.1335(11)	1	0.25(7) b
	O3	-0.5488(9)	-0.3777(10) -0.3752(13)	1	0.25(7) b
	O4	-0.1306(9)	-0.0281(8)	-0.1579(11)	1	0.25(7) b
	O5	-0.8920(9)	0.0603(8)	0.3509(10)	1	0.25(7) b
	O6	0.75	0.2792(11)	0.1387(13)	1	0.25(7) b
	O7	0.75	-0.1248(15) 0.0674(17)	1	0.25(7) b
	O8	0.25	0.246(3)	0.3174(12)	1	0.25(7) b
	O9	0.25	0.1029(14)	0.5740(17)	1	0.25(7) b
	O10	0.25	-0.0964(11) 0.220(2)	0.8 a	0.25(7) b

a Fixed to the nominal composition. b Constrained to refine to the same value.

Table A . 31. Final refined La1.8Ba0.2Ga3O7

 A

	Atom	x	Y	z	Occ	Biso
	La1/Ba1	0.3359(2)	0.1641(2)	0.5021(10)	0.9/0.1 a	4.18(13)
	Ga1	0	0	0	1	1.94(17)
	Ga2	0.1462(4)	0.3539(4)	-0.0411(16)	1	3.72(16)
	O1	0.5	0	0.192(8)	1	1.4(3) b
	O2	0.1118(19)	0.3882(19)	0.303(5)	1	1.4(3) b
	O3	0.0882(16)	0.1649(18)	0.797(5)	1	1.4(3) b
	O4	0.3359(2)	0.1641(2)	-0.01(3)	0.2 a	1.4(3) b
	a Fixed to the nominal composition

.4 (x = 0.8) composition structural parameters (S.G. P𝟒 ̅ 21m, a= b= 8.06223(7) Å, c= 5.26848(12) Å). b Constrained to refine to the same value

Table A . 32. Final refined La1.85Ba0.15Ga3O7.425 (x = 0.85) composition structural parameters (S.G. Ima2, a= 11.45216(8) Å, b= 11.35246(7) Å, c= 10.53719(5) Å).

 A

	Atom	x	y	z	Occ	Biso
	La1/Ba1	-0.58709(4)	0.2505(3)	0.48323(7)	0.95/0.05 a	0.597(11)
	La2/Ba2	0.75	0.0860(3)	-0.01311(13) 0.9/0.1 a	1.38(6)
	La3/Ba3	0.75	0.4168(3)	-0.03437(12) 0.9/0.1 a	0.66(5)
	Ga1	-0.88662(8)	-0.2465(2)	0.21383(14)	1	0.88(2)
	Ga2	0	0	0.2318(5)	1	0.20(5)
	Ga3	0.5	0.5	0.2385(4)	1	0.59(6)
	Ga4	0.75	-0.1035(3)	-0.2536(4)	1	1.15(8)
	Ga5	0.25	0.0996(3)	0.2448(3)	1	0.46(7)
	O1	-0.8864(5)	-0.2573(13) -0.1119(6)	1	0.70(5) b
	O2	-0.4713(9)	0.3722(9)	0.1365(8)	1	0.70(5) b
	O3	-0.5436(9)	-0.3751(9)	-0.3789(9)	1	0.70(5) b
	O4	-0.1192(8)	-0.0391(8)	-0.1597(8)	1	0.70(5) b
	O5	-0.8885(7)	0.0622(7)	0.3414(8)	1	0.70(5) b
	O6	0.75	0.2888(9)	0.1369(10)	1	0.70(5) b
	O7	0.75	-0.1276(11) 0.0693(12)	1	0.70(5) b
	O8	0.25	0.2579(17)	0.3202(8)	1	0.70(5) b
	O9	0.25	0.1069(12)	0.5737(12)	1	0.70(5) b
	O10	0.25	-0.0855(10) 0.2182(14)	0.85 a	0.70(5) b

a Fixed to the nominal composition. b Constrained to refine to the same value.

Table A . 33. Final refined La1.85Ba0.15Ga3O7.425 (x = 0.85) composition structural parameters (S.G. P𝟒 ̅ 21m, a= b= 8.05604(13) Å, c= 5.26135(15) Å).

 A

	Atom	x	Y	z	Occ	Biso
	La1/Ba1	0.33729	0.16271	0.50966	0.925/0.075 a	1 b
	Ga1	0	0	0	1	1 b
	Ga2	0.14537	0.35463	-0.03938	1	1 b
	O1	0.5	0	0.22063	1	1 b
	O2	0.10528	0.39472	0.28488	1	1 b
	O3	0.08388	0.17379	0.78697	1	1 b
	O4	0.33729	0.16271	-0.02503	0.2125 a	1 b
	a Fixed to the nominal composition

b

Fixed to 1 due to the negative refined vlues

Table A . 35. Final NPD HI refined data of La1.3Ba0.7Ga3O7.15 (x = 0.3) composition structural parameters (S.G. P𝟒 ̅ 21m, a= b= 8.13053(4) Å, c= 5.35381(6) Å).

 A

	Atom	x	y	z	Occ	Biso
	La1/Ba1	0.33682(10) 0.16318(10) 0.5091(3)	0.676(8)/0.324(8) 0.76(4)
	Ga1	0	0	0	1	0.46(5)
	Ga2	0.14189(12) 0.35811(12) -0.0308(2)	1	0.72(4)
	O1	0.5	0	0.1843(5)	1	1.81(10)
	O2	0.13865(19) 0.36135(19) 0.3054(3)	1	1.76(6)
	O3	0.08327(16) 0.16343(18) 0.8016(3)	1	1.66(6)
	O4	0.333(2)	0.167(2)	0.008(5)	0.075(3)	1

Table A . 36. Refined anisotropic thermal parameters of La1.3Ba0.7Ga3O7.15 (x = 0.3) composition from NPD HI data.

 A

	Atom	B11	B22	B33	B12	B13	B23
	La1/Ba1	0.60(2)	0.60(3)	1.10(6)	0.31(4)	0.02(4)	-0.02(4)
	Ga1	0.32(4)	0.32(4)	0.76(6)	0	0	0
	Ga2	0.73(3)	0.73(3)	0.70(6)	-0.07(4)	0.14(3)	-0.14(3)
	O1	1.94(8)	1.94(8)	1.54(13)	-1.25(10)	0	0
	O2	2.33(6)	2.33(6)	0.62(6)	-0.47(7)	-0.14(5)	0.14(5)
	O3	2.65(7)	0.95(6)	1.38(6)	-0.45(6)	0.77(5)	0.10(6)

Table A . 37. Final NPD HR refined data of La1

 A

	Atom	x	y	z	Occ	Biso
	La1/Ba1	0.33670(11) 0.16330(11) 0.5086(3)	0.662(8)/0.338(8) 0.81(4)
	Ga1	0	0	0	1	0.53(5)
	Ga2	0.14198(11) 0.35802(11) -0.0316(3)	1	0.79(4)
	O1	0.5	0	0.1833(5)	1	1.98(10)
	O2	0.13843(19) 0.36157(19) 0.3055(3)	1	1.76(6)
	O3	0.08330(17) 0.16336(19) 0.8027(3)	1	1.72(6)
	O4	0.337(2)	0.163(2)	0.012(5)	0.075(3)	1

.3Ba0.7Ga3O7.15 (x = 0.3) composition structural parameters (S.G. P𝟒 ̅ 21m, a= b= 8.1280(12) Å, c= 5.3522(8) Å).

Table A . 38. Refined anisotropic thermal parameters of La1.3Ba0.7Ga3O7.15 (x = 0.3) composition from NPD HR data.

 A

	Atom	B11	B22	B33	B12	B13	B23
	La1/Ba1	0.72(2)	0.71(3)	1.00(6)	0.25(4)	0.02(4)	-0.02(4)
	Ga1	0.32(4)	0.32(4)	0.96(7)	0	0	0
	Ga2	0.75(3)	0.75(3)	0.87(6)	-0.13(5)	0.15(3)	-0.15(3)
	O1	2.20(8)	2.20(8)	1.54(13)	-1.30(11)	0	0
	O2	2.26(6)	2.25(6)	0.77(6)	-0.40(8)	-0.13(5)	0.13(5)
	O3	2.61(7)	1.06(6)	1.50(6)	-0.62(6)	0.71(5)	0.09(5)

Table A . 39. Final NPD HI refined data of La1.6Ba0.4Ga3O7.3 (x = 0.6) composition structural parameters (S.G. P𝟒 ̅ 21m, a= b= 8.09083(4) Å, c= 5.30112(6) Å).

 A

	Atom	x	y	z	Occ	Biso
	La1/Ba1	0.33657(9)	0.16343(9)	0.5075(3)	0.799(7)/0.201(7) 0.85(4)
	Ga1	0	0	0	1	0.50(5)
	Ga2	0.14198(11) 0.35802(11) -0.0313(3)	1	0.96(4)
	O1	0.5	0	0.1875(5)	1	2.57(10)
	O2	0.13771(15) 0.36229(15) 0.3091(3)	1	1.23(5)
	O3	0.08307(15) 0.16396(18) 0.7970(2)	1	1.92(6)
	O4	0.3363(10)	0.1637(10)	-0.001(2)	0.152(3)	1

Table A . 40. Refined anisotropic thermal parameters of La1.6Ba0.4Ga3O7.3 (x = 0.6) composition from NPD HI data.

 A

	Atom	B11	B22	B33	B12	B13	B23
	La1/Ba1	0.58(3)	0.58(3)	1.39(6)	0.37(3)	-0.02(3)	0.02(3)
	Ga1	0.35(4)	0.35(4)	0.77(6)	0	0	0
	Ga2	1.12(3)	1.12(3)	0.64(6)	-0.10(5)	0.01(3)	-0.01(3)
	O1	3.09(9)	3.09(7)	1.52(13)	-2.14(11)	0	0
	O2	1.56(5)	1.56(5)	0.58(6)	-0.14(6)	-0.06(3)	0.06(3)
	O3	3.37(7)	0.83(5)	1.56(6)	-0.68(5)	1.34(4)	-0.09(5)

Table A . 41. Final NPD HR refined data of La1

 A

	Atom	x	y	z	Occ	Biso
	La1/Ba1	0.33671(10) 0.16329(10) 0.5071(3)	0.804(8)/0.196(8) 0.90(4)
	Ga1	0	0	0	1	0.53(5)
	Ga2	0.14209(12) 0.35791(12) -0.0314(3)	1	1.02(5)
	O1	0.5	0	0.1877(5)	1	2.52(11)
	O2	0.13770(16) 0.36230(16) 0.3095(3)	1	1.22(5)
	O3	0.08321(16) 0.16384(19) 0.7977(3)	1	1.88(7)
	O4	0.3377(11)	0.1623(11)	0.001(2)	0.143(3)	1

.6Ba0.4Ga3O7.3 (x = 0.6) composition structural parameters (S.G. P𝟒 ̅ 21m, a= b= 8.08771(3) Å, c= 5.29899(5) Å).

Table A . 42. Refined anisotropic thermal parameters of La1.6Ba0.4Ga3O7.3 (x = 0.6) composition from NPD HR data.

 A

	Atom	B11	B22	B33	B12	B13	B23
	La1/Ba1	0.63(3)	0.63(3)	1.44(6)	0.41(4)	-0.03(3)	0.03(4)
	Ga1	0.43(4)	0.43(4)	0.75(6)	0,00	0,00	0
	Ga2	1.18(4)	1.18(4)	0.68(6)	-0.21(5)	-0.02(3)	0.02(3)
	O1	3.00(10)	3.00(10)	1.57(13)	-1.85(12)	0,00	0
	O2	1.52(5)	1.52(5)	0.62(6)	0.05(6)	-0.10(4)	0.10(4)
	O3	3.13(8)	1.02(5)	1.48(6)	-0.65(6)	1.16(4)	-0.10(5)

Table A . 43. Final NPD HI refined data of La1.7Ba0.3Ga3O7.35 (x = 0.7) composition structural parameters (S.G. P𝟒 ̅ 21m, a= b= 8.07722(4) Å, c= 5.28401(6) Å).

 A

	Atom	x	y	z	Occ	Biso
	La1/Ba1	0.33604(10) 0.16396(10) 0.5079(3)	0.853(8)/0.147(8) 0.86(4)
	Ga1	0	0	0	1	0.50(5)
	Ga2	0.14179(11) 0.35821(11) -0.0318(3)	1	0.98(5)
	O1	0.5	0	0.1889(5)	1	2.89(11)
	O2	0.13695(16) 0.36305(16) 0.3102(3)	1	1.17(5)
	O3	0.08251(16) 0.1636(2)	0.7951(3)	1	2.09(7)
	O4	0.3384(9)	0.1616(9)	0.0024(18)	0.180(3)	1

Table A . 44. Refined anisotropic thermal parameters of La1.7Ba0.3Ga3O7.35 (x = 0.7) composition from NPD HI data.

 A

	Atom	B11	B22	B33	B12	B13	B23
	La1/Ba1	0.63(3)	0.63(3)	1.33(6)	0.28(4)	-0.14(4)	0.14(4)
	Ga1	0.50(4)	0.50(4)	0.51(6)	0	0	0
	Ga2	1.22(4)	1.22(4)	0.52(6)	-0.01(5)	0.15(3)	-0.15(3)
	O1	3.74(10)	3.74(10)	1.17(12)	-2.73(12)	0	0
	O2	1.50(5)	1.50(5)	0.51(6)	-0.29(6)	-0.13(3)	0.13(3)
	O3	3.80(8)	1.00(5)	1.46(6)	-0.60(6)	1.56(5)	0.03(5)

Table A . 45. Final NPD HR refined data of La1

 A

	Atom	x	y	z	Occ	Biso
	La1/Ba1	0.33591(10) 0.16409(10) 0.5078(3)	0.868(8)/0.132(8) 0.87(4)
	Ga1	0	0	0	1	0.54(5)
	Ga2	0.14168(12) 0.35832(12) -0.0324(3)	1	1.00(5)
	O1	0.5	0	0.1893(5)	1	2.80(12)
	O2	0.13701(17) 0.36299(17) 0.3101(3)	1	1.19(6)
	O3	0.08251(17) 0.1634(2)	0.7955(3)	1	2.10(7)
	O4	0.3393(10)	0.1607(10)	0.002(2)	0.168(3)	1

.7Ba0.3Ga3O7.35 (x = 0.7) composition structural parameters (S.G. P𝟒 ̅ 21m, a= b= 8.07364(4) Å, c= 5.28175(6) Å).

Table A . 46. Refined anisotropic thermal parameters of La1.7Ba0.3Ga3O7.35 (x = 0.7) composition from NPD HR data.

 A

	Atom	B11	B22	B33	B12	B13	B23
	La1/Ba1	0.68(3)	0.68(3)	1.26(6)	0.21(4)	-0.17(4)	0.17(4)
	Ga1	0.60(4)	0.60(4)	0.43(6)	0	0	0
	Ga2	1.18(4)	1.18(4)	0.64(6)	-0.02(5)	0.15(3)	-0.16(3)
	O1	3.71(11)	3.71(11)	0.97(12)	-2.78(14)	0	0
	O2	1.45(6)	1.45(6)	0.66(6)	-0.21(6)	-0.18(4)	0.18(4)
	O3	3.77(9)	1.01(6)	1.52(6)	-0.62(6)	1.45(5)	0.05(6)

Table A . 47. Final NPD HI refined data of La1.8Ba0.2Ga3O7.4 (x = 0.8) composition structural parameters

 A

	Atom	x	y	z	Occ	Biso
	La1/Ba1	0.3355(15)	0.1645(15)	0.478(4)	0.9/0.1	2.4(6)
	Ga1	0	0	0	1	1.7(6) a
	Ga2	0.1479(16)	0.3521(16)	-0.027(4)	1	1.7(6) a
	O1	0.5	0	0.191(7)	1	2.0(6) b
	O2	0.1405(19)	0.3595(19)	0.314(4)	1	2.0(6) b
	O3	0.0859(16)	0.161(2)	0.792(4)	1	2.0(6) b
	O4	0.342(7)	0.158(7)	0.016(18)	0.20(4)	1
	a,b Constrained to refine to the same value.

(S.G. P𝟒 ̅ 21𝒎, 𝒂= 𝒃= 8.0575(6) Å, 𝒄= 5.2605(9) Å).

Table A . 48. Final NPD HI refined data of La1.8Ba0.2Ga3O7.4 (x = 0.8) composition structural parameters (S.G. Ima2, a= 11.46696(19) Å, b= 11.33164(19) Å, c= 10.5347(2) Å).

 A

	Atom	x	y	z	Occ	Biso
	La1/Ba1	-0.5864(2)	0.2497(7)	0.4769(4)	0.929(7)/0.076(11) 0.21(10)
	La2/Ba2	0.75	0.0865(9)	-0.0253(10) 0.85(2)/0.16(3)	1.2(3)
	La3/Ba3	0.75	0.4154(8)	-0.0371(8)	0.92(2)/0.09(3)	0.8(3)
	Ga1	-0.8872(3)	-0.2468(7)	0.2095(4)	1	0.49(7) a
	Ga2	0	0	0.2288(10)	1	0.49(7) a
	Ga3	0.5	0.5	0.2269(10)	1	0.49(7) a
	Ga4	0.75	-0.1051(8)	-0.2546(10) 1	0.49(7) a
	Ga5	0.25	0.1000(8)	0.2402(10)	1	0.49(7) a
	O1	-0.8869(4)	-0.2503(11) -0.1174(5)	1	0.87(7) b
	O2	-0.4746(5)	0.3684(6)	0.1364(7)	1	0.87(7) b
	O3	-0.5447(6)	-0.3805(6)	-0.3854(7)	1	0.87(7) b
	O4	-0.1270(6)	-0.0368(6)	-0.1705(8)	1	0.87(7) b
	O5	-0.8883(6)	0.0589(6)	0.3388(8)	1	0.87(7) b
	O6	0.75	0.2789(6)	0.1291(9)	1	0.87(7) b
	O7	0.75	-0.1195(11) 0.0671(11)	1	0.87(7) b
	O8	0.25	0.2490(13)	0.3164(7)	1	0.87(7) b
	O9	0.25	0.1114(12)	0.5716(12)	1	0.87(7) b
	O10	0.25	-0.0892(10) 0.2254(13)	0.77(2)	1

a,b Constrained to refine to the same value.

Table A . 49. Final NPD HR refined data of La1.8Ba0.2Ga3O7.4 (x = 0.8) composition structural parameters (S.G. P𝟒 ̅ 21m, a= b= 8.0578(6) Å, c= 5.2611(9) Å).

 A

	Atom	x	y	z	Occ	Biso
	La1/Ba1	0.3361(17)	0.1639(17)	0.471(4)	0.9/0.1	1.4(6)
	Ga1	0	0	0	1	0.8(6) a
	Ga2	0.1505(17)	0.3496(17)	-0.023(4)	1	0.8(6) a
	O1	0.5	0	0.184(7)	1	1.1(6) b
	O2	0.139(2)	0.361(2)	0.313(5)	1	1.1(6) b
	O3	0.0820(17)	0.158(2)	0.784(4)	1	1.1(6) b
	O4	0.341(10)	0.159(10)	-0.02(2)	0.20(5)	1
	a,b Constrained to refine to the same value.

Table A . 50. Final NPD HR refined data of La1.8Ba0.2Ga3O7.4 (x = 0.8) composition structural parameters (S.G. Ima2, a= 11.46505(19) Å, b= 11.32986(19) Å, c= 10.5331(2) Å).

 A

	Atom	x	y	z	Occ	Biso
	La1/Ba1	-0.5859(3)	0.2492(8)	0.4775(4)	0.928(7)/0.076(11) 0.28(11)
	La2/Ba2	0.75	0.0853(9)	-0.0266(10) 0.85(2)/0.16(3)	1.2(3)
	La3/Ba3	0.75	0.4167(10)	-0.0374(10) 0.92(2)/0.09(3)	1.4(3)
	Ga1	-0.8869(4)	-0.2467(8)	0.2095(4)	1	0.67(7) a
	Ga2	0	0	0.2273(12)	1	0.67(7) a
	Ga3	0.5	0.5	0.2263(12)	1	0.67(7) a
	Ga4	0.75	-0.1041(9)	-0.2563(12) 1	0.67(7) a
	Ga5	0.25	0.1010(9)	0.2416(12)	1	0.67(7) a
	O1	-0.8870(5)	-0.2501(12) -0.1176(6)	1	0.96(7) b
	O2	-0.4744(6)	0.3690(7)	0.1363(8)	1	0.96(7) b
	O3	-0.5445(7)	-0.3787(7)	-0.3822(8)	1	0.96(7) b
	O4	-0.1295(6)	-0.0360(6)	-0.1709(8)	1	0.96(7) b
	O5	-0.8882(7)	0.0585(6)	0.3384(8)	1	0.96(7) b
	O6	0.75	0.2798(7)	0.1275(10)	1	0.96(7) b
	O7	0.75	-0.1196(13) 0.0680(14)	1	0.96(7) b
	O8	0.25	0.2495(15)	0.3162(8)	1	0.96(7) b
	O9	0.25	0.1130(14)	0.5712(15)	1	0.96(7) b
	O10	0.25	-0.0916(11) 0.2239(14)	0.76(2)	1

a,b Constrained to refine to the same value.

Table A . 51. Final NPD HI refined data of La1.9Ba0.1Ga3O7.45 (x = 0.9) composition structural parameters (S.G. Ima2, a= 11.47152(16) Å, b= 11.29287(17) Å, c= 10.50526(18) Å).

 A

	Atom	x	y	z	Occ	Biso
	La1/Ba1	-0.5868(2)	0.2502(7)	0.4861(3)	0.966(6)/0.028(10) 0.27(7)
	La2/Ba2	0.75	0.0870(6)	-0.0081(6)	0.892(17)/0.11(3)	0.4(2)
	La3/Ba3	0.75	0.4165(6)	-0.0346(6)	0.969(17)/0.04(3)	0.49(18)
	Ga1	-0.8858(3)	-0.2422(5)	0.2191(3)	1	0.33(3) a
	Ga2	0	0	0.2388(9)	1	0.33(3) a
	Ga3	0.5	0.5	0.2391(8)	1	0.33(3) a
	Ga4	0.75	-0.1056(6)	-0.2466(7)	1	0.33(3) a
	Ga5	0.25	0.0966(6)	0.2485(8)	1	0.33(3) a
	O1	-0.8859(3)	-0.2488(8)	-0.1079(4)	1	0.42(7)
	O2	-0.4761(6)	0.3658(6)	0.1456(7)	1	0.80(12)
	O3	-0.5395(5)	-0.3775(5)	-0.3750(7)	1	0.32(10)
	O4	-0.1248(5)	-0.0357(5)	-0.1591(7)	1	0.87(11)
	O5	-0.8909(5)	0.0617(5)	0.3485(6)	1	0.59(11)
	O6	0.75	0.2835(6)	0.1341(9)	1	1.13(14)
	O7	0.75	-0.1227(9)	0.0752(9)	1	0.74(19)
	O8	0.25	0.2501(10)	0.3267(6)	1	0.58(9)
	O9	0.25	0.1082(10)	0.5845(9)	1	0.60(17)
	O10	0.25	-0.0858(7)	0.2296(9)	0.892(15)	1

a Constrained to refine to the same value.

Table A . 52. Final NPD HR refined data of La1.9Ba0.1Ga3O7.45 (x = 0.9) composition structural parameters (S.G. Ima2, a= 11.46923(16) Å, b= 11.29077(17) Å, c= 10.50358(18) Å).

 A

	Atom	x	y	z	Occ	Biso
	La1/Ba1	-0.5862(2)	0.2504(8)	0.4858(4)	0.968(6)/0.028(10) 0.38(8)
	La2/Ba2	0.75	0.0870(6)	-0.0090(7)	0.894(18)/0.11(3)	0.3(2)
	La3/Ba3	0.75	0.4166(7)	-0.0364(7)	0.971(18)/0.04(3)	0.6(2)
	Ga1	-0.8857(3)	-0.2425(6)	0.2192(4)	1	0.43(4) a
	Ga2	0	0	0.2373(10)	1	0.43(4) a
	Ga3	0.5	0.5	0.2394(10)	1	0.43(4) a
	Ga4	0.75	-0.1067(7)	-0.2467(8)	1	0.43(4) a
	Ga5	0.25	0.0956(7)	0.2498(8)	1	0.43(4) a
	O1	-0.8870(4)	-0.2483(9)	-0.1078(5)	1	0.57(8)
	O2	-0.4760(7)	0.3659(6)	0.1444(8)	1	0.86(14)
	O3	-0.5396(6)	-0.3778(6)	-0.3728(8)	1	0.61(13)
	O4	-0.1258(6)	-0.0362(6)	-0.1581(8)	1	1.23(13)
	O5	-0.8907(6)	0.0614(6)	0.3481(7)	1	0.87(13)
	O6	0.75	0.2845(7)	0.1345(10)	1	1.47(18)
	O7	0.75	-0.1223(10) 0.0758(10)	1	0.8(2)
	O8	0.25	0.2487(12)	0.3279(7)	1	0.55(10)
	O9	0.25	0.1080(11)	0.5833(10)	1	0.61(19)
	O10	0.25	-0.0872(8)	0.2297(10)	0.878(17)	1

a Constrained to refine to the same value.

Table A . 53. Final 525°C NPD HI refined data of La1.9Ba0.1Ga3O7.45 (x = 0.9) composition structural parameters (S.G. Ima2, a= 11.5006(2) Å, b= 11.3487(2) Å, c= 10.5398(2) Å).

 A

	Atom	x	y	z	Occ	Biso
	La1/Ba1	-0.5867(3)	0.2508(7)	0.4877(4)	0.967(6)/0.045(10) 1.19(9)
	La2/Ba2	0.75	0.0871(8)	-0.0079(8)	0.945(18)/0.06(3)	1.7(3)
	La3/Ba3	0.75	0.4169(8)	-0.0298(8)	0.945(18)/0.05(3)	1.6(2)
	Ga1	-0.8852(3)	-0.2411(5)	0.2228(4)	1	1.06(4) a
	Ga2	0	0	0.2382(11)	1	1.06(4) a
	Ga3	0.5	0.5	0.2368(11)	1	1.06(4) a
	Ga4	0.75	-0.1049(7)	-0.2427(9)	1	1.06(4) a
	Ga5	0.25	0.0984(7)	0.2494(10)	1	1.06(4) a
	O1	-0.8857(4)	-0.2481(8)	-0.1069(5)	1	1.00(8)
	O2	-0.4771(6)	0.3663(6)	0.1461(8)	1	1.75(14)
	O3	-0.5402(6)	-0.3770(5)	-0.3737(7)	1	0.83(12)
	O4	-0.1242(6)	-0.0338(6)	-0.1591(8)	1	1.68(14)
	O5	-0.8895(6)	0.0626(6)	0.3522(7)	1	1.28(12)
	O6	0.75	0.2792(7)	0.1382(9)	1	1.60(16)
	O7	0.75	-0.1246(9)	0.0759(10)	1	1.08(19)
	O8	0.25	0.2519(13)	0.3271(8)	1	1.72(12)
	O9	0.25	0.1065(11)	0.5844(12)	1	1.9(2)
	O10	0.25	-0.0836(9)	0.2318(10)	0.871(19)	1.8(2)

Table A . 54. Final 525°C NPD HR refined data of La1.9Ba0.1Ga3O7.45 (x = 0.9) composition structural parameters (S.G. Ima2, a= 11.5005(2) Å, b= 11.3482(2) Å, c= 10.5396(2) Å).

 A

	Atom	x	y	z	Occ	Biso
	La1/Ba1	0.3362(6)	0.1638(6)	0.514(2)	0.95(2)/0.05(2)	2.2(2)
	Ga1	0	0	0	1	1.82(17)
	Ga2	0.1398(7)	0.3602(7)	-0.028(2)	1	1.82(17)
	O1	0.5	0	0.206(3)	1	2.0(3)
	O2	0.1382(9)	0.3618(9)	0.308(2)	1	2.4(2)
	O3	0.0873	0.1645(10)	0.7959(17)	1	2.7(2)
	O4	0.326(2)	0.174(2)	0.006(8)	0.234(17)	1
	Atom	x	y	z	Occ	Biso
	La1/Ba1	-0.5862(3)	0.2502(9)	0.4885(5)	0.988(6)/0.002(10) 1.08(10)
	La2/Ba2	0.75	0.0866(8)	-0.0082(9)	0.902(19)/0.10(3)	1.4(3)
	La3/Ba3	0.75	0.4173(9)	-0.0305(9)	0.902(19)/0.10(3)	1.6(3)
	Ga1	-0.8855(4)	-0.2413(6)	0.2219(5)	1	1.10(4) a
	Ga2	0	0	0.2380(13)	1	1.10(4) a
	Ga3	0.5	0.5	0.2393(12)	1	1.10(4) a
	Ga4	0.75	-0.1048(8)	-0.2435(10) 1	1.10(4) a
	Ga5	0.25	0.0987(8)	0.2492(11)	1	1.10(4) a
	O1	-0.8866(4)	-0.2489(10) -0.1072(5)	1	1.02(9)
	O2	-0.4777(8)	0.3672(8)	0.1464(10)	1	2.12(19)
	O3	-0.5402(6)	-0.3766(6)	-0.3707(9)	1	0.86(14)
	O4	-0.1250(7)	-0.0351(7)	-0.1576(9)	1	1.82(17)
	O5	-0.8889(7)	0.0622(7)	0.3519(9)	1	1.52(16)
	O6	0.75	0.2801(8)	0.1385(10)	1	1.68(19)
	O7	0.75	-0.1252(10) 0.0769(12)	1	1.4(2)
	O8	0.25	0.2513(15)	0.3273(8)	1	1.53(14)
	O9	0.25	0.1068(12)	0.5830(13)	1	1.5(2)
	O10	0.25	-0.0844(10) 0.2316(12)	0.85(2)	1.7(3)

a Constrained to refine to the same value.

Table A . 56. Final 720°C NPD HI refined data of La1.9Ba0.1Ga3O7.45 (x = 0.9) composition structural parameters (S.G. Ima2, a= 11.5122(3) Å, b= 11.3611(3) Å, c= 10.5622(4) Å).

 A

	Atom	x	y	z	Occ	Biso
	La1/Ba1	-0.5870(4)	0.2502(9)	0.4862(7)	0.954(11)/0.036(18) 1.37(15)
	La2/Ba2	0.75	0.0842(10)	-0.0112(11) 0.95(2)/0.06(4)	2.0(4)
	La3/Ba3	0.75	0.4154(10)	-0.0291(12) 0.94(2)/0.07(4)	1.9(3)
	Ga1	-0.8859(5)	-0.2409(8)	0.2231(8)	1	1.77(13)
	Ga2	0	0	0.2456(11)	1	1.2(2)
	Ga3	0.5	0.5	0.2340(11)	1	0.79(18)
	Ga4	0.75	-0.1067(9)	-0.2443(11) 1	1.1(2)
	Ga5	0.25	0.0948(9)	0.2513(12)	1	1.3(2)
	O1	-0.8870(7)	-0.2457(9)	-0.1079(7)	1	1.18(14)
	O2	-0.4829(9)	0.3647(8)	0.1536(10)	1	1.86(18)
	O3	-0.5434(7)	-0.3797(7)	-0.3790(10) 1	1.41(17)
	O4	-0.1205(9)	-0.0346(8)	-0.1577(11) 1	1.9(2)
	O5	-0.8912(8)	0.0646(7)	0.3520(9)	1	1.33(17)
	O6	0.75	0.2794(9)	0.1477(15)	1	2.2(3)
	O7	0.75	-0.1251(12) 0.0775(15)	1	1.9(3)
	O8	0.25	0.2490(19)	0.3271(13)	1	2.6(2)
	O9	0.25	0.1088(13)	0.5823(14)	1	1.4(3)
	O10	0.25	-0.0824(13) 0.227(2)	0.79(3)	1

Table A . 57. Final 720°C NPD HR refined data of La1.9Ba0.1Ga3O7.45 (x = 0.9) composition structural parameters (S.G. P𝟒 ̅ 21m, a= b= 8.1177(3) Å, c= 5.2782(4) Å).

 A

	Atom	x	y	z	Occ	Biso
	La1/Ba1	0.3362(6)	0.1638(6)	0.518(2)	0.95(1)/0.05(2)	2.2(2)
	Ga1	0	0	0	1	2.1(2)
	Ga2	0.1399(7)	0.3601(7)	-0.026(2)	1	2.1(2)
	O1	0.5	0	0.194(4)	1	2.4(3)
	O2	0.1360(10)	0.3640(10)	0.308(3)	1	2.6(3)
	O3	0.0873	0.1639(12)	0.795(2)	1	3.6(3)
	O4	0.322(3)	0.178(3)	-0.003(12)	0.182(17)	1

Table A . 58. Final 720°C NPD HR refined data of La1.9Ba0.1Ga3O7.45 (x = 0.9) composition structural parameters (S.G. Ima2, a= 11.5103(3) Å, b= 11.3588(3) Å, c= 10.5592(3) Å).

 A

	Atom	x	y	z	Occ	Biso
	La1/Ba1	-0.5867(5)	0.2495(10)	0.4869(7)	0.954(12)/0.046(19) 1.26(16)
	La2/Ba2	0.75	0.0853(10)	-0.0093(12) 0.95(2)/0.05(4)	1.5(4)
	La3/Ba3	0.75	0.4165(12)	-0.0302(13) 0.93(2)/0.07(4)	2.0(4)
	Ga1	-0.8860(6)	-0.2412(9)	0.2220(8)	1	1.54(13)
	Ga2	0	0	0.2438(13)	1	1.1(2)
	Ga3	0.5	0.5	0.2352(13)	1	0.74(19)
	Ga4	0.75	-0.1063(10) -0.2440(12) 1	0.9(2)
	Ga5	0.25	0.0938(10)	0.2508(14)	1	1.3(3)
	O1	-0.8889(7)	-0.2463(11) -0.1086(8)	1	1.04(14)
	O2	-0.4802(10)	0.3663(10)	0.1514(12)	1	1.9(2)
	O3	-0.5418(9)	-0.3779(8)	-0.3768(11) 1	1.29(19)
	O4	-0.1224(10)	-0.0328(9)	-0.1569(12) 1	1.7(2)
	O5	-0.8894(10)	0.0644(8)	0.3514(10)	1	1.34(19)
	O6	0.75	0.2782(10)	0.1439(15)	1	1.6(3)
	O7	0.75	-0.1238(14) 0.0776(17)	1	1.7(3)
	O8	0.25	0.247(2)	0.3299(16)	1	2.7(3)
	O9	0.25	0.1080(15)	0.5814(16)	1	1.4(3)
	O10	0.25	-0.0827(13) 0.227(2)	0.89(3)	1
						240

Table A . 59. Final 770°C NPD HI refined data of La1.9Ba0.1Ga3O7.45 (x = 0.9) composition structural parameters (S.G. P𝟒 ̅ 21m, a= b= 8.11246(16) Å, c= 5.2807(3) Å).

 A

	Atom	x	y	z	Occ	Biso
	La1/Ba1	0.3357(4)	0.1643(4)	0.5097(16)	0.955(10)/0.051(17) 2.11(15)
	Ga1	0	0	0	1	1.34(14)
	Ga2	0.1417(5)	0.3583(5)	-0.0260(15)	1	2.22(13)
	O1	0.5	0	0.200(2)	1	2.11(18)
	O2	0.1356(6)	0.3644(6)	0.3125(16)	1	2.29(16)
	O3	0.0873	0.1621(7)	0.7917(12)	1	2.66(13)
	O4	0.326(2)	0.174(2)	-0.011(6)	0.218(13)	1
	Table A. 60. Final 770°C NPD HI refined data of La1.9Ba0.1Ga3O7.45 (x = 0.9) composition structural
	parameters (S.G. Ima2, a= 11.5107(4) Å, b= 11.3705(4) Å, c= 10.5663(5) Å).
	Atom	x	y	z	Occ	Biso
	La1/Ba1	-0.5861(8)	0.2501(13)	0.4812(11)	0.963(18/0.03(3)	1.9(2)
	La2/Ba2	0.75	0.0829(17)	-0.0175(19) 0.95(3)/0.07(6)	2.5(6)
	La3/Ba3	0.75	0.4114(16)	-0.0288(18) 0.93(3)/0.07(5)	1.8(5)
	Ga1	-0.8855(8)	-0.2436(12) 0.2216(11)	1	1.19(18)
	Ga2	0	0	0.2477

Table A . 61. Final 770°C NPD HR refined data of La1.9Ba0.1Ga3O7.45 (x = 0.9) composition structural parameters (S.G. P𝟒 ̅ 21m, a= b= 8.11146(14) Å, c= 5.2804(3) Å).

 A

	Atom	x	y	z	Occ	Biso
	La1/Ba1	0.3361(4)	0.1639(4)	0.5107(15)	0.956(12)/0.05(2) 2.08(17)
	Ga1	0	0	0	1	1.00(14)
	Ga2	0.1417(5)	0.3583(5)	-0.0259(15)	1	2.17(13)
	O1	0.5	0	0.196(2)	1	1.99(19)
	O2	0.1366(6)	0.3634(6)	0.3114(16)	1	2.16(16)
	O3	0.0873	0.1629(8)	0.7916(14)	1	3.05(15)
	O4	0.3156(18)	0.1845(18)	-0.033(5)	0.256(13)	1
	Table A. 62. Final 770°C NPD HR refined data of La1.9Ba0.1Ga3O7.45 (x = 0.9) composition structural
	parameters (S.G. Ima2, a= 11.5095(4) Å, b= 11.3697(4) Å, c= 10.5639(5) Å).
	Atom	x	y	z	Occ	Biso
	La1/Ba1	-0.5852(7)	0.2543(14)	0.4621(12)	0.97(2)/0.03(3)	1.5(3)
	La2/Ba2	0.75	0.083(2)	-0.032(2)	0.94(4)/0.07(6)	3.0(7)
	La3/Ba3	0.75	0.4134(15)	-0.0508(17) 0.93(3)/0.07(5)	1.3(5)
	Ga1	-0.8852(8)	-0.2398(12) 0.2007(11)	1	1.0(2)
	Ga2	0	0	0.2242
	O1	-0.8917(11)	-0.2449(14) -0.1105(11) 1	0.9(2)
	O2	-0.4881(13)	0.3615(11)	0.1568(15)	1	1.7(3)
	O3	-0.5465(10)	-0.3805(10) -0.3789(13) 1	0.6(2)
	O4	-0.1191(14)	-0.0379(14) -0.1608(17) 1	1.9(3)
	O5	-0.8923(14)	0.0670(12)	0.3532(14)	1	1.6(3)
	O6	0.75	0.2832(18)	0.154(3)	1	3.1(5)
	O7	0.75	-0.1243(17) 0.077(2)	1	1.0(4)
	O8	0.25	0.257(3)	0.327(2)	1	2.7(4)
	O9	0.25	0.1053(19)	0.584(2)	1	1.7(4)
	O10	0.25	-0.088(2)	0.221(3)	0.89(5)	1
						241

Table A . 63. Final 820°C NPD HI refined data of La1.9Ba0.1Ga3O7.45 (x = 0.9) composition structural parameters (S.G. P𝟒 ̅ 21m, a= b= 8.11195(7) Å, c= 5.28584(10) Å).

 A

	Atom	x	y	z	Occ	Biso
	La1/Ba1	0.33517(14) 0.16483(14) 0.5069(4)	0.951(2)/0.050(3)	2.10(6)
	Ga1	0	0	0	1	1.48(8)
	Ga2	0.14122(18) 0.35878(18) -0.0297(4)	1	1.85(6)
	O1	0.5	0	0.1911(9)	1	4.13(18)
	O2	0.1367(2)	0.3633(2)	0.3104(4)	1	2.07(8)
	O3	0.0873	0.1637(3)	0.7955(4)	1	3.86(12)
	O4	0.3259(7)	0.1741(7)	0.0009(19)	0.225(4)	1

Table A . 64. Refined anisotropic thermal parameters of La1.9Ba0.1Ga3O7.45 (x = 0.9) composition from 820°C NPD HI data.

 A

	Atom	B11	B22	B33	B12	B13	B23
	La1/Ba1	1.96(5)	1.96(5)	2.37(8)	0.74(6)	0.13(6)	-0.13(6)
	Ga1	0.94(6)	0.94(6)	2.57(12)	0	0	0
	Ga2	2.16(6)	2.16(6)	1.21(8)	-0.32(8)	0.01(6)	-0.01(6)
	O1	4.82(16)	4.82(16)	2.76(24)	-3.32(24)	0	0
	O2	2.

Table A . 65. Final 820°C NPD HR refined data of La1

 A

	Atom	x	y	z	Occ	Biso
	La1/Ba1	0.33538(16) 0.16462(16) 0.5083(5)	0.950(2)/0.050(4)	2.12(7)
	Ga1	0	0	0	1	1.45(9)
	Ga2	0.14099(19) 0.35901(19) -0.0302(4)	1	1.86(7)
	O1	0.5	0	0.1915(9)	1	3.92(18)
	O2	0.1370(3)	0.3630(3)	0.3100(4)	1	2.22(10)
	O3	0.0873	0.1640(3)	0.7957(5)	1	4.05(13)
	O4	0.3262(8)	0.1738(8)	0.002(2)	0.225(4)	1

.9Ba0.1Ga3O7.45 (x = 0.9) composition structural parameters (S.G. P𝟒 ̅ 21m, a= b= 8.10865(6) Å, c= 5.28369(9) Å).

Table A . 66. Refined anisotropic thermal parameters of La1.9Ba0.1Ga3O7.45 (x = 0.9) composition from 820°C NPD HR data.

 A

	Atom	B11	B22	B33	B12	B13	B23
	La1/Ba1	1.93(6)	1.93(6)	2.50(10)	0.67(6)	0.14(7)	-0.14(7)
	Ga1	0.98(7)	0.98(7)	2.39(12)	0	0	0
	Ga2	2.22(6)	2.22(6)	1.15(9)	0.27(8)	0.13(6)	-0.13(6)
	O1	4.66(16)	4.66(16)	2.45(24)	-3.40(24)	0	0
	O2	2.87(10)	2.87(10)	0.92(10)	0.05(12)	0.09(6)	-0.09(6)
	O3	6.32(15)	2.23(10)	3.59(13)	-1.13(10)	2.57(10)	-0.29(11)

Table A . 67. Extracted activation energies from Arrhenius plots of the La1+xBa1-xGa3O7+x/2 solid solution compositions.

 A

	x value	Ea (eV)
	1	1.21(3) (300 -600 °C) / 1.62(2) (600 -800 °C)
	0.9	1.25(2) (300-800 °C)
	0.8	1.08(2) (300 -650 °C) / 0.50(6) (650 -800 °C)
	0.725	0.95(3) (300 -650 °C)
	0.7	0.96(3) (300 -600 °C)
	0.6	0.92(3) (300 -500 °C)
	0.5	0.96(4) (300 -500 °C) / 0.48(2)(500 -650 C)

Table A . 68. Refined structural parameters obtained from SPD data collected at room temperature on Ca5Ga6O14 (x = 0) (Cmc2 space group, a= 11.50564(7) Å, b= 11.27722(8) Å and c= 10.48698(8) Å) sample.

 A

	Atom	Wyck x	y	z	Occ	Biso
	Ca1 Ca2 Ca3 Ga1 Ga2 Ga3 Ga4 O1 O2 O3 O4 O5 O6 O7 O8 O9	8b 8b 4a 8b 4a 4a 8b 8b 4a 8b 8b 4a 8b 4a 8b 4a	0.1581(2) 0.3570(2) 0 0.35656(9) 0 0 0.24473(12) 0.2842(6) 0 0.2665(7) 0.3722(7) 0 0.3415(5) 0 0.1285(6) 0	0.1023(2) 0.31652(19) 0.5248(3) 0.14580(12) 0.30107(15) -0.00041(15) 0.40228(10) 0.2793(6) 0.6104(8) 0.0277(5) 0.4361(6) 0.1437(9) 0.1463(6) 0.0080(8) 0.3726(6) 0.2944(8)	0.25 0.2004(3) 0.2448(4) 0.5088(3) 0.4422(3) 0.4644(3) 0.4764(3) 0.5855(7) 0.5776(9) 0.5955(7) 0.3773(7) 0.3805(9) 0.3408(7) 0.6334(11) 0.3621(7) 0.6167(10)	1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1	0.44(5) 0.54(5) 0.35(8) 0.27(3) 0.33(4) 0.51(4) 0.30(2) 0.13(5) 0.13(5) 0.13(5) 0.13(5) 0.13(5) 0.13(5) 0.13(5) 0.13(5) 0.13(5)

Table A . 69. Refined structural parameters obtained from SPD data collected at room temperature on La0

 A

	Atom	Wyck x	y	z	Occ	Biso
	Ca1/La1 8b Ca2 8b Ca3/La3 4a Ga1 8b Ga2 4a Ga3 4a Ga4 8b O1 8b O2 4a O3 8b O4 8b O5 4a O6 8b O7 4a O8 8b O9 4a	0.1614(3) 0.3559(3) 0 0.35621(9) 0 0 0.24453(12) 0.2814(6) 0 0.2725(7) 0.3692(7) 0 0.3457(6) 0 0.1242(6) 0	0.1031(2) 0.3218(2) 0.5223(2) 0.14654(12) 0.29818(16) 0.00029(15) 0.40138(10) 0.2810(6) 0.6236(8) 0.0238(5) 0.4370(6) 0.1399(10) 0.1476(7) 0.0091(9) 0.3707(7) 0.2982(8)	0.25 0.2001(4) 0.2412(3) 0.5097(3) 0.4415(3) 0.4649(3) 0.4767(3) 0.5849(8) 0.5781(10) 0.5988(8) 0.3835(8) 0.3683(10) 0.3462(8) 0.6331(12) 0.3572(7) 0.6112(11)	0.990(3)/0.010(3) 1.52(8) 1 1.16(6) 0.756(4)/0.244(4) 0.90(8) 1 0.38(3) 1 0.36(4) 1 0.37(4) 1 0.31(2) 1 0.37(5) 1 0.37(5) 1 0.37(5) 1 0.37(5) 1 0.37(5) 1 0.37(5) 1 0.37(5) 1 0.37(5) 1 0.37(5)

.25Ca4.75Ga6O14.125 (x = 0) (Cmc2 space group, a= 11.47670(8) Å, b= 11.29646(11) Å and c= 10.51206(10) Å) sample.

Table A . 70. Refined structural parameters obtained from NPD (HI) data collected at room temperature on Ca5Ga6O14 (x = 0) (Cmc21 space group, a= 11.51140(13) Å, b= 11.28267(12) Å and c= 10.49288(12) Å) sample.

 A

	Atom	Wyck x	y	z	Occ	Biso
	Ca1/La1 8b Ca2 8b Ca3/La3 4a Ga1 8b Ga2 4a Ga3 4a Ga4 8b O1 8b O2 4a O3 8b O4 8b O5 4a O6 8b O7 4a O8 8b O9 4a	0.1584(3) 0.3582(4) 0 0.35648(19) 0 0 0.2454(2) 0.2850(2) 0 0.2674(3) 0.3727(3) 0 0.3394(2) 0 0.1261(3) 0	0.1013(3) 0.3164(3) 0.5251(5) 0.1462(2) 0.2993(3) -0.0009(3) 0.4018(2) 0.2781(3) 0.6162(4) 0.0271(3) 0.4350(3) 0.1467(4) 0.1497(3) 0.0087(4) 0.3732(3) 0.2991(4)	0.25 0.2028(6) 0.2453(6) 0.5103(5) 0.4446(5) 0.4660(5) 0.4793(5) 0.5863(5) 0.5744(6) 0.5958(6) 0.3816(6) 0.3831(6) 0.3382(5) 0.6392(7) 0.3668(6) 0.6145(6)	1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1	0.87(6) 0.79(7) 0.73(10) 0.21(4) 0.45(6) 0.30(6) 0.13(4) 0.51(5) 0.83(8) 0.75(6) 0.47(5) 0.54(7) 0.44(5) 0.93(8) 0.95(6) 0.44(9)

Table A . 71. Refined structural parameters obtained from NPD (HI) data collected at room temperature on La0.25Ca4.75Ga6O14.125 (x = 0.25) (Cmc21 space group, a= 11.48245(16) Å, b= 11.30189(16) Å and c= 10.51841(17) Å) sample. La content was constrained to refine near the nominal value (penalty function used), which led a refined composition of: La0.27(7)Ca4.73(7)Ga6O14. Note that the composition is not charge balanced due to the interstitial oxide not added to the structure.

 A

	Atom	Wyck x	y	z	Occ	Biso
	Ca1/La1 8b Ca2 8b Ca3/La3 4a Ga1 8b Ga2 4a Ga3 4a Ga4 8b O1 8b O2 4a O3 8b O4 8b O5 4a O6 8b O7 4a O8 8b O9 4a	0.1580(5) 0.3557(5) 0 0.3560(2) 0 0 0.2437(3) 0.2832(3) 0 0.2730(3) 0.3732(4) 0 0.3407(3) 0 0.1270(4) 0	0.1012(5) 0.3165(4) 0.5212(5) 0.1469(3) 0.2979(4) 0.0003(4) 0.4012(3) 0.2771(3) 0.6220(5) 0.0251(3) 0.4350(3) 0.1469(5) 0.1493(4) 0.0089(6) 0.3722(4) 0.3002(5)	0.25 0.2038(7) 0.2429(7) 0.5121(6) 0.4444(7) 0.4682(6) 0.4805(6) 0.5867(7) 0.5754(7) 0.5971(7) 0.3838(7) 0.3822(7) 0.3401(6) 0.6409(8) 0.3660(7) 0.6140(8)	0.97(2)/0.03(2) 1 0.79(3)/0.21(3) 1 1 1 1 1 1 1 1 1 1 1 1 1	1.77(13) 1.41(9) 0.85(14) 0.25(4) 1.00(9) 0.50(8) 0.44(5) 0.68(6) 1.59(11) 1.05(7) 0.73(7) 0.76(9) 0.85(7) 1.18(10) 1.43(8) 1.24(12)

Table A . 72. Refined structural parameters obtained from NPD (HR) data collected at room temperature on Ca5Ga6O14 (x = 0) (Cmc21 space group, a= 11.5019(2) Å, b= 11.2734(2) Å and c= 10.4840(2) Å) sample using the Rietan program.

 A

	Atom	Wyck x	y	z	Occ	Biso
	Ca1/La1 8b Ca2 8b Ca3/La3 4a Ga1 8b Ga2 4a Ga3 4a Ga4 8b O1 8b O2 4a O3 8b O4 8b O5 4a O6 8b O7 4a O8 8b O9 4a	0.1586(4) 0.3578(4) 0 0.3552(2) 0 0 0.2450(2) 0.2848(3) 0 0.2681(3) 0.3734(3) 0 0.3391(3) 0 0.1273(3) 0	0.1019(4) 0.3161(3) 0.5253(5) 0.1464(2) 0.2995(3) -0.0005(3) 0.4021(2) 0.2779(3) 0.6169(4) 0.0269(3) 0.4341(3) 0.1467(4) 0.1496(3) 0.0087(4) 0.3731(3) 0.2985(4)	0.25 0.2036(6) 0.2439(7) 0.5104(5) 0.4433(5) 0.4667(5) 0.4795(5) 0.5873(5) 0.5763(6) 0.5938(6) 0.3823(6) 0.3829(6) 0.3382(5) 0.6387(7) 0.3666(6) 0.6157(6)	1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0	0.79(6) 0.69(7) 0.85(11) 0.31(4) 0.32(6) 0.61(7) 0.36(4) 0.58(5) 0.58(8) 0.58(6) 0.45(6) 0.61(7) 0.57(2) 0.75(8) 0.83(6) 0.75(9)

Table A . 73. Refined structural parameters obtained from NPD (HR) data collected at room temperature on

 A

	Atom	Wyck x	y	z	Occ	Biso
	Ca1/La1 8b Ca2 8b Ca3/La3 4a Ga1 8b Ga2 4a Ga3 4a Ga4 8b O1 8b O2 4a O3 8b O4 8b O5 4a O6 8b O7 4a O8 8b O9 4a	0.1573(5) 0.3580(5) 0.0 0.3565(2) 0.0 0.0 0.2429(3) 0.2840(3) 0.0 0.2724(3) 0.3724(4) 0.0 0.3408(3) 0.0 0.1240(4) 0.0	0.0993(5) 0.3171(4) 0.5217(5) 0.1469(3) 0.2982(4) -0.0002(4) 0.4020(3) 0.2773(3) 0.6243(5) 0.0246(3) 0.4345(3) 0.1480(5) 0.1477(4) 0.0110(5) 0.3712(4) 0.3018(5)	0.25 0.2044(8) 0.2414(7) 0.5112(6) 0.4444(7) 0.4689(7) 0.4805(6) 0.5855(7) 0.5777(7) 0.5950(7) 0.3830(7) 0.3825(7) 0.3407(6) 0.6407(8) 0.3661(7) 0.6153(8)	0.93(2)/0.07(2) 1.0 0.87(3)/0.13(3) 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0	2.10(13) 1.77(10) 0.89(14) 0.32(5) 0.78(8) 0.50(8) 0.46(5) 0.72(6) 1.90(11) 0.89(6) 0.87(8) 0.71(8) 0.77(7) 0.91(10) 1.20(8) 1.02(11)

La0.25Ca4.75Ga6O14.125 (x = 0.25) (Cmc21 space group, a= 11.4716(3) Å, b= 11.2913(2) Å and c= 10.5082(2) Å) sample using the Rietan program.

Table A . 74. Comparison of the different refined Ca/La content and the reliability factors on both high intensity (HI) and high resolution (HR) NPD data refinements, with and without constraints.

 A

	Data set		NPD HI
	Refinement type	No constraints	Constrained La content
	Atom site	Ca1/La1	Ca3/La3	Ca1/La1	Ca3/La3
	Refined occupancy	0.99(2)Ca1 0.01(2)La1	0.83(3)Ca3 0.17(3)La3	0.97(2)Ca1 0.03(2)La1	0.79(3)Ca3 0.21(3)La3
	Reliability factors	Rwp= 2.72% GOF= 0.89	Rwp= 2.76% GOF= 0.90
	Data set		NPD HR
	Refinement type	No constraints	Constrained La content
	Site	Ca1/La1	Ca3/La3	Ca1/La1	Ca3/La3
	Refined occupancy	0.99(2)Ca1 0.01(2)La1	0.91(3)Ca3 0.09(3)La3	0.96(2)Ca1 0.04(2)La1	0.81(3)Ca3 0.18(3)La3
	Reliability factors	Rwp= 3.20% GOF= 0.59	Rwp= 3.21% GOF= 0.60

Table 1 .

 1 Structural Parameters of Cation-Ordered SrYbGa 3 O 7 Obtained by Rietveld Refinement against SPD and NPD Data (Combined) at Room Temperature (P2 1 2 1 2 Space Group, a = 23.70167(7) Å, b = 7.92110(3) Å, and c = 5.21162(2) Å)

	atom	site	xyz	occ	U(eq)
	Yb1/Sr1	4c	0.21967(3)	0.14373(8)	0.49426(12)	0.5/0.5	0.0077(2) a
	Yb2	4c	0.38103(2)	0.30934(6)	0.45529(9)	1	0.0101(1) a
	Sr3	4c	0.05795(4)	0.33953(11)	0.50839(18)	1	0.0098(2) a
	Ga1	4c	0.44940(4)	0.14505(14)	0.0131(2)	1	0.0054(3)
	Ga2	2a	0	0	0.9759(4)	1	0.0066(4)
	Ga3	4c	0.17317(5)	0.48007(13)	0.0014(3)	1	0.0047(2)
	Ga4	4c	0.28948(4)	0.33540(13)	0.9535(2)	1	0.0056(3)
	Ga5	4c	0.11858(5)	0.12314(12)	0.03036(19)	1	0.0065(3)
	O1	4c	0.45607(14)	0.3444(5)	0.2033(7)	1	0.0089(7)
	O2	4c	0.38457(14)	0.0730(4)	0.1899(6)	1	0.0043(7)
	O3	4c	0.29223(14)	0.3327(5)	0.3001(7)	1	0.0190(10)
	O4	4c	0.44114(14)	0.1434(5)	0.6766(6)	1	0.0095(7)
	O5	4c	0.12726(17)	0.1121(5)	0.6862(6)	1	0.0150(8)
	O6	2b	0.5	0	0.1551(9)	1	0.0082(10)
	O7	4c	0.22859(17)	0.4269(5)	0.7736(8)	1	0.0156(8)
	O8	4c	0.04632(15)	0.1439(5)	0.1532(7)	1	0.0167(9)
	O9	4c	0.29646(16)	0.1315(6)	0.7764(8)	1	0.0173(9)
	O10	4c	0.15349(17)	0.2993(5)	0.2025(7)	1	0.0170(9)
	O11	4c	0.34815(14)	0.4525(4)	0.7940(6)	1	0.0079(7)

a

Table 2 .

 2 A-O Interatomic Distances and Bond Valence Sums Calculated for the Three Crystallographic A Sites of Cation-Ordered SrYbGa 3 O 7

	bond	length (Å)	bond	length (Å)	bond	length (Å)
	(Sr/Yb)1-O9	2.342(4) Yb2-O1	2.228(3) Sr3-O8	2.430(4)
	(Sr/Yb)1-O5	2.421(4) Yb2-O11	2.238(3) Sr3-O6	2.565(3)
	(Sr/Yb)1-O3	2.494(4) Yb2-O4	2.256(4) Sr3-O4	2.593(4)
	(Sr/Yb)1-O10	2.508(4) Yb2-O3	2.262(3) Sr3-O5	2.608(4)
	(Sr/Yb)1-O7	2.531(4) Yb2-O2	2.329(3) Sr3-O2	2.783(3)
	(Sr/Yb)1-O11	2.671(3) Yb2-O5	2.517(4) Sr3-O10 2.788(4)
	(Sr/Yb)1-O7	2.682(4) Yb2-O9	2.967(4) Sr3-O4	2.935(3)
	(Sr/Yb)1-O3	2.702(4) Yb2-O11	3.711(3) Sr3-O1	3.195(4)
	BVS (Sr)	2.68	BVS (Sr) 3.84	BVS (Sr) 1.76
	BVS (Yb)	1.87	BVS (Yb)	2.68	BVS (Yb)	1.23

Refined structural parameters obtained from SPD data collected at room temperature on cation-ordered SrErGa3O7 (P21212 space group, a = 23.7790(1) Å, b = 7.93013(4) Å and c = 5.22786(2) Å).

	Atom Tables S5. Atom Tables S7.	Site	Site x	x	y	Y	z	z	Occ	Occ	Uiso U iso
	Tm1/ Sr1 Tm2 Er1/ Sr1 4c	4c 4c	0.21996(3) 0.38119(2) 2.400(12)	0.14458(8) 0.31222(6) 2.400(12)	0.49507(13) 0.45491(10) 2.400(12)	0.5/0.5 1 0.504(3)/0.496(3)	0.0060(2) 0.0069(1) 0.0081(3)
	Sr3 Er2/ Sr2	4c	4c	0.05781(4) 2.431(12)	0.33948(13) 2.431(12)	0.5090(2) 2.431(12)	1 0.863(3)/0.137(3)	0.0086(3) 0.0057(2)
	Ga1 Sr3/Er3	4c	4c	0.44927(5) 0.05550(6)	0.14431(16) 0.33884(18)	0.0101(3) 0.5025(3)	1 0.868(4)/0.132(4)	0.0051(3) 0.0114(4)
	CONTENT * sı Supporting Information Ga2 2a Ga3 4c Ga1 4c 0.44958(8) 0 0.17290(6)	0 0.48152(15) 0.1445(2)	0.9800(4) 0.9992(3) 0.0139(3)	1	1 1	0.0048(4) 0.0036(3) 0.0041(4)
	The Supporting Information is available free of charge at Ga4 4c 0.28920(5) 0.33617(15) Ga2 2a 0 0 https://pubs.acs.org/doi/10.1021/acs.inorgchem.1c01565. Ga5 4c 0.11827(6) 0.12410(14) Ga3 4c 0.17125(8) 0.4862(2) Structure solution description; photograph of samples, in situ X-ray powder diffraction data, Rietveld refine-O1 4c 0.4575(3) 0.3414(10) O2 4c 0.3860(3) 0.0699(9) Ga4 4c 0.28803(7) 0.3416(2) ment plots, transmission electron microscopy, stability domains and optical properties (Figures S1-S7); O3 4c 0.2907(3) 0.3382(10) Ga5 4c 0.11858(9) 0.1279(2) Refined structural parameters and interatomic distances O4 4c 0.4439(3) 0.1450(10) O1 4c 0.4580(5) 0.3503(15) (Tables S1-S20) (PDF) Accession Codes O5 4c 0.1282(3) 0.1206(9) O6 2b 0.5 0 O2 4c 0.3834(5) 0.0776(13) CCDC 2081671-2081676 and 2081688-2081692 contain the supplementary crystallographic data for this paper. These O7 4c 0.2258(3) 0.4230(10) O3 4c 0.2903(4) 0.3408(14)	0.9518(2) 0.9854(7) 0.0312(2) 0.0016(6) 0.2031(14) 0.1978(14) 0.9573(3) 0.3003(12) 0.0331(3) 0.6755(13) 0.195(2) 0.6855(11) 0.1570(18) 0.206(2) 0.7708(17) 0.3119(17)	1 1 1 1 1 1 1	1 1 1 1 1 1 1 1 1	0.0045(6) 0.0029(3) 0.0043(3) 0.0035(3) 0.0129(6) a 0.0129(6) a 0.0033(4) 0.0036(4) 0.0129(6) a 0.0129(6) a 0.0112(7) a 0.0129(6) a 0.0112(7) a 0.0129(6) a 0.0129(6) a 0.0112(7) a
	data can be obtained free of charge via www.ccdc.cam.ac.uk/ data_request/cif, or by emailing data_request@ccdc.cam.ac. uk, or by contacting The Cambridge Crystallographic Data O8 4c 0.0482(3) 0.1424(10) O9 4c 0.2982(3) 0.1308(10) O4 4c 0.4425(5) 0.1491(15) O10 4c 0.1519(3) 0.3020(10) O5 4c 0.1279(6) 0.1195(13) Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: +44 1223 336033. O11 4c 0.3467(3) 0.4558(10) O6 2b 0.5 0	0.1656(14) 0.7806(17) 0.6797(18) 0.1986(14) 0.6936(15) 0.7984(12) 0.152(2)	1 1 1	1 1 1 1	0.0129(6) a 0.0112(7) a 0.0129(6) a 0.0129(6) a 0.0112(7) a 0.0129(6) a 0.0112(7) a
	O7 ■ AUTHOR INFORMATION 4c 0.2276(5) Corresponding Authors O8 4c 0.0489(5)	0.4305(14) 0.1335(14)	0.768(2) 0.170(2)	1 1		0.0112(7) a 0.0112(7) a
	O9	4c		0.2989(5)	0.1465(15)	0.785(2)	1		0.0112(7) a
	O10	4c		0.1491(5)	0.3086(14)	0.195(2)	1		0.0112(7) a
	O11	4c		0.3441(5)	0.4570(13)	0.7905(16)	1		0.0112(7) a
	Ga2-O8			1.877(8)			Ga4-O7		1.906(8)

a : constrained to refine to the same Uiso values

Refined structural parameters obtained from SPD data collected at room temperature on cation-ordered SrHoGa3O7 from SPD data (P21212 space group, a = 23.8034(1) Å, b = 7.93800(4) Å and c = 5.23828(2) Å).

	Atom	Site	x	y	z	Occ	U iso
	Ho1/ Sr1	4c	0.21976(4)	0.14841(10)	0.49652(14)	0.499(2)/0.501(2)	0.0080(2)
	Ho2/Sr2	4c	0.38174(3)	0.31544(8)	0.45774(11)	0.924(2)/0.076(2)	0.0072(2)
	Sr3/ Ho3	4c	0.05660(5)	0.33980(16)	0.5059(2)	0.924(3)/0.076(3)	0.0146(3)
	Ga1	4c	0.44942(6)	0.14477(19)	0.0122(3)	1	0.0072(4)
	Ga2	2a	0	0	0.9842(5)	1	0.0078(4)
	Ga3	4c	0.17200(6)	0.48408(18)	0.0028(4)	1	0.0058(3)
	Ga4	4c	0.28820(6)	0.33958(18)	0.9549(3)	1	0.0052(3)
	Ga5	4c	0.11873(7)	0.12693(18)	0.0329(2)	1	0.0051(3)
	O1	4c	0.4568(4)	0.3471(12)	0.2000(17)	1	0.0133(6) a
	O2	4c	0.3862(4)	0.0749(11)	0.1940(17)	1	0.0133(6) a
	O3	4c	0.2893(4)	0.3454(12)	0.3003(12)	1	0.0133(6) a
	O4	4c	0.4412(4)	0.1512(12)	0.6774(13)	1	0.0133(6) a
	O5	4c	0.1263(5)	0.1161(11)	0.6915(11)	1	0.0133(6) a
	O6	2b	0.5	0	0.1534(19)	1	0.0133(6) a
	O7	4c	0.2258(4)	0.4286(11)	0.7706(18)	1	0.0133(6) a
	O8	4c	0.0489(4)	0.1336(11)	0.1682(16)	1	0.0133(6) a
	O9	4c	0.2975(4)	0.1355(12)	0.7869(19)	1	0.0133(6) a
	O10	4c	0.1509(4)	0.3098(12)	0.2047(16)	1	0.0133(6) a
	O11	4c	0.3455(4)	0.4564(10)	0.7999(12)	1	0.0133(6) a

a : constrained to refine to the same Uiso values

Table S8 . Refined interatomic distances (dA-O up to 3 Å) obtained in cation-ordered SrHoGa3O7 from SPD data.

 S8

	Tables S9.
	Bond	Length(Å)	Bond	Length(Å)	Bond	Length(Å)

Refined structural parameters obtained from SPD data collected at room temperature on cation-ordered SrLuGa3O7 (P21212 space group, a = 23.6710(2) Å, b = 7.91556(8) Å and c = 5.20516(4) Å). Note that the oxide x, y, z coordinates and U values were subjected to soft restraints to keep them close to the corresponding values from SrYbGa3O7 (see main text).

	a , b , c : constrained to refine to the same Uiso values
	Atom	Site	x	y	z	Occ	U iso
	Lu1/Sr1	4c	0.22070(6)	0.14247(18)	0.4963(3)	0.520(4)/0.480(4)	0.0119(4)
	Lu2/Sr2	4c	0.38160(5)	0.31180(14)	0.4570(2)	0.891(3)/0.109(3)	0.0111(4)
	Sr3/Lu3	4c	0.0496(2)	0.3225(7)	0.5062(14)	0.455(2)/0.045(2)	0.0126(9) a
	Sr3/Lu3'	4c	0.0640(2)	0.3547(6)	0.5045(15)	0.455(2)/0.045(2)	0.0126(9) a
	Ga1	4c	0.44881(10)	0.1435(3)	0.0138(6)	1	0.0067(2) b
	Ga2	2a	0	0	0.9723(9)	1	0.0067(2) b
	Ga3	4c	0.17413(12)	0.4805(3)	0.9982(8)	1	0.0067(2) b
	Ga4	4c	0.28907(10)	0.3346(3)	0.9555(5)	1	0.0067(2) b
	Ga5	4c	0.11930(12)	0.1239(3)	0.0287(5)	1	0.0067(2) b
	O1	4c	0.4540(7)	0.341(2)	0.201(3)	1	0.0285(13) c
	O2	4c	0.3857(7)	0.070(2)	0.182(3)	1	0.0285(13) c
	O3	4c	0.2947(6)	0.337(2)	0.305(3)	1	0.0285(13) c
	O4	4c	0.4404(7)	0.148(2)	0.690(3)	1	0.0285(13) c
	O5	4c	0.1266(8)	0.114(2)	0.701(2)	1	0.0285(13) c
	O6	2b	0.5	0	0.149(4)	1	0.0285(13) c
	O7	4c	0.2271(8)	0.435(2)	0.776(4)	1	0.0285(13) c
	O8	4c	0.0490(6)	0.140(2)	0.160(3)	1	0.0285(13) c
	O9	4c	0.2953(7)	0.131(2)	0.774(4)	1	0.0285(13) c
	O10	4c	0.1519(7)	0.296(2)	0.199(3)	1	0.0285(13) c
	O11	4c	0.3483(7)	0.446(2)	0.790(2)	1	0.0285(13) c

Table S10 . Interatomic distances (dA-O up to 3 Å) obtained in cation-ordered SrLuGa3O7 from SPD data.

 S10

	Tables S11.
	Bond	Length(Å)	Bond	Length(Å)	Bond	Length(Å)

Refined structural parameters obtained from laboratory PXRD data collected at room temperature on cation- ordered SrDyGa3O7 from laboratory PXRD data (P21212 space group, a = 23.8404(3) Å, b = 7.9510(1) Å and c = 5.24314(2) Å).

	a: constrained to refine to the same Uiso values
	Atom	Site	x	y	z	Occ	U iso
	Dy1/Sr1	4c	0.2210(2)	0.1475(5)	0.4976(6)	0.50(1)/0.50(1)	0.017(2)
	Dy2/Sr2	4c	0.38229(17)	0.3203(4)	0.4609(5)	0.90(9)/0.100(9)	0.012(1)
	Sr3/Dy3	4c	0.0558(2)	0.3372(7)	0.5076(7)	0.90(1)/0.10(1)	0.018(2)
	Ga1	4c	0.0558(2)	0.3372(7)	0.5076(7)	1	0.010(2)
	Ga2	2a	0.4501(3)	0.1441(9)	0.0111(10)	1	0.020(3)
	Ga3	4c	0	0	0.998(2)	1	0.003(1)
	Ga4	4c	0.1710(3)	0.4826(8)	0.9962(18)	1	0.012(2)
	Ga5	4c	0.2873(3)	0.3374(9)	0.9535(11)	1	0.009(2)
	O1	4c	0.1182(3)	0.1274(9)	0.0322(8)	1	0.004(2) a
	O2	4c	0.4541(12)	0.330(4)	0.226(5)	1	0.004(2) a
	O3	4c	0.3927(12)	0.077(3)	0.175(5)	1	0.004(2) a
	O4	4c	0.2888(14)	0.360(4)	0.295(3)	1	0.004(2) a
	O5	4c	0.4417(11)	0.150(4)	0.650(4)	1	0.004(2) a
	O6	2b	0.1217(15)	0.120(4)	0.672(4)	1	0.004(2) a
	O7	4c	0.5	0	0.146(5)	1	0.004(2) a
	O8	4c	0.2226(14)	0.433(4)	0.805(6)	1	0.004(2) a
	O9	4c	0.0510(10)	0.126(4)	0.149(4)	1	0.004(2) a
	O10	4c	0.3051(12)	0.116(3)	0.730(5)	1	0.004(2) a
	O11	4c	0.1451(12)	0.312(3)	0.261(4)	1	0.004(2) a

Table S12 . Refined interatomic distances (dA-O up to 3 Å) obtained from cation-ordered SrDyGa3O7 from laboratory PXRD data.

 S12

	Bond	Length(Å)	Bond	Length(Å)	Bond	Length(Å)

Table S13 . Refined structural parameters of disordered SrYbGa3O7 from laboratory PXRD data (P-421m space group, a = b = 7.91985(9) Å and c = 5.21070(7) Å).

 S13

a : constrained to refine to the same Uiso values

Table S14 . Refined interatomic distances of disordered SrYbGa3O7 from laboratory PXRD data.

 S14

	Bond	Length(Å)	Bond	Length(Å)	Bond	Length(Å)
	(Yb1/Sr1)-O3	2.387(7)	Ga1-O3	1.875(7)	Ga2-O2	1.716(8)
	(Yb1/Sr1)-O3	2.387(7)	Ga1-O3	1.875(7)	Ga2-O1	1.800(6)
	(Yb1/Sr1)-O2	2.449(9)	Ga1-O3	1.875(7)	Ga2-O3	1.875(7)
	(Yb1/Sr1)-O1	2.507(9)	Ga1-O3	1.875(7)	Ga2-O3	1.875(7)
	(Yb1/Sr1)-O2	2.613(7)
	(Yb1/Sr1)-O2	2.613(7)
	(Yb1/Sr1)-O3	2.885(7)
	(Yb1/Sr1)-O3	2.885(7)

Table S15 . Refined structural parameters of disordered SrTmGa3O7 from SPD data (P-421m space group

 S15

	Atom	Site	x	y	z	Occ	U iso
	Yb1/Sr1	4e	0.33863(9)	0.16137(9)	0.5123(4)	0.5/0.5	0.0353(5)
	Ga1	2a	0	0	0	1	0.0254(8)
	Ga2	4e	0.14503(15)	0.35497(15)	0.9698(5)	1	0.0289(7)
	O1	2c	0.5	0	0.179(2)	1	0.050(2)
	O2	4e	0.1438(9)	0.3562(9)	0.2990(14)	1	0.050(2)
	O3	8f	0.0932(7)	0.1615(8)	0.7782(15)	1	0.050(2)
	Atom	Site	x	y	z	Occ	U iso
	Tm1/Sr1	4e	0.33812(3)	0.16188(3)	0.51362(10)	0.5/0.5	0.0226(1)
	Ga1	2a	0	0	0	1	0.0136(2)
	Ga2	4e	0.14401(4)	0.35599(4)	0.96889(14)	1	0.0135(2)
	O1	2c	0.5	0	0.1854(11)	1	0.0420(7) a
	O2	4e	0.1418(3)	0.3582(3)	0.3109(6)	1	0.0420(7) a
	O3	8f	0.0956(3)	0.1603(3)	0.7952(6)	1	0.0420(7) a

, a = b = 7.92455(3) Å, and c = 5.21558(2) Å).

a : constrained to refine to the same Uiso values

Table S16 . Refined interatomic distances of disordered from SPD data SrTmGa3O7. Table S17. Refined structural parameters of disordered SrErGa3O7 from SPD data (P-421m space group, a = b

 S16

	Å, and c = 5.22367(2) Å).	= 7.93227(2)

Table S18 . Refined interatomic distances of disordered SrErGa3O7 from SPD data.

 S18

	Atom	Site	x	y	z	Occ	U iso
	Er1/Sr1	4e	0.33837(2)	0.16163(2)	0.51404(8)	0.5	0.02116(8)
	Ga1	2a	0	0	0	1	0.0138(2)
	Ga2	4e	0.14408(4)	0.35592(4)	0.96875(12)	1	0.0134(1)
	O1	2c	0.5	0	0.1852(9)	1	0.0403(6) a
	O2	4e	0.1414(3)	0.3586(3)	0.3095(5)	1	0.0403(6) a
	O3	8f	0.0944(3)	0.1603(3)	0.7932(5)	1	0.0403(6) a
	Bond	Length(Å)	Bond		Length(Å)	Bond	Length(Å)

Table S19 . Refined structural parameters of disordered SrHoGa3O7 from laboratory PXRD data (P-421m space group, a = b = 7.93999(2) Å, and c = 5.23060(2) Å, Rp = 1.413% Rwp = 2.081%).

 S19

	Atom	Site	x	y	z	Occ	U iso
	Ho1/Sr1	4e	0.33867(5)	0.16133(5)	0.51151(14)	0.5/0.5	0.0134(2)
	Ga1	2a	0	0	0	1	0.0077(3)
	Ga2	4e	0.14444(7)	0.35556(7)	0.96831(17)	1	0.0097(3)
	O1	2c	0.5	0	0.1757(10)	1	0.0287(8) a
	O2	4e	0.1422(4)	0.3578(4)	0.3186(6)	1	0.0287(8) a
	O3	8f	0.0940(4)	0.1626(4)	0.7916(6)	1	0.0287(8) a
	a : constrained to refine to the same Uiso values

Table S20 . Refined interatomic distances of disordered SrHoGa3O7 from laboratory PXRD data.

 S20

	Bond	Length(Å)	Bond	Length(Å)	Bond	Length(Å)

Table 2 .

 2 Refined Structural Parameters Obtained from NPD Data Collected at Room Temperature on Ca 3 ZnGe 5 O 14 (P321 Space Group, a = 8.0308(3) Å and c = 5.0164(4) Å)

	atom	position	xyz	Occ	B iso
	Ca	3e	0.4198(8)	0	0	1	1.18(13)
	Zn1/Ge1	1a	0	0	0	0.52(4)/0.48(4)	1.09(8) a
	Zn2/Ge2	3f	0.7674(5)	0	1/2	0.16(1)/0.84(1)	1.09(8) a
	Ge3	2d	1/3	2/3	0.5295(12)	1 b	1.09(8) a
	O1	2d	1/3	2/3	0.1854(17)	1	2.17(7) a
	O2	6g	0.4617(7)	0.3173(5)	0.3139(10)	1	2.17(7) a
	O3	6g	0.2227(6)	0.0785(6)	0.7585(10)	1	2.17

Table 3 .

 3 Cation Oxide Interatomic Distances and Bond Valence Sums Calculated for all Ga and Ge Sites of Ca 3 Ga 2 Ge 4 O 14

	site	bond	length (Å)	site	bond	length (Å)	site	bond	length (Å)
	B(1a)	M-O3 x6	1.926(3)	C(3f)	M-O3 x2	1.787(4)	D(2d)	M-O1 x1	1.704(7)
					M-O2 x2	1.853(5)		M-O2 x3	1.776(4)
		BVS (Ga) a	3.53(2)		BVS (Ga) a	3.37(2)		BVS (Ga) a	3.72(3)
		BVS (Ge) a	3.71(2)		BVS (Ge) a	3.49(2)		BVS (Ge) a	3.91(3)

a Calculated with a distance cut off at 3 Å.

Table 4 .

 4 Cation Oxide Interatomic Distances and Bond Valence Sums Calculated for All Zn and Ge Sites of Ca 3 ZnGe 5 O 14

	site	bond	length (Å)	site	bond	length (Å)	site	bond	length (Å)
	B(1a)	M-O3 x6	1.984(6)	C(3f)	M-O3 x2	1.767(6)	D(2d)	M-O1 x1	1.73(1)
					M-O2 x2	1.862(6)		M-O2 x3	1.770(6)
		BVS (Zn) a	2.74(2)		BVS (Zn) a	3.06(2)		BVS (Zn) a	3.29(3)
		BVS (Ge) a	3.17(2)		BVS (Ge) a	3.58(2)		BVS (Ge) a	3.89(4)

a

Table 5 .

 5 Refined Structural Parameters Obtained from NPD Data Collected at Room Temperature on Ca 3 GaZn 0.5 Ge 4.5 O 14 (x = 0.5) (P321 Space Group, a = 8.0460(2) Å and c = 4.9994(2) Å) Sample

	atom	position	xyz	occupancy	B iso
	Ca	3e	0.4198(7)	0	0	1	1.12(11)
	Ga1/Ge1/Zn1	1a	0	0	0	0.25(2)/0.531(15)/0.22(3)	0.98(6) a
	Ga2/Ge2/Zn2	3f	0.7648(4)	0	1/2	0.250(8)/0.656(5)/0.094(10)	0.98(6) a
	Ge3	2d	1/3	2/3	0.5283(9)	1	0.98(6) a
	O1	2d	1/3	2/3	0.1874(13)	1	1.66(5) a
	O2	6g	0.4629(5)	0.3175(4)	0.3120(7)	1	1.66(5) a
	O3	6g	0.2208(5)	0.0788(4)	0.7631(7)	1	1.66(5) a

a Constrained to refine to the same B iso values.

Table 6 .

 6 Refined Occupancies for Zn, Ga, and Ge on the 1a, 3f, and 2d Sites, Extracted from NPD Data and STEM-EDS Maps Errors were estimated by calculating standard deviation from the fitted areas of the 1D EDS profiles over the averaged 4 (1a, 3f sites) on the cell corners, shown in Figure6d-f. b Mean values from zone 1 and zone 2 refinements. See TableS11for zone1 and zone2 individual refined occupancies.

		site atom	1a	3f	2d
	NPD refinement	Zn	0.22(3)	0.09(1)	0
		Ga	0.25(2)	0.25(1)	0
		Ge	0.53(2)	0.66(1)	1
	1D refinement	Zn	0.23(10) a	0.09(4) a	0
		Ga	0.28(8) a	0.24(3) a	0
		Ge	0.54(5) a	0.67(2) a	1
	2D refinement	Zn	0.18(3) b	0.11(3) b	0
		Ga	0.24(2) b	0.26(2) b	0
		Ge	0.59(2) b	0.64(2) b	1

a

Table 7 .

 7 Comparison between the Reported C2 14 and NPD Refined P321 M-O Bond of the Ca 3 ZnGe 5 O 14 (x =1 ) Composition

	reported C2r e fined P321

a M-O atoms notation taken from C2 model; see Table

S10

for the P321 analogue atoms.

Table 8 .

 8 Comparison between the Refined Occupancies of Ga and Ge in the 1a, 3f, and 2d Sites from Melt-Crystallized (This Work) and Single Crystal 33 on the Ca 3 Ga 2 Ge 4 O 14 (x = 0) Compound

		melt-crystallized			single crystal 33
	site atom	1a	3f	2d	1a	3f	2d
	Ga	0.51(8)	0.50(3)	0	0.2	0.6	0
	Ge	0.49(8)	0.50(3)	1	0.8	0.4	1

Table S5 .

 S5 Refined structural parameters obtained from SPD data collected at room temperature on Ca 3 Ga 0.5 Zn 0.75 Ge 4.75 O 14 (x=0.75) (P321 space group, a= 8.03574(2) Å and c= 5.009068(17) Å) sample. Site was set to be fully occupied without refining each atom occupancy a : constrained to refine to the same B iso values.

	Atom	Position	x	y	z	Occ	B iso
	Ca	3e	0.41827(11) 0	0	1	0.92(2)
	Ga1/Ge1/Zn1 1a	0	0	0	1*	1.26(2)
	Ga2/Ge2/Zn2 3f	0.76488(6)	0	0.5	1*	0.971(1)
	Ge3	2d	1/3	2/3	0.52939(14) 1	0.79(1)
	O1	2d	1/3	2/3	0.1880(7)	1	1.26(4) a
	O2	6g	0.4676(3)	0.3187(3)	0.3224(4)	1	1.26(4) a
	O3	6g	0.2203(2)	0.0763(3)	0.7527(4)	1	1.26(4) a

*

Table S6 .

 S6 Refined structural parameters obtained from SPD data collected at room temperature on Ca 3 ZnGe 5 O 14 (x=1) (P321 space group, a= 8.02913(3) Å and c= 5.014309(19) Å) sample. No strain modelled. Site was put to be fully occupied without refining each atom occupancy a : constrained to refine to the same B iso values.

	Atom	Position	x	y	z	Occ	B iso
	Ca	3e	0.41841(8)	0	0	1	1.16(1)
	Zn1/Ge1	1a	0	0	0	1*	1.48(1)
	Zn2/Ge2	3f	0.76499(4)	0	0.5	1*	1.154(7)
	Ge3	2d	1/3	2/3	0.52849(11) 1	1.009(9)
	O1	2d	1/3	2/3	0.1919(6)	1	1.95(3) a
	O2	6g	0.4671(2)	0.3189(2)	0.3233(3)	1	1.95(3) a
	O3	6g	0.22055(19) 0.0773(2)	0.7504(3)	1	1.95(3) a

*

Table S7 .

 S7 Refined structural parameters obtained from SPD data collected at room temperature on Ca 3 ZnGe 5 O 14 (x=1) (P321 space group, a= 8.02916(2) Å and c= 5.014362(17) Å) sample. Modelled strain. Site was put to be fully occupied without refining each atom occupancy a : constrained to refine to the same Biso values.

	Atom	Position	x	y	z	Occ	B iso
	Ca	3e	0.41846(8)	0	0	1	1.15(1)
	Zn1/Ge1	1a	0	0	0	1*	1.47 (1)
	Zn2/Ge2	3f	0.76506(4)	0	0.5	1*	1.126(7)
	Ge3	2d	1/3	2/3	0.52816(11) 1	0.999(8)
	O1	2d	1/3	2/3	0.1926(5)	1	1.91(3) a
	O2	6g	0.4676(2)	0.3195(2)	0.3230(3)	1	1.91(3) a
	O3	6g	0.22065(19) 0.0772(2)	0.7502(3)	1	1.91(3) a

*

Table S8 .

 S8 Refined structural parameters obtained from SPD data collected at room temperature on Ca 3 ZnGe 5 O 14 (C2 space group, a= 13.91669(9) Å, b= 8.02315(5) Å, c= 5.01415(2) Å and β= 90.0759(4) °) sample. No strain modelled. : constrained to refine to the same B iso values.

	Atom	Position	x	y	z	Occ	B iso
	Ca1	2a	0.5	0.7623(5)	0	1	1.44(8)
	Ca2	4c	0.2917(2)	0.3948(4)	0.0006(7)	1	1.02(4)
	Zn1	1a	0.11841(10) 0.56943(16) 0.4969(4)	1	1.39(3)
	Ge1	4c	0.33313(10) 0.6860(2)	0.47222(13) 1	0.96(1)
	Ge2	2b	0.5	0.41986(18) 0.5	1	0.92(4)
	Ge3	4c	0.5	0.1858(3)	0	1	1.00(1)
	O1	4c	0.1177(4)	0.6953(9)	0.7829(10)	1	1.21(4) a
	O2	4c	0.1611(6)	0.3732(11)	0.680(2)	1	1.21(4) a
	O3	4c	0.4249(5)	0.5748(11)	0.3031(15)	1	1.21(4) a
	O4	4c	0.4317(5)	0.3296(9)	0.7441(13)	1	1.21(4) a
	O5	4c	0.3341(6)	0.6729(11)	0.8088(6)	1	1.21(4) a
	O6	4c	0.0234(4)	0.4947(8)	0.2834(13)	1	1.21(4) a
	O7	4c	0.2304(5)	0.5907(10)	0.3407(17)	1	1.21(4) a

a

Table S9 .

 S9 Refined structural parameters obtained from SPD data collected at room temperature on Ca 3 ZnGe 5 O 14 (C2 space group, a= 13.90286(11) Å, b= 8.03170(7) Å, c= 5.014276(16) Å and β= 89.9544(10) °) sample. Modelled strain. : constrained to refine to the same B iso values.

	Atom	Position	x	y	z	Occ	B iso
	Ca1	2a	0.5	0.7601(4)	0	1	0.45(6)
	Ca2	4c	0.2903(2)	0.3895(5)	0.0005(8)	1	1.55(4)
	Zn1	1a	0.11569(10) 0.55532(16) 0.5034(4)	1	1.25(3)
	Ge1	4c	0.33367(13) 0.6757(3)	0.47220(10) 1	0.980(7)
	Ge2	2b	0.5	0.4145(2)	0.5	1	1.07(5)
	Ge3	4c	0.5	0.1800(4)	0	1	0.97(1)
	O1	4c	0.1017(4)	0.7363(7)	0.7201(10)	1	1.46(3) a
	O2	4c	0.1562(6)	0.3734(13)	0.674(2)	1	1.46(3) a
	O3	4c	0.4298(6)	0.5696(13)	0.3262(18)	1	1.46(3) a
	O4	4c	0.4377(4)	0.3391(9)	0.7873(9)	1	1.46(3) a
	O5	4c	0.3344(7)	0.679(2)	0.8071(4)	1	1.46(3) a
	O6	4c	0.0451(5)	0.4900(9)	0.2636(13)	1	1.46(3) a
	O7	4c	0.2364(6)	0.5876(13)	0.3066(17)	1	1.46(3) a

a

Table S10 .

 S10 Atom Wyckoff positions in the hexagonal P321 structure and their equivalents in the monoclinic C2 cell.

	Origin in P321		Analogue in C2
	Atom	Wyk. Pos.	Atom	Wyk. Pos.
	Ca1	3f	Ca1	2a
			Ca2	4c
	Ge1/Zn1	1a	Zn1	2a
	Ge2/Zn2	3f	Ge1	4c
			Ge3	4c
	Ge3	2d	Ge2	2b
	O1	2d	O5	4c
	O2	6g	O2	4c
			O3	4c
			O7	4c
	O3	6g	O1	4c
			O4	4c
			O6	4c

Table S11 .

 S11 Extracted (refined) occupancies from the 2D EDS maps refinements in both zone1 and zone2, for the Ca 3 GaZn 0.5 Ge 4.5 O 14 (x=0.5) composition.

		Site	1a	3f	2d
		Atom
		Zn	0.19(6)	0.10(6)	0
	Zone1	Ga	0.22(3)	0.26(3)	0
		Ge	0.59(3)	0.64(3)	1
		Zn	0.16(6) a	0.11(6) a	0

Table A. 25. Final refined La1.775Ba0.225Ga3O7.3875 (x = 0.775) composition cell 2 structural parameters (S.G. Ima2, a= 11.43792(8) Å, b= 11.36654(8) Å, c= 10.5397(1) Å).

Table A. 34. Final refined La1.9Ba0.1Ga3O7.45 (x = 0.9) composition structural parameters (S.G. Ima2, a= 11.476307(15) Å, b= 11.295461(18) Å, c= 10.509301(17) Å).

Figure A. 24. Room temperature NPD (a) HI, (b) HR data Rietveld refinement of the La1.3Ba0.7Ga3O7.15 (x = 0.3) composition.

Figure A. 25. Room temperature NPD (a) HI, (b) HR data Rietveld refinement of the La1.6Ba0.4Ga3O7.3 (x = 0.6) composition.

Figure A. 26. Room temperature NPD (a) HI, (b) HR data Rietveld refinement of the La1.7Ba0.3Ga3O7.35 (x = 0.7) composition.

Figure A. 27. Room temperature NPD (a) HI, (b) HR data Rietveld refinement of the La1.8Ba0.2Ga3O7.4 (x = 0.8) composition.

Figure A. 29. 525°C NPD (a) HI, (b) HR data Rietveld refinement of the La1.9Ba0.1Ga3O7.45 (x = 0.9) composition.

Figure A. 30. 720°C NPD (a) HI, (b) HR data Rietveld refinement of the La1.9Ba0.1Ga3O7.45 (x = 0.9) composition.

Figure A. 31. 770°C NPD (a) HI, (b) HR data Rietveld refinement of the La1.9Ba0.1Ga3O7.45 (x = 0.9) composition.

Figure A. 32. 820°C NPD (a) HI, (b) HR data Rietveld refinement of the La1.9Ba0.1Ga3O7.45 (x = 0.9) composition.

Table A. 55. Final 720°C NPD HI refined data of La1.9Ba0.1Ga3O7.45 (x = 0.9) composition structural parameters (S.G. P𝟒 ̅ 21m, a= b= 8.1201(3) Å, c= 5.2791(4)) Å).

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Acknowledgements

previously reported studies [4]- [6], [10], [11] it is clear that the melilite compounds are of interest in designing new conductive materials operating at intermediate temperatures. 250 « Last but not least, I wanna thank me. I wanna thank me for believing in me. I wanna thank me for doing all this hard work. I wanna thank me for having no days off. I wanna thank me for, for never quitting. » Snoop Dogg

I would like first to acknowledge the Region Centre Val-de-Loire, Agence National de la Recherche (ANR) and the CEMHTI laboratory for the provided financial support over three years of my PhD. Many thanks to Dr. Gwenaelle Rousse (CSE, Paris) and Dr. Pascal Roussel

A = Pb). The mixed (Zn,Ge)O4 and GeO4 sites was related to make a considerable contribution to the SHG effect of these compounds. In contrast with the synthesised and described Ca3ZnGe5O14 compound in this work, exhibiting Zn/Ge disorder over the B-and C-sites, it could be interesting to study the SHG response of this material with Ca 2+ substitution for Pb 2+ cations.

the biggest Biso value for the O2 atom. This O2 behaviour can be related to a high positional disorder of this atom, distorting the local environment of the Ca3 site. Similar features can be discerned in the melilite compounds when an interstitial oxide is located in the [GaO4]5 pentagons centre, causing distortions of the Ga-O-Ga angles, which pushes the equivalent oxide to our O2 atom in those systems far from its initial position enlarging the A-sites channels (shown in Figure V.16b) [8], [9], [22]. Further MEM calculation using the NPD (HI) data and an advanced MEM calculation (derived constraints MEM) are under investigations Density functional theory (DFT) calculations and determination of the most energetically stable structure.

Computational prediction of crystal structures can be useful in the accelerated discovery of novel compounds with new crystal structures and optimised properties [11]- [13], [38], [39].

Regarding this aspect, Meigeng Gao (University of Liverpool, UK) has showed in her thesis the potential of probing/predicting the crystal structure of new oxide ion conductor materials by DFT calculations [40]. This approach is described in this section to define the most energetically stable configuration of the La-doped Ca5Ga6O14 structure with an interstitial oxide. The pellets were polished until a thickness of 0.7 mm was reached, then annealed at 900°C for 6h under O2 gas flow to remove as much carbon as possible from the pellets; at the end of this heat treatment the samples retained a light grey colour (Figure V.23). Previous trials with a longer annealing process and temperatures higher than 900°C revealed unsuccessful, as the colour remained the same for the 6h treatment, or the sample decomposed.

Impedance measurements.

The final prepared samples described above (section V.4.1) were coarsely polished to obtain two parallel faces. Silver paste was coated on both opposite faces of the pellets and fired at 600°C for 30min to evaporate the organic components from the paste and form electrodes.

Impedance measurements were then carried out using the Solartron SI 1260 apparatus by Leire Del Campo at the CEMHTI laboratory. Data were acquired in the 0.1Hz -32MHz frequency range from room temperature to 800°C using a step of 4°C/min. In Figure V.24a and Figure

V.24b showing the evolution of complex impedance plots for both LaxCa5-xGa6O14+x/2 x = 0 and x = 0.25 compounds, it is clear that no signal is recorded for the La-free sample for temperatures below 600°C. This reflects the very low electrical conductivity of this material below 600°C.

Moreover, no clear separation between two semi-circles can be discerned on the Nyquist plots, making it hard to distinguish the bulk from grain boundaries responses. Therefore, only the total conductivity was deducted from the semi-circle interception with the x-axis.

Chapter A.I: Experimental methods.

A.I.1. Synthesis. A.I.1.1. Through glass or melt crystallisation.

Before operating glass synthesis, a homogeneous composition was prepared by mixing stoichiometric amounts of the starting precursors in an agate mortar using ethanol. The composition was dried in a conventional oven at 100°C or over the bench for few minutes. The resulting powder mixture was either melted in an open atmosphere furnace or using the aerodynamic levitation coupled to two CO2 lasers.

A.I.1.1.1. Using conventional furnace (T≤1750°C).

The mixture is placed in a Pt crucible and introduced in an open atmosphere furnace at 20°C higher than the melting temperature determined from the phase diagram of the studied system in order to melt the sample. After 1 hour, the Pt crucible was taken out from the furnace and either air or water quenched, which allowed to achieve a glass material. This method is easy to operates and allows to synthesis large batches of glass in one go. Despite its simplicity and wide usage, this routine has few down points which can be challenging to overcome: (i) the cooling rates are not always sufficient to obtain glass for systems that energetically favours crystallisation. (ii) This approach implies the sample to be in contact with the crucible, which can be a source of impurities; moreover, the contact surface between the sample and the crucible acts as a nucleation centre which can trigger the samples crystallisation, highly disfavoured in glass synthesis.

A.I.1.1.2. Using aerodynamic levitation (ADL) coupled to two CO2 lasers (max T ≈ 3100°C).

In the CEHMTI laboratory, to overcome the downsides of conventional melt quench synthesis of glass, listed earlier in section A.I.1.1.1, aerodynamic levitation (ADL) coupled to two CO2 lasers was opted as an alternative synthesis approach (see Figure A. 1).

In order to operates the material synthesis using the ADL apparatus, the starting sample need to be compacted, typically in pellet form. The pellet is broken into small pieces and a fragment is then placed into the nozzle. A gas flow is turned on to help the sample levitate in its liquid form. A pair of CO2 lasers (10.6 µm) are used to heat the sample from above and below to ensure its homogeneity. A set of pyrometers are used to read the samples temperatures from its emissivity, which allows a complete control of the heating and the cooling processes. Moreover, it can also provide insight information about the sample purity (phase indexation) to a certain precision degree.

The principle of X-ray diffraction is fairly simple; the X-rays are generated by application of a potential difference between the cathode and anode, these rays are directed toward the Electron diffraction is a technique for probing crystals at the nanometric scale, where each crystallite can be diffracted individually; this is a great advantage in multiphase samples, as each phase can be studied independently. Electron diffraction allows each hkl peak to be diffracted individually, as seen in single crystals X-ray diffraction, which is highly valued for accurately determining cell parameters and space group symmetry of the crystalline phase. In our case, the observed samples were either under powder or thin foil form: (i) for powder specimens, a small amount of sample was ground in an agate mortar and dispersed in ethanol; a droplet of this suspension was then deposited onto a copper grid layered by a holey amorphous carbon film. (ii) for thn foil specimens, the starting sample was first mechanically polished using a tripod and inlaid diamond discs until a thickness of 50µm was reached; The thin foil was then obtained by argon ion milling (PIPS GATAN).

Electron diffraction was performed using a CM20 transmission electronic microscope (TEM) operating at 200kV or a JEOL ARM200F (JEOL Ltd.) Cold FEG TEM. Both are equipped with a double-tilt holder that allows orienting the crystals in all specific directions.

A.I.2.2.5. Maximum entropy method (MEM).

The maximum entropy method is a model-free calculation process, able to reconstruct the whole electron or nuclear density within the unit cell using X-ray or neutron phased structure factors. This method was introduced as an alternative to the inverse Fourier transform calculation process due to the limits and artefacts associated to the calculation of 𝜌(𝑟) from the A.I.6.Other characterisation techniques.

A.I.6.1. Density measurements by Archimedes law.

To characterise the pellets density post SPS process, Archimedes method was pursued using the montage illustrated in Chapter A.V: Supplementary information for Chapter V.

Résumé en Français

DSC et des mesures diffraction des rayons X réalisées in situ à des températures variables en fonction du ratio de la taille des deux cations occupant le site A.

Finalement, des mesures de photoluminescence sur les composés SrErGa3O7 montrent une intensité supérieure (×2) de la bande d'émission du Er 3+ pour la mélilite P21212 comparée à la phase parent et l'analogue vitreux, confirmant ainsi la mise en ordre observée sur le site A.

Structure solution of SrYbGa3O7 from powder diffraction data

Using the unit cell and space group derived by powder indexing and SAED (a = 23.7 Å x b = 7.9 Å x c = 5.2 Å, P21212; see Figure 1 of main manuscript), a Le Bail refinement was performed on SPD data, followed by charge flipping (implemented in Jana2006 through the Superflip software) to obtain the cation coordinates of a starting structural model. Convergence was rapidly achieved and eight chemically-plausible cation positions were identified, consistent with the melilite structure (7x 4c positions corresponding to three Yb/Sr sites and four Ga sites, and 1x 2a position corresponding to a Ga site). At this stage, A sites were considered to be occupied 50/50 by Yb/Sr. Using this cation-only model, a combined Rietveld refinement was performed on both SPD and NPD data by refining the occupancies of the three Yb/Sr cationic sites (subject to a compositional constraint to an overall stoichiometry of SrYbGa3, and individual constraints to keep each site fully occupied by cations). Fourier difference maps were then calculated to determine the oxygen positions by an iterative process: eleven oxygen sites were thus localized on residual density peaks situated at 1.8-1.9 Å of Ga and 2.2-2.7 Å of Yb/Sr cations, completing the structural model. Rietveld refinement then proceeded as described in the main manuscript (section 3.2). occupied exclusively by Ge. We then populated the 1a and 3f sites with the remaining Zn, Ga, and Ge atoms, weighted according to their apparent site preferences from STEM-EDS and end-member Rietveld refinements (0.25Ga/0.251Zn/ 0.5Ge and 0.25Ga/0.083Zn/0.667Ge for 1a and 3f, respectively). Constraints were then applied to (i) keep each site fully occupied by cations (Zn + Ga + Ge = 1) and (ii) fix the global composition to the nominal value Ca 3 GaGe 4.5 Zn 0.5 O 14 . The Zn, Ga, and Ge occupancies of 1a and 3f were then refined subject to these constraints. The refined Zn and Ge occupancies on both sites led to a Zn distribution close to the one in the Ca 3 ZnGe 5 O 14 , x =1 compound, where Zn and Ga are disposed in a 43(6)%/ 57(6)% and 25(2)%/75(2)% ratios between the two 1a and 3f sites, respectively, while Ge is disposed between the 1a, 3f, and 2d sites in a 0.12(1)%/0.44(1)%/0.44% ratio; see Figure 9 and Table 5 for refined plot and parameters. The results show good agreement between the Rietveld refinement and the STEM-EDS results, as shown in Table 6.

DISCUSSION

High-resolution SPD shows that the crystal structures of Ca 3 Ga 2-2x Ge 4+x Zn x O 14 (0 ≤ x ≤ 1) can all be indexed to a trigonal unit cell (P321) when crystallized from precursor glasses or directly from their melts. This is consistent with the reported crystal structure of Ca 3 Ga 2 Ge 4 O 14 , which is also trigonal when synthesized by single-crystal growth methods, but it contrasts with a previous study on Ca 3 ZnGe 5 O 14 single crystals which are metrically monoclinic. As described in Section 3.2, the refinement of trigonal and monoclinic models against the acquired SPD pattern of Ca 3 ZnGe 5 O 14 (x =1 ) produced very similar fits and near-identical structures, and we thus retained the simpler trigonal model as the most appropriate structural description. The underlying difference between trigonal glass-crystallized Ca 3 ZnGe 5 O 14 and monoclinic single-crystal Ca 3 ZnGe 5 O 14 14 lies in the distribution of Zn 2+ and Ge 4+ between the octahedral (1a) and tetrahedral (3f) sites. In single-crystal Ca 3 ZnGe 5 O 14 , 14 these cations are The feasibility of classic solid-state methods for the synthesis of Ca 3 Ga 2 Ge 4 O 14 (x=0) was evaluated by in-situ PXRD. A reaction mixture was prepared from high purity reagents CaCO 3 , Ga 2 O 3 and GeO 2 which were ground in an agate mortar under ethanol. Once dried, the mixture was loaded into a platinum-lined corundum sample holder for variable temperature powder X-ray diffraction measurements (VT-PXRD). The reaction products at 1200 °C were a langasite type compound "Ca 3 Ga 2 Ge 4 O 14 " as the main phase, with a substantial amount of CaGeO 3 and Ga 2 O 3 as secondary phases (see Figure I.1, below), indicating an incomplete reaction. The melting point of the mixture at ~1250°C precludes the use of higher temperatures, implying that several cycles of grinding and refiring at ~1200°C would be required to obtain a phase pure Ca 3 Ga 2 Ge 4 O 14 ceramic in this system.