Acknowledgement

As this thesis work is mainly done in the laboratories IRTES -LERMPS and Femto-ST-MN2S, as well as supported by China Scholarship Council and UTBM in the framework of UT-INSA (2012), my thanks first go to all the collaborating parties which made this work possible at all. I would express my greatest gratitude to my thesis supervisors Prof. FENINECHE Nouredine and Prof. ELKEDIM Omar, who have been extremely supportive along this journey of scientific research, where difficulties are only the stairs for one to climb up. It is not only the knowledge I could learn from them, but also the confident and cheerful attitude toward obstacles is of great inspiration to me on this road of science in the future. I would also like to say thanks to them for their patience to guide me through all this work. I am very thankful for Mrs. BERTRAND Ghislaine and Mr. GUESSASMA Sofiane to take the time to be the reviewers and help improve the thesis.

I feel honored to have Mr. LIAO Hanlin and Mr. CHERIF Salim Mourad to be present in the jury of the thesis defense session. I would also like to extend my deep appreciation to M. MOLIERE Michel, who has contributed a lot to this work in the first place. I was already lucky enough to meet him in person in a laboratory seminar, but he also kindly provided much assistance to improve my work with both the methods and technologies. Today I can still recall his detailed teachings from chemical reaction mechanisms to the experimental equipment design. In addition, we had spent very good time when we found some nice bistros in the city. His enthusiasm toward science and the passion for life will always be my inspiration and spur me to pursue excellence when doing science.

I must appreciate the collaboration with M. BRIOIS Pascal on co-completing this work with the measurement of the electrical properties. Contribution from you is invaluable to this work.

Many thanks go to the recommendations and assistances from the professors: M. Hanlin Liao, M. Pierre Bertrand, M. Joel Chauvelot and Mrs. Pascale Hoog.

I have received countless help from many nice working fellows, my colleagues in our lab. They are: Soumia Lardjane, Nicolas Bruno, Jean-Baptiste Devillers, Emilie Aubignat, Xinkun Suo, Taikai Liu, Min Yu, Xiaohua Feng, Jiangwei Liu, Duo Yi, Amal Masmoudi, Chunjie Huang, Zexin Yu, Bilel Hosni et al. and peers from different sections: Hui Wang-Liao, Marc Cescutti et al. Especially our "scientific interest group": Shuo Yin, Chaoyue Chen, Zhao Zhang and Yingchun Xie, thank you for giving some academic discussions, yielding us steady progress.

My thanks go to all the people that make my life in France a wonderful experience. Especially, M. Chengzhong Zhou, thank you for giving me the opportunity to have all the pleasant time with my dear brothers and sisters. It will always be the best memory to recall.

Most importantly, I would like to thank my wife. Her support, encouragement, "quiet patience" and unwavering love were undeniably the bedrock upon which the past two years of my life have been built.

Finally, I owe to my parents at the moment, who have been the ones standing firmly behind my back, despite the physical distance between us. Like always, during my study in France, they have been giving me wise advice and are always helping me to be a better person. My sisters deserve my wholehearted thanks as well for their endless love, support and encouragement. 30. Proposed conduction pathway between adjacent oxide-ion channels via two "SN2"-type processes, with accompanying rotation of the silicate tetrahedra, obtained from computer simulation results of La9.33(SiO4)6O2. The incorporation of a periphery interstitial oxide-ion (yellow) (a) forces a silicate oxygen (orange) in between the two SiO4 units forming an Si2O9 unit (b), the top silicate unit rotates to form an Si2O9 unit with a neighboring silicate unit (c), and an oxygen on the top silicate unit (green) is released as an interstitial in a different channel (d)

Index of Figures and Tables

Introduction

The desire to develop alternative energy sources, along with the ever-diminishing fossil fuel supply results in a present push for new energy conversion technology. With various advantages to directly and efficiently convert chemical energy to electrical energy, fuel cells have been investigated and applied in many fields. Fuel cells are direct chemical to electrical energy conversion devices that operate via an electrochemical reaction involving a fuel source (e.g. any hydrogen containing gas such as gasified coal and various hydrocarbons) and an oxygen source (e.g. oxygen and air). Among them, solid oxide fuel cell (SOFC) is one type of fuel cell which are defined by their ceramic and oxide electrolyte and it has an eliminate corrosion or leakage problems comparing to some other liquid electrolyte fuel cells. There are three basic components in a SOFC, namely, porous anode, cathode and dense electrolyte. The electrolyte material plays a very important role in the SOFC to transport oxygen ions and isolate airflow.

Recently, the SOFC draws much attention in commercial application with a solid material, most commonly a ceramic material named Yttria-Stabilized Zirconia (YSZ), as the electrolyte. This type of electrolyte has excellent ionic conductivity negligible electronic conduction over a wide range of oxygen partial pressure. Nevertheless, the operating temperature of this type SOFC is too high (800℃-1000℃). The high temperature causes many problems, such as the ageing of constituent components, the choice of the matched interconnectors or electrodes, and the maintenance of high temperature itself will cost much which would restrict the application in many fields.

At present, IT-SOFC (intermediate temperature SOFC) holds great promise of meeting the commercial needs to overcome the high temperature problems, attributing to the development of high ionic conductivity materials as the electrolyte. The electrolyte plays a very important role to transport the ions, which directly affects the power and energy density of a cell. Nowadays, apatite type ionic conductors, rare earths silicates and germ with the chemical formula REx(MO4)6Oy, RE = rare earth, M = Si and Ge, x = 9.33~ 10, y = 2~3, attract many interests due to the superior transport properties with high ionic conductivity and low activation energy. They can operate stably at intermediate temperature over a wide oxygen partial pressure range and maintain excellent performances, being considered as a candidate for IT-SOFC electrolytes. Among this series of conductors, the La-Si-O type has a higher conductivity and the performance would be improved with different doping elements.

To modify the apatite La10Si6O27 performance as an electrolyte, various doping elements influences also have been studied. Generally, there are two doping sites: La site with doping elements, such as Mg, Sr, Ba alkaline earth metal elements, and Si site with doping elements Ge, Mn, Al, Fe, etc. Because of the similar chemical properties with La, Sr has been chosen as suitable element doping at La site. Recently, Sr-doped LSO La9Sr1Si6O26.5 has been synthesized by Bonhomme et al with solid state reaction and the ionic conductivity is 2.4-2.6 mS•cm -1 at 700 ℃. L. Zhang et al has improved the synthesized process with a water-based gel-casting route and obtained La9Sr1Si6O26.5 with the highest ionic conductivity of 0.57 mS•cm -1 at 500℃, however, the calcination temperature is as high as 1400℃. As for the influence of different doping ratios, A. Orera et al. has investigated the ionic conductivity of La8+xSr2-x(SiO4)(6)O2+0.5x (0 ≤ x ≤1.0) with 29 Si NMR and Raman technologies.

On one hand, many synthesis methods have been employed to obtain the pure phase composition, including some traditional methods: solid state reaction, freeze drying, and some new process with auxiliary chemicals: DEA precipitation, sol-gel, etc. High calcination temperature (around 1700℃) is necessary to reduce the secondary products and incomplete reacted chemicals with the traditional synthesis methods. The new processes are widely applied to improve the calcination condition and reduce the production cost. In recent years, the sol-gel method becomes a research focus for its low cost and relatively simple realization in the synthesis fields with TEOS and La2O3.

On the other hand, to reduce the cost of the experiment, more and more researchers choose the calculation to predict the characteristics of materials. Among these methods of calculation, DFT (Density functional theory) is one of the highest precision results so it has been widely used.

We chose the VASP (Vienna Ab initio Simulation Package) package to start the calculation of its high efficiency and precision results.

The main goal of the present work focuses on the calculation, characterization and optimization of the apatite-type La10-xSrxSi6O27-0.5x (LSO) as the electrolyte material in IT-SOFC. We use a dual approach: a simulation approach and an experimental approach to optimize the electrolyte materials for fuel cells at an intermediate temperature.

We have divided the thesis into four stages as follows:

-Study the fundamental properties of Sr, Ge doping La10Si6O27 using the DFT methods;

-Check the results of the simulation by the realization of these materials; -Study and compare different synthesis methods to obtain an efficient, simple approach; -Investigation of the experimental impact factor to achieve pure phase products (with and without Sr doping) for fine ionic conductivity.

Chapter I gives a review on SOFC work mechanism and its component materials, especially the apatite-type phase lanthanum silicates electrolyte materials.

Chapter II presents the synthesis methods for our electrolyte materials, characterization involving in this work and the theoretical foundation of ab initio calculations, particularly for the ceramic calculation.

Chapter III is composed with the calculation study of the apatite-type LSO. We investigated the influence of Sr doping, as well as discovering the relationship between electric properties and crystal microstructures.

Chapter IV gives preliminary experimental exploration of co-precipitation, molten salts and HDP (homogenous deposition precipitation) methods. The co-precipitation method has been presented as a high efficiency, alternative way to obtain the apatite-type lanthanum silicate as an electrolyte in SOFC. With which the apatite phase can be achieved with facile procedure at low temperature.

Chapter V contains experimental methods to synthesize pure phase, high crystallization LSO.

We developed the traditional sol-gel method, reduced the synthesis process and cost. The relevant synthesis parameters have been investigated to get pure, highly crystalline powders.

The mechanisms occurring in the sol-gel reactions are discussed. The electrical performance indicates that the obtained LSO has the possibility to be a considerable candidate as electrolyte material in IT-SOFC.

Annex I illustrates the publications and conferences list.

CHAPTER I Overview of the solid oxide fuel cells (SOFC) and apatite-type materials as electrolyte in SOFC

This chapter gives a brief review for principles of solid oxide fuel cell (SOFC) system to the material involved in their construction. This review will include its history, principle, structure and materials as well as the apatite type materials that will be introduced as promising electrolytes in SOFC's and as the subject of the present thesis study.

I.1 Solid Oxide Fuel Cells (SOFCs)

I.1.1 Historic

The Fuel cells (FC) [1][2][3][4][5] are the energy conversion devices able to produce electric energy from chemical energy directly with high efficiency. The original idea of FC was firstly proposed by a Welsh physicist William Grove in the mid-nineteenth century. [6,7] At the time, the mechanism of electrical conduction investigation just started by some pioneers (e.g. Benjamin

Franklin, Georg Simon Ohm, Andre Marie Ampere et al.). Almost simultaneously, the operating principle of fuel cells was discovered by Christian Friedrich Schönbein. From then, fuel cells came in many varieties. Originally the concept and basic materials on solid electrolyte were proposed by Nernst and his colleagues at Göttingen in late nineteenth century [10][11][12]. But considerable progress in the theory and experiment came out still in 110 years. Composition of 85% zirconia and 15% yttrium oxide by mass, as said by Nernst, was first used to improve the ionic conductivity. Zirconia based ceramics were used initially in the fuel cell, which was the first attempt of making a high operating temperature solid oxide fuel cell (SOFCs) in 1937 by Baur and Preis [13,14].

In 1960s, Kiukkola and Wagner [15] reported thermodynamic investigations on metal / metal oxide systems, and the paper stimulated numerous activities [16,17] in the field of solid state electrochemistry in various regions of the world. With the development of the conductive properties of the stabilized zirconia, SOFCs were being extensively studied. A growing number of patents and papers on SOFC appeared in several countries.

In United States, Westinghouse Electric Corporation had developed industrial SOFC stacks [18]. Planar and tubular cells with platinum electrodes were produced and connected in pack, using a gold / nickel solder. In Europe, after Palguyev and Volchenkova [19,20] [21][22][23]. In Asia, Takahashi [24,25]investigated with electrolytes of alkaline carbonate in Japan, which began SOFC research there.

In the mid-1990s, the development of SOFC had a rapid increase since the new materials, oxides of the lanthanide ion conductor were found using as electrolyte in SOFC by Ishihara in 1994 [26]. This form of doped lanthanum and gallium oxide provided an excellent conductivity at intermediate temperature, which started the studying intermediate temperature solid oxide fuel cells (IT-SOFC). It partly solved the problems of high operating temperature that was faced hitherto as it will be discussed in Section I.3. At the same time, polarization losses and importance of the electrode catalysis reactions increased. A large variety of new design concepts and cellular systems were being pursued and new solid electrolyte materials were imminent [27][28][29]. To some extent, it can be stated that the development of the SOFC technology is linked with the improvement of high performance solid electrolytes.

Recently, the search for improved electrolyte materials has attracted much attention to enlarge the application range of the SOFC. So far, fuel cells have been widely used in power plants [30,31], automobiles [32,33], domestic use [34,35] and even digital products [36]. Such promising future is tied with the numerous advantages offered by the power generation equipment, namely in terms of conversion efficiencies, reduced environmental impact, low noise emissions and moderate cost.

I.1.2 Fuel cell structure and operation

I.1.2.

Principle of operation

Fuel cells [37][38][39] have many pack types with multiple geometries and packing: i) tubular fuel cell firstly designed by Westinghouse co.; ii) planar fuel cell which has higher power density than the tubular one; iii) micro tubular fuel cell which possess higher energetic density, better resistance to thermal stresses, and smaller starting times as compared with conventional planar stacks . In this diagram, hydrogen is taken as fuel. The hydrogen comes into the anode (the oxidation electrode), to be absorbed by the material, in which it undergoes a catalytic dissociation that generates protons. Meanwhile, the adsorption and catalytic dissociation of oxygen molecules at the cathode (the reduction electrode) lead to the generation of oxygen ions. These ions pass through the electrolyte, meet the hydrogen ions at the anode. Both ions are consumed at the same time, and combined to generate water. In addition, this formation of water promotes the consumption reaction in both electrodes. Since the electrolyte is designed for electronic insulation, electrons can only pass through an external circuit from the anode to the cathode, whereby generating the wanted current.

-Chemical thermodynamics In the cells, the non-volume work 𝑊 ′ , which is the electrical work, is equal to the change in the Gibbs energy under isothermal and isobaric conditions.

We assume that there is 1 mol hydrogen involved in the chemical reaction of equation I.1, thus 2 moles of electrons pass through the external circuit. The electrical work is given in the equation I. 6.

𝑊 ′ = -2𝐹 • 𝐸 = ∆𝐺 EQN I.6
Then,

𝐸 = ∆𝐺 -2𝐹 EQN I.7
where 𝐸 is the electromotive force of the fuel cell and 𝐹 is the Faraday constant that represents the total electricity of the charges of one mole elementary, and the value is 96 485 C/mol;.

For example, when the product of the hydrogen fuel cell is vapor at the operating temperature of 200℃ , the value of ∆𝐺 is -220.82 kJ/mol. the electromotive force is 1.14V.

-Fuel cells efficiency

First of all, we compare the energy conversion efficiency of the engine which is a traditional device commonly used for the conversion of chemical energy. According to the second law of thermodynamics, efficiency of work is to follow the Carnot efficiency, and it is given in equation I. 8.

𝜂 = -𝑊 𝑄 = 1 - 𝑇 2 𝑇 1 EQN I.8
Where, 𝑊, 𝑄, 𝑇 1 and 𝑇 2 are the work function, heat absorbing from the high temperature source, the high temperature and low temperature. The temperature difference between inside and outside of engine is high, then there is more effectively. Currently, the limit of the theoretical efficiency of the car engine is about 50%, while the actual efficacy is much lower.

The theoretical efficiency [40] of the cell is defined as the equation I. where ∆𝐻 is the enthalpy change, which is the heat emission by burning the same amount of fuel.

Table I In some reactions, such as oxidation of Carbon, the Gibbs free energy is even higher than the enthalpy change. That is to say, the reactions in cell absorb heat during the conversion process from chemical energy to electrical energy. Compared to combustion, the efficiency is even higher than 100%. Table I.1 shows the electromotive forces and the efficiency of common fuel cells.

-The energy density and power density

I.1.2.2 Structure of fuel cell

In this section, the three most important parts are presented by their uses and conditions to be fulfilled.

-An oxygen electrode (cathode)

This is a place for the reduction reaction of oxygen. It must match a porous structure (a porosity about 30% ~ 40%) to increase specific surface, as well as to permit the oxidant to reach the interface between cathode and electrolyte. In addition, it needs to have the properties:

-Chemical compatibility with the other contact components (usually the electrolyte and interconnect) in operating conditions;

-A thermal expansion coefficient (TEC) corresponding to those of other components;

-The chemical stability and microstructure in an oxidizing atmosphere during fabrication and operation;

-Adhesion to the surface of the electrolyte.

It is an electric and ion conductor. Meanwhile, it needs to have the ability of oxygen adsorption and catalytic cracking. The most common materials of the cathode are metals which can form the oxygen adsorption bonds easily. Figure I.5 shows evolution of the oxygen reduction activity of the different metals [42]. Among them, Pt shows the best performance. -A fuel electrode (anode)

This is a place for the oxidation reaction of the fuel. It must exhibit a porous structure to allow the fuel to reach the interface between anode and electrolyte. It is an electron and ion conductor.

Meanwhile, it needs to have the possibility of processing hydrogen (or other fuel) adsorption and catalytic cracking.

Hydrogen oxidation reaction as the easiest, but the most typical reaction in the anode is shown as an example to explain the catalytic oxidation process. The oxidation of hydrogen molecules takes place on the surface of noble metals. Figure I.7 shows the exchange current density on the different metals as the anode materials [43][44][45]. The density largely depends on the metalhydrogen bond: if the bond is very strong, it is difficult for the products separating from the metal, thereby interfering with the reaction continuation. And if the bond is very weak, the bond formation is not so stable that the hydrogen molecules are easy to be desorbed. Among them, Pt shows the best performance, and Pt was used as an electrode material of test electrolyte. Due to crystal defects or their particular structures, these substances provide channels for rapid ion transition. At certain temperatures, they have high ion conductivity (> 1~10 -6 𝑆 • 𝑐𝑚 -1 ), also called as fast oxygen ion conductors. The performance of ionic conduction is dependent by the ion diffusion efficiency in the substances [46][47][48]. -Vacancy diffusion. This diffusion takes place among the lattice sites, and it is based on the vacancies in crystal defects. To jump from lattice site to lattice site, atoms need energy to break bonds with neighbors, and to cause the necessary lattice distortions during jump. This energy comes from the thermal energy of atomic vibrations and electric field force in some cases.

-Interstitial diffusion. Interstitial diffusion is generally faster than vacancy diffusion because bonding of interstitials to the surrounding atoms is normally weaker and there are many more interstitial sites than vacancy sites to jump to. Requires small impurity atoms (e.g. C, H, O) to fit into interstices in host.

-Ions exchange. An ion exchanges with another neighbor ion. This mechanism creates very important local distortions repulsion. However this does not assume an existence of permanent point defects in the crystal. To further understand the factors that influence diffusion, thermally activated process is discussed in this part. First of all, the activation energy has to be drawn into the conception to describe the diffusion, even the conductivity. To jump from lattice site to lattice site, atoms need energy to break bonds with neighbors, and to cause the necessary lattice distortions during jump. The energy necessary for motion, Em, is called the activation energy.

The probability of such fluctuation or frequency of jumps, Rj, depends exponentially on temperature and can be described by equation I.12 that is attributed to Swedish chemist Arrhenius:

𝑅 𝑗 = 𝑅 0 𝑒𝑥𝑝 ( -𝐸 𝑚 𝑘 𝐵 𝑇 ⁄ ) EQN I.12
Where 𝑅 0 is so-called "attempt frequency" proportional to the frequency of atomic vibrations.

Correspondingly, Diffusion coefficient, which is the measure of mobility of diffusing species, can be given in equation I.13

𝐷 = 𝐷 0 𝑒𝑥𝑝 ( -𝑄 𝑑 𝑅𝑇 ⁄ ) EQN I.13
Where 𝐷 0temperature independent pre-exponential (m 2 /s) 𝑄 𝑑the activation energy for diffusion (J/mol or eV) Rthe gas constant (8.31 J/mol•K or 8.62×10 -5 eV/ K) Tabsolute temperature (K)

The above equation can be written as:

ln𝐷 = ln𝐷 0 - 𝑄 𝑑 𝑅 ( 1

I.1.3 Comparison of some alternative fuel cells

According to different types of electrolyte, fuel cells can be classified into multiple categories.

Some relatively important alternatives or competitive fuel cells have to be presented here in order to further understand the features of SOFC. Table I The cubic perovskite type oxides with general formula ABO3 are mainly used as cathode materials [52]. These materials, with the electronic and the oxide ionic conductivity, are known with the name MIEC (Mixed Ionic-Electronic Conducting oxides). In 1966, La1-xSrxCoO3-δ (LSC) was the first perovskite-type material, reported by Button and

Archer, to be used as cathodes for SOFCs [53]. This was followed by synthesis of several perovskite materials which were subsequently tested for their usability. From 1973, La1-xSrxMnO3-δ (LSM) has been used exclusively for the purposes of the cathode, and until today it remains the most studied cathode material for SOFCs [54,55]. In the case of LaMnO3, Sr 2+ cation dopant is most widely used because of the small difference in ionic size between Sr 2+ and La 3+ . However, on substitution of La 3+ with Sr 2+ cations, instead of compensation by the formation of positively charged oxygen vacancy, an oxidation of manganese cations occurs, which effectively increases the electron-hole concentration and improves electrical conductivity [56]. This process is similar to p-type doping in the p-type semiconductor. The defect reaction can be given in the form of Kröger-Vink notation as shown in EQN I.15.

𝑆𝑟𝑂 + 1 2 𝑂 2 𝐿𝑎𝑀𝑛𝑂 3 → 2𝑆𝑟 𝐿𝑎 ′ + 𝑀𝑛 𝑀𝑛 . + 3𝑂 𝑂 × EQN I.15
A linear increase in the electron conductivity of La1-xSrxMnO3-δ with the increase of x has been reported by Mizusaki et al [57]. However, the conductivity reaches a maxima at x = 0.5. Zhang oxygen vacancies for the perovskites and interstitials for Ln2MO4+δ. [59] The performance of the existed cathode materials is listed in the Table I. The compatibility of cathode on the electrolyte was first studied in 1969 by Tedmon et al [60]., with the porous LaCoO3 cathode on YSZ electrolyte. From then on, this field study became a hot point till today. * TECthermal expansion coefficient; σethe electronic conductivity; σithe ionic conductivity; DOdiffusion coefficient of the oxygen ; k-oxygen surface exchange coefficient

I.2.2 Anode materials -Ni-cermet

As mentioned before, certain metals can be candidates as the anode materials of SOFCs for their catalytic ability. No doubts, Pt has very good performance in hydrogen catalytic field, however the high cost and volatile feature under high operating temperature are big obstacles for the application in SOFC. Ni becomes the most commonly used anode metallic material due to its low overvoltage and low price. Considering the effective combination of metal and ceramic electrolyte, the optimization of metal electrodes, cermet (e.g. Ni-YSZ) and the metal oxide has been introduced. Ni-based cermet, particularly Ni-YSZ has been applied in various ways as commercial anode materials due to its high electrical conductivity [61,[START_REF] Ramirez-Cabrera | Catalytic steam reforming of methane over Ce0. 9Gd0. 1O2-x[END_REF]. However, these materials have high sulfur poisoning [START_REF] Rasmussen | The effect of H 2 S on the performance of Ni-YSZ anodes in solid oxide fuel cells[END_REF] and carbon deposition [START_REF] Nikooyeh | Effect of hydrogen on carbon formation on Ni/YSZ composites exposed to methane[END_REF] problems. This phenomenon can lead to the loss of material activity, reducing the cell life. (the ingredient of synthesis gas: CH4 23.64% ; CO 7.60% ; CO2 14.27% ; H2 49.48% ; H2O 5.00%) [START_REF] Chen | Evaluation of carbon deposition behavior on the nickel/yttrium-stabilized zirconia anode-supported fuel cell fueled with simulated syngas[END_REF].

-Cu-cermet

Cu cermet was found inactive to the carbon deposition in the reforming of hydrocarbon fuels, such as CH4 and syngas [START_REF] Costa-Nunes | Comparison of the performance of Cu-CeO 2-YSZ and Ni-YSZ composite SOFC anodes with H 2, CO, and syngas[END_REF]. However, Cu has a lower melting point (1083℃) relative to that of Ni (1453℃), therefore, sintering at elevated temperatures is impractical. Beside them, Lu et al [START_REF] Lu | A comparison of Cu-ceria-SDC and Au-ceria-SDC composites for SOFC anodes[END_REF]. studied that Cu does not give any catalytic activity for cracking hydrocarbons in the anode, however, it acts only as electronic conductors to the anode. Thus, some high catalytic activation of metals are used in Cu-based anode to improve the performance.

-Ceria

Cerium oxide and its compounds are introduced as anode materials due to their high electronionic conductivity in reducing atmosphere. Its ionic conductivity can be controlled by adding acceptor dopant oxides such as CaO, Y2O3, GdO3 and Sm2O3. In addition, it acts as a catalyst for the direct oxidation of hydrocarbon-containing fuels. Further, it also has a good compatibility with the component materials of adjacent cells. M-CeO2 or M-CeO2-Y2O3 are very common forms of anode materials [START_REF] Murray | A direct-methane fuel cell with a ceria-based anode[END_REF][START_REF] Steele | Appraisal of Ce 1-y Gd y O 2-y/2 electrolytes for IT-SOFC operation at 500[END_REF][START_REF] Omar | Crystal structure-ionic conductivity relationships in doped ceria systems[END_REF][START_REF] Omar | A co-doping approach towards enhanced ionic conductivity in fluorite-based electrolytes[END_REF][START_REF] Omar | Higher ionic conductive ceria-based electrolytes for solid oxide fuel cells[END_REF].

-perovskite structure, double-perovskite

In a quest to develop sulfur tolerant materials of anode, other than Ni-based structures, nickel free conductive metal oxide based perovskites were proposed. [START_REF] Gong | Sulfur-tolerant anode materials for solid oxide fuel cell application[END_REF] The common chemical formula for these materials is ABO3 (A = La, Sr, Ce, Mg and B = Ti, V, Mn, Mo, Nb high valence elements). The conductivity of SrTiO3 has been found to increase to 100 S/cm (at 800 ℃) when the lanthanides and yttrium replaces strontium [START_REF] Hui | Evaluation of yttrium-doped SrTiO 3 as an anode for solid oxide fuel cells[END_REF][START_REF] Hui | Electrical properties of yttrium-doped strontium titanate under reducing conditions[END_REF]. Nb doping in the Ti site has also been reported to increase the conductivity of 120 S/cm [START_REF] Blennow | Electrochemical characterization and redox behavior of Nb-doped SrTiO 3[END_REF]. These materials have good chemical stability, thus many doping elements are employed to improve the conductivity.

-pyrochlores

Pyrochlores are A2B2O7 type oxides usually with A III / B IV and A II / B V , which displays diverse electrical, magnetic, dielectric and catalytic properties [START_REF] Deng | Highly conducting redox stable pyrochlore oxides[END_REF][START_REF] Blundred | New oxidation states and defect chemistry in the pyrochlore structure[END_REF][START_REF] Subramanian | Oxide pyrochlores-a review[END_REF]. The different composition of A and B results in a lack of oxygen or excess stoichiometric. Pyrochlores (Ln0.9Ca0.1)2Ti2O7 (Ln = Gd, Y and Yb) are reported to exhibit good ionic conductivity at high temperatures [START_REF] Kramer | Conduction in titanate pyrochlores: role of dopants[END_REF][START_REF] Kramer | A novel titanate-based oxygen ion conductor: Gd 2 Ti 2 O 7[END_REF]. Under reductive condition, Gd2(Ti1-xMox)2O7 (0.1≤x≤0.7) with Mo (+IV) exhibits high electronic conductivity (> 10 S/cm) [START_REF] Porat | Stability and mixed ionic electronic conduction in Gd 2 (Ti 1-x Mo x) 2 O 7 under anodic conditions[END_REF].

I.2.3 Interconnect materials

The interconnect corresponds to a metal or ceramic layer which is used to assemble the cell units in series or in parallel and finally to constitute the stack. It must separate the fuel gas from the oxygen. Interconnect materials must be stable under reduction and oxidization atmospheres, and must possess a predominant electrical conductivity.

-Ceramic interconnect materials

The most commonly used ceramics as interconnects are lanthanum chromite (LaCrO3) based materials which are among most stable perovskite-type oxides [START_REF] Zhu | Development of interconnect materials for solid oxide fuel cells[END_REF][START_REF] Akashi | Transport of lanthanum ion and hole in LaCrO 3 determined by electrical conductivity measurements[END_REF]. LaCrO3 has high electrical conductivity (~1 S/cm à 1000℃) compared to other ceramics, high melting point (2510℃), low CTE disagreement with YSZ (CTELaCrO3~ 9,5×10 -6 /K et CTEYSZ~10,5×10 -6 /K) [START_REF] Tietz | Thermal expansion of SOFC materials[END_REF] and relatively good compatibility with the other components of the cell, making it be a suitable interconnect. One or some elements of Ca, Mg, V, Co et al are selected to be doped in the material to improve its performance.

I.2.4 Materials for electrolytes

To achieve high ion conductivity of the electrolyte materials, their crystal structure must have a large open space or defects that allows high level of point defect disorder, and low migration enthalpy ≤1eV [START_REF] Fergus | Solid oxide fuel cells: materials properties and performance[END_REF]. In these compounds, the metal cations have a certain level of vibration around their site due to their sizes are much smaller than of the oxide ion, as well as the metal cations also possess high valence charge, which does not allow the free movement within the network. This phenomenon leads to local defect to allow the ions crossing the structure.

-Fluorite structure oxides

EQN I.16

It is experimentally observed that the ionic conductivity reaches a maximum at dopant concentration of about 10-20 mol% depending on the type of dopant. Based on this phenomenon, some composite oxides have been investigated as promising candidates of electrolyte.

As mentioned, Y2O3 stabilized ZrO2 (YSZ) materials are typical commercial electrolytes owing to their high oxide ion conductivity. Among them, 8mol% Y2O3-ZrO2 (8YSZ) is reported to have highest ionic conductivity of 0.1S/cm at 1000℃ [17]. Besides Y2O3, the Sc2O3 also has been adopted as dopant in ZrO2 (ScSZ), and 11ScSZ is reported to exhibit quite high ionic conductivity, close to 1.5 S/cm at 850℃ [START_REF] Badwal | Oxygen-ion conducting electrolyte materials for solid oxide fuel cells[END_REF]. It can be used in intermediate temperature SOFC as well as considering its wide range of oxygen partial pressures and good thermochemical properties. However, some obstacles should be addressed before commercial application, for example, phase transitions with the working temperature changes and high market price.

δ-Bi2O3 based ceramics

In fact, Bi2O3 structure is attributed to fluorite category, while it has particular defects differing from common MO2 fluorite structure. This results in its high ionic conductivity, as well as good electro catalytic activity for O2 conversion at low temperature [START_REF] Shuk | Oxide ion conducting solid electrolytes based on Bi 2 O 3[END_REF][START_REF] Kharton | Research on the electrochemistry of oxygen ion conductors in the former Soviet Union[END_REF]. Bi2O3 has four different polymorphs, denoted as monoclinic α, tetragonal β, body-centered cubic γ, and face-centered cubic δ. where the high conductivity is shown by δ -phase, whose structure is presented in S/cm and ~2.3×10 -2 S/cm at 700 ℃ and 500 ℃, respectively [START_REF] Verkerk | High oxygen ion conduction in sintered oxides of the Bi2O3-Er2O3 system[END_REF][START_REF] Kruidhof | Thermochemical stability and nonstoichiometry of erbia-stabilized bismuth oxide[END_REF].

Other Bi oxide based electrolyte materials BiMeVOx, obtained by partial substitution of V in γ-Bi4V2O11 by additive metal (Me = Co, Cu, Ta), exhibit high ionic conductivity. [START_REF] Abraham | The BIMEVOX series: a new family of high performances oxide ion conductors[END_REF][START_REF] Lazure | Composition dependence of oxide anion conduction in the BIMEVOX family[END_REF] The conductivity of BuCuVOx which corresponds to the partial substitution of V in Bi4V2O11 by 10% of Cu is reported of two orders of magnitude higher than YSZ at 400℃.Unfortunately, at high temperature, bismuth oxide is easily reduced into bismuth metal which is liquid at The ionic conductivity of pyrochlore based oxides (e.g., Gd2Zr2O7 ~ 5 ×10 -2 S/cm) exhibits considerable performance, and the ionic conduction in these materials can be tailored either by chemical substitution [START_REF] Kramer | A novel titanate-based oxygen ion conductor: Gd 2 Ti 2 O 7[END_REF]. Among various pyrochlore compositions, Gd1.8Ca2Ti2O7-δ (x = 0.20) is reported to exhibits the highest conductivity [START_REF] Kramer | Conduction in titanate pyrochlores: role of dopants[END_REF]. The substitution increases the p-type conductivity and lowers the n-type electronic conductivity of the material.

-Perovskite-based ceramics

As a typical perovskite ceramic, LaGaO3 was investigated as ionic conductors by various groups [26,[START_REF] Feng | A superior oxide-ion electrolyte[END_REF]. The migrating ion is expected to migrate through the center of triangle formed by two La 3+ A-site cations and one Ga 3+ B-site cation. The ionic radii ratio of the A-and B-site cations becomes an important factor, which significantly influences the ionic conductivity in the perovskite material. The ionic conductivity can be enhanced by either decreasing the size of A-site cation (minimum 0.95 Å) or increasing the size of B-size cation [START_REF] Cherry | Oxygen ion migration in perovskite-type oxides[END_REF].

Addition of acceptor dopant cation to LaGaO3 oxides, such as, Sr 2+ , Ca 2+ , Mg 2+ or Ba 2+ at La 3+ or Ga 3+ sites have been reported to enhance the catalytic activity and ionic conductivity. [2,[START_REF] Tascon | Structure and reactivity of perovskite-type oxides[END_REF][START_REF] Hu | Review of p-type doped perovskite materials for SOFC and other applications[END_REF] These dopant cations create oxygen vacancies as a compensating defect, which, in turn, increase the ionic conductivity. Typically, with Sr 2+ , Mg 2+ at La 3+ , Ga 3+ sites respectively, La1-xSrxGa1-yMgyO3-δ (LSGM) series have maximum ionic transport with x and y lying in the range of 0.10-0.20 and 0.15-0.20. [START_REF] Hayashi | Structural consideration on the ionic conductivity of perovskite-type oxides[END_REF] Some trivalent elements (such as Al 3+ , In 3+ , Sc 3+ and Y 3+ ) have also been used to occupy at B sites of LnBO3. These materials offer good mechanical compatibility during fabrication and good stability to reduction and volatilization. However, they possess relatively low ionic conductivity and high p-type electronic conduction in oxidizing atmosphere. Doping Sr 2+ at Asite is a common way to enhance the conductivity and lower vacancy-association.

La0.9Sr0.1AlO3 has been reported has the maximum conductivity value, being close to 100 mS/cm at 1000℃ [START_REF] Nomura | Electrical conduction behavior in (La 0.9 Sr 0.1) M III O 3-δ (M III= Al, Ga, Sc, In, and Lu) perovskites[END_REF].

-Brownmilleritetype ceramics

Oxides having a brownmillerite structure (with the chemical formula of A2B2O5) consists of alternating layers of perovskite sharing corner with BO6 octahedra and BO4 tetrahedra, as shown in figure I.23. [START_REF] Fisher | Electrical conductivity of brownmillerite-structured oxide ceramics[END_REF][START_REF] Ferguson | Epitaxial oxygen getter for a brownmillerite phase transformation in manganite films[END_REF] These materials are considered as oxygen deficient pervoskites, thus oxygen vacancies are observed to order along (0 1 0) direction which can be good candidate as ionic transport channel. As the most common material of this series, Ba2In2O5 exhibits high ionic conductivity in dry air, as well as the electronic conductivity existing [START_REF] Goodenough | Oxide-ion conduction in Ba 2 In 2 O 5 and Ba 3 In 2 MO 8 (M= Ce, Hf, or Zr)[END_REF][START_REF] Schober | Phase transition in the oxygen and proton conductor Ba 2 In 2 O 5 in humid atmospheres below 300[END_REF]. The disordered cubic perovskite phase can be stabilized by substituting In-sites with higher-valance cations, e.g., Zr 4+ , Ce 4+ , Sn 4+ or Hf 4+ that can enhance intermediate temperature ionic conduction [START_REF] Schober | The oxygen and proton conductor Ba 2 In 2 O 5: Thermogravimetry of proton uptake[END_REF]. La 3+ , Sr 2+ are also used to dope in Ba sites to modify the conductivity performance [START_REF] Kakinuma | Oxide-ion conductivity of the perovskite-type solid-solution system,(Ba 1-x-y Sr x La y) 2 In 2 O 5+[END_REF]. At 800℃, the maximum conductivity of ~ 0.12 S/cm is reported in (Ba0.3Sr0.2La0.5)2In2O5.5 composition, which exceeds that of Y2O3 stabilized ZrO2. The oxide ion conductivity in LAMOX was found to be ~ 6×10 -2 S/cm, firstly reported by Lacorre et al. in year 2000 [START_REF] Lacorre | The LPS concept, a new way to look at anionic conductors[END_REF]. Doping with W to form La2Mo2-xWxO9 solid solutions (with x ≤ 1.6) were reported to exhibit ionic conductivity of ~ 0.11 S•cm -1 (x = 0) to 0.05 S•cm -1 (x = 1.5) at 750 ℃ [START_REF] Marrero-López | Applicability of La 2 Mo 2-y W y O 9 materials as solid electrolyte for SOFCs[END_REF].

-Apatite structure

Apatite based materials have a general formula of A10(MO4)6X2±δ(where A is a rare earth or alkaline earth cation or Pb, M is a p-block element, such as, Si, Ge, P or V and X is OH -, O 2-or halides). The structure comprises of isolated MO4 tetrahedra arranged in a way to form distinct anion and La channels running parallel to the c-axis. The oxide ion channels being in central position participate in ionic conductivity [START_REF] Kendrick | Developing apatites for solid oxide fuel cells: insight into structural, transport and doping properties[END_REF]. This series of materials will be presented in details in section I.4.

I.3 Encountered difficulties of operating temperature

Comparing with some other electrolytes using for PAFC (Phosphoric Acid Fuel Cell), PEMFC (Proton Exchange Membrane Fuel Cell) and MCFC (Molten Carbonate Fuel Cell) etc., solid state electrolyte has lower ionic conductivity. In order to achieve a considerable conductivity, SOFC inevitably should work at high operating temperature.

Too high operating temperature leads some disadvantages in application:

-extended startup time;

-high thermal stress;

-weak components compatibility and the ageing of constituent components;

-the difficult choice of the matched interconnectors or electrodes -high maintenance cost.

This will lead to the usage restriction in various fields, e.g., military and transportation, and also limit the application of some good performance materials as components in SOFC. Thus, more attention is paid to intermediate operating temperature (IT-SOFC), which results in many benefits: reducing manufacture costs and increase the selection range of materials. Meanwhile, the operation of FCs becomes environment-friendly, as well as decreasing the implementation difficulties of sealing technology.

The realization of IT-SOFC heavily depends on the development of electrolyte materials. The oxide ionic conductivity of traditional electrolyte materials decreases rapidly by reducing the operation temperature.

Recently, some new solid electrolyte materials have been developed to overcome these problems. These materials have common feature: high ionic conductivity and intermediate operating temperature. Among these materials, apatite rare-earth silicates, with a common formula RE10Si6O27 (RE=La, Pr, Nd, Sm, Gd, Dy), have been considered as a promising solid electrolyte for IT-SOFC since they were firstly reported to have higher conductivity than YSZ below 600℃ by S. Nakayama et al [START_REF] Nakayama | Electrical properties of new type high oxide ionic conductor RE 10 Si 6 O 27[END_REF][START_REF] Nakayama | Ionic conductivity of lanthanoid silicates, Ln 10 (SiO 4) 6 O 3[END_REF].

I.4 Apatite-type phase lanthanum silicate electrolyte

I.4.1 Structure
The lanthanum silicates using as electrolyte of IT-SOFC are apatite-type phase which has a general formula (A 2+ )10(MO4 There are two types of parallel tunnels along the c axis [START_REF] Sun | Caracté risation de revê tements de silicate de lanthane de structure apatite dopé au magné sium ré alisé s par projection plasma en vue d'application comme é lectrolyte de pile à combustible de type IT-SOFC[END_REF]:

(x,y,z) (-y,x-y,z) (-x+y,-x,z) (-x,-y,z+1/2) (y,-x+y,z+1/2) (x-y,x,z+1/2) (-x,-y,-z) (y,-x+y,-z) (x-y,x,-z) (x,y,-z+1/2) (-y,x-y,-z+1/2) (-x+y,-x,-z+1/2) X 2a -6.. ( 0
-the first one is occupied by A1 cations.

-the second one which has larger diameters than the previous ones, contain the six A2 cations and X anion. It can be the major channel for this ionic conductor.

In the case of using apatite as the solid electrolyte for IT-SOFC, the anion X -will be substituted by O 2-ion in order to raise the electrical conductivity, the element A 2+ is rare earth or alkali metal element and M represents P block element (P, Si or Ge). The composition in actual material has an alternative formula La9.33(SiO4)6O2, which has the same structure as described in the preceding paragraph. This is due to the cation valence change causing by ions substitution. To keep the balance valence, the substitution, A 2+ → La 3+ and XO4 3-→ SiO4 4-, leads to a 0.67 vacancy at A site.

Table I.5 gives the atoms coordinates of this structure [START_REF] León-Reina | Interstitial oxide positions in oxygen-excess oxy-apatites[END_REF]. The single cell is built by some symmetry operations of these initial coordinates. [START_REF] Nakayama | Electrical properties of new type high oxide ionic conductor RE 10 Si 6 O 27[END_REF][START_REF] Nakayama | Ionic conductivity of lanthanoid silicates, Ln 10 (SiO 4) 6 O 3[END_REF][START_REF] Nakayama | Electrical properties of apatite-type oxide ionic conductors RE9. 33 (SiO4) 6O2 (RE= Pr, Nd and Sm) single crystals[END_REF] The conductivities were shown to be enhanced in samples containing oxygen excess (x > 0), (e.g.σ (500 °C) =1.1×10 -4 Scm -1 for La9.33(SiO4)6O2, vs 1.3×10 -3 Scm -1 for La9.67(SiO4)6O2.5). [START_REF] Najib | Doping strategies to optimise the oxide ion conductivity in apatite-type ionic conductors[END_REF]These initial results suggested that interstitial oxide-ions were important in promoting high oxide-ion conductivity in these apatite systems.

Typically non-stoichiometry ranges of 0 ≤ x ≤ 0.34 are possible for the larger rare earth elements before impurities such as Ln2SiO5 appear. For the smaller rare earths, e.g. Gd, lower non-stoichiometry ranges are observed, which suggests that less space is available to accommodate the extra interstitial oxide-ions as the unit cell size is reduced. In addition a general decrease in conductivity and increase in activation energy is observed as the size of the rare earth is reduced. [START_REF] Kendrick | Developing apatites for solid oxide fuel cells: insight into structural, transport and doping properties[END_REF] Table I. 6 shows different conductivities at 500℃ of lanthanum silicates containing various oxygen excess [START_REF] Bé Chade | Synthesis of lanthanum silicate oxyapatite materials as a solid oxide fuel cell electrolyte[END_REF]. To some extent, oxygen excess visibly affects the ionic conductivity.

However, the synthesis process has an influential function to accurate the formula of the products. Anyway, this series materials have much higher ionic conductivities than commercial electrolyte material YSZ at intermediate temperature. it is accommodated at the channel periphery, rather than the channel center. Based on the preliminaries, no doubt the major migration channel is located along c-axis. The experimental studies on detailed conductivity of single crystal have shown that the conductivity is anisotropic, with the conductivity parallel to c (the direction of the oxygen channels) significantly higher than that perpendicular (e.g. Nd9.33(SiO4)6O2, σc = 6.4×10 -3 S cm -1 , σab = 1.3×10 -3 S cm -1 at 500 °C, both activation energies are fairly similar around 0.6 eV) [START_REF] Nakayama | Ionic conductivities of apatite type NdX (SiO4) 6O1. 5X-12 (X= 9.20 and 9.33) single crystals[END_REF]. The results suggest that although the main conduction pathway is down the oxide-ion channels, there is also significant conduction perpendicular to the channels (i.e. inter-channel conduction).

Figure I.30 exhibits one possible explanation for inter-channel conduction [START_REF] Kendrick | Developing apatites for solid oxide fuel cells: insight into structural, transport and doping properties[END_REF][START_REF] León-Reina | Interstitial oxygen conduction in lanthanum oxy-apatite electrolytes[END_REF]. This

shows that the local relaxation around the interstitial site leads to reduction in the distance to a neighboring SiO4 unit. This could effectively create a pathway, whereby an interstitial oxideion is moved between adjacent channels by a series of two cooperative "SN2"-type processes (SN2 = bimolecular nucleophilic substitution), with accompanying rotation of the tetrahedral. There are three types of doping possibility according to the doping sites:

-La Site: Ca, Sr, Ba, Bi.

-Si Site: B, Al, Ga, Zn, Ti, Ge, Fe, P.

-La and Si sites: Mg, Mn, Ni, Cu, Co.

Table I.7 shows some comparison of electric properties of doped LSO [START_REF] Kendrick | Developing apatites for solid oxide fuel cells: insight into structural, transport and doping properties[END_REF][START_REF] Najib | Doping strategies to optimise the oxide ion conductivity in apatite-type ionic conductors[END_REF]. Apatites LSO, in which we substitute some dopant of Si 4+ cations, have higher ionic conductivity and lower energy activation. These results are also depended on the purity of the phase by the synthesis process. *measured at 600°C, ref [START_REF] León-Reina | Crystalchemistry and oxide ion conductivity in the lanthanum oxygermanate apatite series[END_REF] I.5 Summary

In this chapter, a brief review from the principles to the materials of SOFC, especially electrolyte materials, is presented. As the basis of the present study, lanthanum silicates (LSO)

system is introduced and discussed, including the structure, electric properties. The doping effects by multiple metal elements are reviewed to find proper candidate doped in our composition.

CHAPTER II. Fundamentals of Experimental, Calculation and Characterization

In this chapter, we present a brief review of synthesis methods, and describe the experimental techniques and characterization used in this study, including the synthesis methods, microstructure characterization (XRD, SEM ) electrolyte properties measurement (ionic conductivity) and a brief introduction of the DFT (Density Functional Theory).

Since the quality of LSO material is of the essence for the highest performances of SOFC devices, we have paid the greatest attention to its synthesis process and explored a large variety of preparation methods and selected the most efficient one.

II.1.2 Casting

Casting is a traditional ceramic manufacturing process in which a liquid material is usually poured into a mold, which contains a hollow cavity of the desired shape, and then allowed to solidify. The solidified part is also known as a casting, which is ejected or broken out of the mold to complete the process. It is low-cost and suitable for making thin wall products with complex shapes and has been used in fabricating yttria stabilized zirconia (YSZ) tubes and cone-shaped electrolyte cylinders. It is developed to adopt the fabrication of electrolyte into tape-casting, slip casting and vacuum casting et al. [3][4][5][6] A fair example of this technology is given by N.O. Shanti et al. [7] who reported that electrolyte of multiple layers with thickness ranging from 10 to 500 µm were produced with a single tape casting step for each layer. The assembled cells made with this technique have maximum current density and power density PVD describes a variety of vacuum deposition methods which can be used to produce thin films.

It uses physical process (such as heating, sputtering [12][13][14][15][16] or electron beam [17,18] etc.) to produce a vapor of material, which is then deposited on the object which requires coating. It is used in the manufacture of electrolyte which require thin dense films for mechanical, chemical and electronic functions. The morphology of the electrolyte fabricated by PVD is shown in Thermal spray is a generic term for a group of processes that utilize a heat source to melt material in powder, wire or rod form. The molten or semi-molten material is propelled toward a prepared surface by expanding process gases. The particles quench rapidly, upon impact with the surface, and bond with the part. Subsequent impacting particles create a coating buildup [23][24][25]. The coating and synthesis process of the fuel cell materials is investigated by the previous work in our laboratory [26][27][28]. Recently, F. Sun reported [29] that better performance and denser apatite products can be obtained by very low pressure plasma spraying (VLPPS) than that by atmospheric plasma spraying (APS). A mount of microcracks can be detected in fracture surface of coating deposited by the latter. When using conventional precipitation, one needs to perform the co-precipitation of the cationic part (lanthanum and possible substituting ions: Sr, Mn etc.) and the anionic part (silicate). This method has been explored and results are reported in Chapter IV.1 and IV.2.

The molten salt method has been lastly studied in Chapter IV.3 using various alkali salts (chlorides, nitrates and sulfates) as the molten media likely to favor the interaction between the lanthanum and silica. The main issues observed have been: i) high level of impurities present in the LSO product (due to the concentrations of the contaminants presents in the starting fusible salts) and ii) the release of heavy smoke in the case of ammonium nitrate.

The HDP method has also been evaluated as well (Chapter IV.4). Here some lanthanum hydroxide is deposited at very low rate on a quite separated silica substrate (silica gel). The essential advantage of this method lies in the fact that precipitate nuclei are extremely fine due to the very low change in the pH during the hydrolysis of urea. However, we have stated that the precipitated lanthanum hydroxide, although well distributed over the silica particles were not able to diffuse inside the very core of the grains, which led to incomplete reaction.

Finally, the sol-gel method proved to be the most adequate and has been selected as the actual synthesis path in this work.

The principle of the sol-gel method is to generate nano-size particles in which the reacting atoms (e.g. La and Si) are located in very close vicinity in a common molecule and are therefore likely to interact easily with each other. The method is used for the fabrication of metal oxides, especially the oxides of silicon and titanium. The process involves conversion of monomers into a colloidal solution (sol) that acts as the precursor for an integrated network (or gel) of either discrete particles or network polymers. The sol and gel formation process is shown in Figure II.7 and two critical steps (condensation and gelation) determine the character of products directly [30]. Sol-gel method is employed as our major way to synthesize lanthanum silicates, thus we will give more details of this method. Doping elements were introduced in order to improve the performance of these compounds with this method. It was shown that substituting Al 3+ for Si 4+ in the SiO4 tetrahedra of the oxyapatite structure increases its ionic conductivity [34,35].

Recently E. Jothinathan et al. [36] prepared Al 3+ , Fe 3+ doped LSO using low temperature (900℃ Currently, some new techniques are derived from the traditional sol-gel technique, such as gel casting, gel printing, water-based sol gel, and so on. [8,38]. These techniques have much advantage in the synthesis of this LSO series as following:

-User-friendly, easy realization; The theoretical value of lanthanum silicates is 5.4 g•cm -3 (evaluated through simulation methods). Higher calcination temperatures seem to lead to higher densities. and the range of this type of SEM is from about 50 times to more than 300,000 times, about 150 times the magnification limit of the best light microscopes.

Energy-dispersive X-ray spectroscopy (EDX) is usually equipped in this equipment used for the elemental analysis or chemical characterization of a sample. As the energies of the X-rays are characteristic of the difference in energy between the two shells and of the atomic structure of the emitting element, EDS allows the elemental composition of the specimen to be measured.

Table II.2 gives characteristic X-ray energy of the elements involved in our study. The electrical conductivity of sintered material is a very important property for the use of the σ is the conductivity having SI units of Siemens per meter (S/m).

The resistance can be measured by the DC method. In order to completely understand the impedance of the sample, in our work, the method of electrochemical impedance spectroscopy (EIS) was applied for the electrochemical characterization of solid electrolytes. In fact, this method makes it possible to distinguish and identify the response of the electrolyte following the application of an alternating voltage disturbance with variable frequency and low amplitude around a stationary operating point. The voltage can be expressed as 𝐸 𝑡 = 𝐸 0 exp (𝑗𝜔𝑡), which is a sinusoidal signal, as well as the current. The impedance, including resistance, capacitance and inductance, is given in EQN II.5. The ionic conductivity can be presented by the analysis of Nyquist plot. The total ionic conductivity of a polycrystalline electrolyte depends upon the contribution from both grain and grain boundary. The separate resistive contributions of both grain interior and the grain boundaries towards the total resistivity can be obtained using AC impedance spectroscopy technique. In our study, this technique is employed to determine the content of crystal water in raw material for precise experiments. Then, the calcination process of our apatite-type LSO is investigated by this technique because the heat flow would be affected with the phase transitions or chemical reactions.

𝑍(ω) =

II.3. Ab initio calculations modeling II.3.1 Introduction of ab initio calculation

The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble ----P.A.M.

Dirac, Proc. Roy. Soc. (London), 123 714 (1929)

Ab initio (or first-principles) calculation [44][45][46] immediately first attempts to develop applicable theories were made. However, a really successful approach providing a solution of this equation for many-body problem that is relevant to solids was done almost 50 years later. The density functional theory (DFT) was invented to include correlation effects without using the very costly wave function methods.

Nowadays, most ab initio methods used in materials science and solid state physics are based on the DFT.

The main advantage of ab initio approach is its independence on experimental data. Unlike in the case of semi-empirical methods, there is no need for calibration or fitting parameters. Thus, ab initio methods can also be used for calculations of some structural and mechanical characteristics of hypothetical systems, i.e., for prediction of properties of materials that have not yet been developed. Meanwhile, such investigations can provide a better understanding of micro mechanisms of materials.

II.3.2 Density functional theory (DFT)

Density functional theory (DFT) is a computational quantum mechanical modelling method used in physics, chemistry and materials science to investigate the electronic structure (principally the ground state) of many-body systems, in particular atoms, molecules, and the condensed phases. In many cases the results of DFT calculations for solid-state systems agree quite satisfactorily with experimental data. Computational costs are relatively low when compared to traditional methods, such as Hartree-Fock theory and its descendants based on the complex many-electron wavefunction.

II.3.2.1 Fundamental Principles

DFT methods model all the electrons in a system, and the zero energy corresponds to having all nuclei and electrons at an infinite distance from one another. Quantum mechanics (QM) is the correct mathematical description of the behavior of electrons and thus of chemistry. In theory, QM can predict any property of an individual atom or molecule exactly. In practice, the QM equations have only been solved exactly for one electron systems. These approximations can be very useful, but this requires an amount of sophistication on the part of the researcher to know when each approximation is valid and how accurate the results are likely to be. The eigenvalues of equation cannot be calculated accurately in the case of hydrogen-like systems. In the case of a multi-electronic system, because of electronic interactions, there is no exact analytical solution of Schrödinger equation. In order to find acceptable solution of the equation, we need to make approximations of Hamiltonian operator. The first approximation is the Born-Oppenheimer approximation [47].

II.3.2.2 Born-Oppenheimer approximation

All methods of solving the Schrödinger equation based on this approximation, where its authors (Born and Oppenheimer) assume that there is a time scale difference between the electronic and nuclear motions due to a big difference in mass between the nuclei and electrons. Therefore, it is possible to decouple the movement of the nuclei and the electrons, then to write the wave function into two wave functions: nuclei and electrons.

𝛹(𝑟 ⃗, 𝑅 ⃗⃗ ) = 𝛹 𝛼 (𝑅 ⃗⃗ ) + 𝛹 𝑒 (𝑟 ⃗, 𝑅 ⃗⃗ ) EQN II.11

Where 𝛹 𝛼 (𝑅 ⃗⃗ ) is the wave function associated to the nuclei and 𝛹 𝑒 (𝑟 ⃗, 𝑅 ⃗⃗ ) is the wave function associated to the electrons and the nuclei are fixed in the position of 𝑅 ⃗⃗ . The total energy is then written as the sum of a nuclear and electronic contribution. Some methods are employed for the solution of this equation. The premier effective method is that of Hartree-Fock based on the assumption of free electrons. This method is quite useful to quantum chemistry to treat the atoms and molecules, but they are less accuracy for solids calculation. The DFT is proved probably to be a more modern and powerful method due to the two theorems by Hohenberg and Kohn [48] established in 1964. These authors have demonstrated that all aspects of the electronic structure of a system in a non-degenerate ground state is completely determined by its electron density instead of its wave function.

II.3.2.3 Hohenberg and Kohn theorems

The Hohenberg and Kohn theorems relate to any system consisting of electrons moving under the influence of an external potential υext(r). Stated simply they are as follows: In this theorem, stated simply, the electrons determine the positions of the nuclei in a system, and also all ground state electronic properties, because υext(r) and N completely define H in Nelectron systems.

Theorem 2:

For a given external potential and a fixed number of electrons, the ground state energy can be obtained variationally: the ground state of the system is the global minimum of the functional 𝐸[𝜌(𝑟 ⃗)] and density which minimizes this function is the density of the ground state 𝜌 0 (𝑟 ⃗).

[

𝜕𝐸[𝜌(𝑟 ⃗)]]

𝜕𝜌(𝑟 ⃗) 𝜌(𝑟 ⃗)=𝜌 0 (𝑟 ⃗) = 0 EQN II.16

Although the Hohenberg-Kohn theorems are extremely powerful, they do not offer a way of computing the ground-state density of a system in practice. About one year after the seminal DFT paper by Hohenberg and Kohn, Kohn and Sham [49] designed a simple method for carrying-out DFT calculations, that retains the exact nature of DFT. This method is described in next.

II.3.2.4 The Kohn-Sham Formulation

The Kohn-Sham formulation centers on mapping the full interacting system with the real potential, onto a fictitious non-interacting system whereby the electrons move within an effective ''Kohn-Sham'' single-particle potential υKS(r). The Kohn-Sham method is still exact since it yields the same ground state density as the real system, but greatly facilitates the calculation.

The Kohn-Sham potential υKS(r) is given by, υ 𝐾𝑆 (r) = υ 𝑒𝑥𝑡 (r) + υ 𝐻 (r) + υ 𝑥𝑐 (r) EQN II.17 The ground state density is obtained in practice by solving the one-electron Schrödinger equations,

[- ℏ 2 2𝑚 𝑖 ∇ 𝑖 2 + υ 𝑒𝑥𝑡 (r) + υ 𝐻 (r) + υ 𝑥𝑐 (r)] 𝜓 𝑖 (𝑟 ⃗) = 𝐸 𝑖 𝜓 𝑖 (𝑟 ⃗), 𝑖 = 1, … 𝑁 EQN II.20
Determining the ground state of the system, then returning to solve, with self-consistent manner, the set of equations (EQN II.20) is known as Kohn-Sham equation. The sum of three υ 𝑒𝑥𝑡 (r) + υ 𝐻 (r) + υ 𝑥𝑐 (r) is an effective potential υKS(r) which can be characterized as it depends only on the parameter r. This method is formally correct, but for the practical calculation, the exchange and correlation energy, which is a density functional, requires the introduction of some approximations.

II.3.2.5 The exchange-correlation functionals

The fact that the DFT gives no information on the form of the exchange-correlation functional 𝐸 𝑥𝑐 [𝜌(𝑟)], meanwhile the approximation have to be introduced for its determination must be applicable to different systems. The actual calculation of the energy and the potential for exchange-correlation is based on a number of approximations.

Local-density approximation (LDA)

The local-density approximation (LDA) relies on the assumption that the electron density varies slowly in space and therefore the exchange-correlation terms depend only on the local value of 𝜌(𝑟); that is to say, it deals with a non-homogeneous system as being locally homogeneous. In this regard, LDA is generally synonymous with functional based on the homogeneous electron gas (HEG) approximation, which are then applied to realistic systems (molecules and solids).

In general, for a spin-unpolarized system, a local-density approximation for the exchangecorrelation energy is written as

𝐸 𝑥𝑐 𝐿𝐷𝐴 [𝜌(𝑟 ⃗)] = ∫ 𝜌(𝑟 ⃗)𝜀 𝑥𝑐 [𝜌(𝑟 ⃗)] 𝑑𝑟 ⃗ EQN II.21
Where 𝜀 𝑥𝑐 [𝜌(𝑟 ⃗)] is the exchange-correlation energy per particle of a homogeneous electron gas of charge density 𝜌(𝑟 ⃗).

The exchange-correlation energy is decomposed into exchange and correlation terms linearly,

𝐸 𝑥𝑐 𝐿𝐷𝐴 [𝜌(𝑟 ⃗)] = 𝐸 𝑥 𝐿𝐷𝐴 [𝜌(𝑟 ⃗)] + 𝐸 𝑐 𝐿𝐷𝐴 [𝜌(𝑟 ⃗)] EQN II.22
The exchange-energy density of a HEG is known analytically. The LDA for exchange employs this expression under the approximation that the exchange-energy in a system where the density is not homogeneous, is obtained by applying the HEG results pointwise, yielding the expression Wilk-Nusair (VWN) [50]; Perdew-Zunger (PZ81) [51]; Cole-Perdew (CP) [52]; Perdew-Wang (PW92) [53].

𝐸 𝑥 𝐿𝐷𝐴 [𝜌(𝑟 ⃗)] = -
The LDA can only describe the ground state of electronic systems but not the excited states.

The wide band gap of semiconductors and insulator are underestimated in this approximation.

For certain strong correlation effects systems, LDA approximation does not properly describe the system properties. In particular, the transition metal compounds of insulating type Mott-Hubbard insulating or charge transfer are predicted metal.

The extension of density functional to spin-polarized systems is straightforward for exchange, where the exact spin-scaling is known, but for correlation further approximations must be employed. A spin polarized system in DFT employs two spin-densities, 𝜌 𝛼 (𝑟 ⃗) and 𝜌 𝛽 (𝑟 ⃗) with 𝜌(𝑟 ⃗) = 𝜌 𝛼 (𝑟 ⃗) + 𝜌 𝛽 (𝑟 ⃗), and the form of the local-spin-density approximation (LSDA) is

𝐸 𝑥𝑐 𝐿𝑆𝐷𝐴 [𝜌 𝛼 (𝑟 ⃗), 𝜌 𝛽 (𝑟 ⃗)] = ∫ 𝜌(𝑟 ⃗)𝜀 𝑥𝑐 [𝜌 𝛼 (𝑟 ⃗), 𝜌 𝛽 (𝑟 ⃗)] 𝑑𝑟 ⃗ EQN II.24

Generalized gradient approximations (GGA)

The Generalized gradient approximations bring an improvement compared to the LDA. In the local approximation, the exchange and correlation potential depends only on the density, whereas in the GGA approximation, the potential is expressed as a function of local electron density and its gradient. In many cases, the GGA approximation provides better results than LDA for total energy, cohesive energies, the volumes to balance and incompressibility modules. However the systems with strong correlations are poorly described.

Hubbard-corrected energy functionals (LDA+U, GGA+U)

The basic idea behind DFT+U is to treat the strong on-site Coulomb interaction of localized electrons, which is not correctly described by LDA or GGA, with an additional Hubbard-like term. The on-site Coulomb interactions are particularly strong for localized d and f electrons, but can be also important for p localized orbitals. The strength of the on-site interactions is usually described by parameters U (on site Coulomb) and J (on site exchange). Hubbard correction is added to the energy functional in order to overcome the imprecision of the strong correlations systems calculation.

𝐸 𝐷𝐹𝑇+𝑈 = 𝐸 𝐷𝐹𝑇 + ∑ 𝑈-𝐽 2 (𝜌 𝑎 - 𝑎 𝜌 𝑎 2 ) EQN II.26
where 𝜌 𝑎 is the atomic orbital occupation matrix.

valence) electrons of an atom and its nucleus with a pseudopotential, so that the Schrödinger equation contains a modified effective potential term instead of the Coulombic potential term for core electrons normally found in the Schrödinger equation.

Some pseudopotentials probably employed in our calculation are introduced as follows:

Norm-conserving pseudopotentials (NCPP)

The necessary characteristics for the construction of a pseudopotential of Norm-conserving pseudopotentials were proposed by Hamann et al. 1979 [54]. It should satisfy four properties:

-Real and Pseudo states have the same eigenvalues (for a given configuration);

-Real and Pseudo wavefunctions agree beyond a cut-off radius;

-The integrals from 0 to r of the real and pseudo charge densities agree for r>rc (Norm-Conserving condition)

4𝜋 ∫ |𝜑 𝑟𝑒𝑎𝑙 (𝑟)| 2 𝑟 2 𝑑𝑟 𝑅 0 = 4𝜋 ∫ |𝜑 𝑝𝑠 (𝑟)| 2 𝑟 2 𝑑𝑟 𝑅 0
EQN II.27

-The logarithmic derivatives and their first energy derivative of real and pseudo wavefunctions match at the cut-off radius.

Ultrasoft pseudopotentials (USPP)

Many modern pseudopotential calculations use a generalisation of the Kleinman-Bylander form known as "ultrasoft" pseudopotentials, which were developed by Vanderbilt in the early 1990s [55]. As the name suggests, ultrasoft pseudopotentials attain much smoother (softer) pseudowavefunctions so use considerably fewer plane-waves for calculations of the same accuracy.

Projector augmented wave method (PAW)

Valence wavefunctions tend to have rapid oscillations near ion cores due to the requirement that they are orthogonal to core states; this situation is problematic because it requires many Fourier components (or in the case of grid-based methods, a very fine mesh) to describe the wavefunctions accurately. The PAW approach addresses this issue by transforming these rapidly oscillating wavefunctions into smooth wavefunctions which are more computationally convenient, and provides a way to calculate all-electron properties from these smooth wavefunctions. [56] The wave function is rewritten as follows:

|𝜓⟩ =|𝜓 𝑝𝑠 ⟩ -∑

II.3.4 Computational application

The DFT calculation is widely used as an efficient and economical way to get crystal parameters, electronic structures, total energy and magnetic properties etc., summarized as ground state

The wave functions used in the VASP are developed on a plane wave basis adapted to the periodic calculation and have the advantage of being easily implemented with calculations using USPP of Vanderbilt and PAW. Blöchl and Kresse et al. [58] showed that the PAW method is especially good for the transition metal oxides, lanthanides, actinides and magnetic systems.

So we used the PAW method for all of our work.

The wave functions which developed in reciprocal space are defined for an infinite number of points k in the Brillouin zone, and each point contributes to the electronic potential. In order to numerically evaluate the integrals on the occupied states of each point, the calculation is performed with a grid of points k finite size. To automatically generate this grid points k in the VASP, the method of Monkhorst and Pack [59] is used. The integration of occupied states may be achieved by the method of the tetrahedra (Jepsen et al. [60]), with the corrections of Blöchl et al. [61]. The VASP code uses conjugate gradient type algorithms to relax the structures. In practice, to relax an atomic structure, we minimizes Hellmann-Feynman forces until the residual force on each atom fall below 0.08 eV/Å.

CHAPTER III. Ab initio study of La 10-

x Sr x (Si,Ge) 6 O 27-0.5x apatite for SOFC electrolyte with internal reforming reactions and electrochemical reactions in the SOFC. It is the most widely used method to investigate the performance of fuel cell system, as well as the materials'

properties. As for the electrolyte, molecular dynamics techniques are employed to explore the diffusion of oxide ions, then to approximate the ionic conductivity of the electrolyte materials.

C.W. Huang et al [4] reported the simulation work on ionic conduction process of oxygen in Ce1-xMxO2-x/2. The ionic conductivity was evaluated from the self-diffusivity of oxygen ions, described by the Nernst-Einstein (N-E) relation. The self-diffusivity can be related with meansquare displacement (MSD) which can be acquired by the molecular dynamics simulation. The simulation illustrates quite few electronic features which can be completed by ab initio calculation.

Ab initio calculation of the SOFC electrolyte is rarely reported in literatures. Recently Sha Xue et al [5] investigated the atomic and electronic structures of the battery electrolyte. It shows this calculation can be well applied in the investigation of fundamental properties of the materials.

III.2 La 10-x Sr x (Si,Ge) 6 O 27-0.5x apatite study Since rare earth silicates with a general formula of RE10-xSi6O27-1.5x were used as an electrolyte in a SOFC by Nakayama et al [6] for the first time, they have attracted considerable attention due to their higher oxide ionic conductivity and lower activation energy. Among these, La10Si6O27 series is more promising due to the higher ionic conductivity compared to some other rare earth apatite. [7] Their properties can be modified by various doping methods.

Currently, the two major applied doping methods are element substitution at the La position and Si position. Mg, Sr, Ba as alkaline earth metal are widely used to substitute the La position, and Sr is the most common element due to its similar chemical properties with La. As an example of Sr substitution is the Sr-doped apatite-type lanthanum silicates (La9Sr1Si6O26.5) synthesized by Bonhomme et al. [8] A large number of works are also focused on the Si position doping. S. Nakayama et al investigated the Ge substitution at Si position and A. Orera et al. [9,10] further expanded the substitution element from Ge to other different elements doping. Table III.1 summaries the ionic conductivities and activation energy obtained from the previous literature. As can be seen, the ionic conductivities show a significant decrease with increasing the ratio of Sr-doping while the amount of La and Sr remains unchanged. Besides, it is also seen that Ge substitution apatite electrolyte has a lower ionic conductivity compared to the Si substitution.

Table III Calculation methods based on the first principle was also widely used to analyze the material microstructure, properties and performances. Meanwhile, the oxygen diffusion in different types of electrolyte including LSO electrolyte has been summarized by A. Chroneos et al. [13],

and the ionic transportation mechanism has been widely studied using atomistic simulation.

However, only few studies focusing on the apatite electrolyte for SOFC using DFT are available.

In the current work, based on DFT, systematic computational results of Sr, Ge -doped LSO apatite for SOFC electrolyte are presented and doping position effect on the ionic conductivity and activation energy are also studied. Calculation results are also compared to previous experimental results.

III.2.1 Calculation details

Ultrasoft pseudo potential [14] method based on density functional theory (DFT) in the generalized gradient approximation (GGA) proposed by Perdew et al was used to perform the (La10Sr0)Ge6 [10] (La10Sr0)Si6 [11, 12] (La9Sr1)Si6 [8] (La8Sr2)Si6 [11, 12] Ionic conductivity (S•cm -1 , 700°C) 5~8×10 -3 10.8~20×10 -2 2.4~2.6×10 -3 2.9×10 -7 Activation energy(eV) -0.47 0.78

calculations [15]. The Vienna ab initio simulation package (VASP) [16][17][18] was used to explore the influence of doping positions by applying a plane-wave basis within the projector augmented-wave method. The DFT is an efficient method to predict the ground state properties and thus to analyze the properties of materials. As a first step, a single apatite cell was built to obtain the DOS (Density of States) calculation results through the structure optimization and static calculation. The Brillouin zone scale was set to 3*3*3 gamma centered k-point mesh in the Monkhorst-Pack scheme. Nevertheless, the k-point was changed to 7*7*7 in the DOS calculation. An energy cut-off of 380 eV was used in all of our calculations.

The activation energy of each group is calculated with a model of oxygen migration along the ionic channel. For the considered doping effect, the migration channel can be supposed directly along c-axis. The energy barrier of oxygen migration could be also approximated as the activation energy. Table III.3 lists the results of the calculated and experimental lattice parameters [10,11]. It is noted that the results are in good agreement with the experimental ones, and more accurate than previous calculations. As the amount of Sr dopant increases, both experimental and calculated cell size increases along the c-axis. However, in a-and b-axis directions, the variation is quite low. This phenomenon has some effects on the oxygen migration which was discussed by J.R.

Tolchard et al. Our work gives some deep effects on the density of states and total energy which directly impact the ionic conductivity. Different ratios of Sr-doping in La position are calculated in this part using the GGA method.

Indeed, it has been reported that the ionic conductivity significantly decreases by partly substituting La by Sr specially for a ratio of La(Sr):Si=10:6. The total energy of each atom is calculated and the values are as follows, La -0.53686 eV; Si -0.16432 eV; O -0.15510 eV; Sr -0.06825 eV; Ge -0.16010 eV.

It is noted that the Fermi level changes correspondingly with ionic conductivity. According to the the doping ratio increase, the Fermi level decreases gradually and thus the ionic conductivity shows a significant decrease. A lower Fermi level leads to a wider band gap. Hence, it is really difficult for an electron to make a transition to the conduction band, which means that the material have higher electron insulation. Furthermore, a wider band gap presents a lower electron delocalization which results in fewer obstacles to the oxygen ion migration. The formation energy can be also observed in The DOS figure shows sharp and multi peaks which mean electron delocalization is weak, therefore the oxygen ions can easily pass through the LSO which is suitable as an oxygen ion conductor. The PDOS also shows that different atoms DOS occupies different energy levels with little overlap. The band between atoms is ionic, thus the LSO can be considered as an ionic crystal which is a basic requirement for an electrolyte in a SOFC. Furthermore, the oxygen states below Fermi level occupy higher energy level which means that oxygen electron transition to the conduction band is easier. Then, oxygen atoms can be ionized more easily than other atoms, hence this material is very appropriate to transfer the oxygen ions as an electrolyte.

In order to compare the distances between the bottom level conduction band and Fermi level, Few band overlaps can be observed, which suggests a poor bonding between atoms. The oxygen ions can easily pass through the atoms interspace with lower electron blocking. Indeed, there is no band crossing the zero energy in AH, KG, GM zone around the Fermi level, which means there is a low electronic conductivity of the crystal along these directions [20,21]. These results confirm that apatite materials are very suitable as an electrolyte in a SOFC.

III.4 Ge-doped LSO study

In order to compare the influence of different doped positions, Ge substitution at Si position is used as a common dopant element at Si position due to their similar electron orbits. In this chapter, some preliminary methods for synthesizing pure phase apatite type La10Si6O27 are explored. They include co-precipitation, melting salt, homogeneous deposition precipitation (HDP). Particularly, the first attempt of co-precipitation gave some interesting results despite some homogeneity issues.

IV.1 Co-precipitation method

The present work explores a modified co-precipitation method based on novel chemical reaction to synthesize apatite-type La10Si6O27 (LSO) fine powder. With which the apatite phase can be achieved with a relatively facile procedure at low temperature. [1] have reported that the formation temperature of La2SiO5 is higher than that of oxy-apatite phase, and the presence of La2O3 at lower temperature leads to the formation of La2SiO5 phase at higher temperature, and the formation temperature is between 1000℃ and 1100℃. This result corroborates our inference. This undesirable byproduct would affect the performance of ionic conductivity. Further work would be necessary to solve this issue. While the calcination temperature is about below 300℃, water gets out from the precipitate.

IV.1.1 Sample preparation

And then, La(OH)3 starts decomposition by seeing the significant peak of the DSC curve.

Concurrently, LSO formation process occurs with the temperature continuous increase. The total mass loss is 88.4% during La(OH)3 decomposition to the final, which corresponds the change of 10La(OH)3+6SiO2 (expected precipitates) to 5La2O3+6SiO2. We have noted some endothermic peaks exist in the DSC curve above 900℃, which is due to the entropy change of apatite LSO grain growth process, instead of the formation process reported in some previous work. show the morphologies of the samples treated with 700℃ to 1000℃. The crystallization process can be discovered with the calcination temperature increasing. Small grains have formed starting from 700℃ and they become bigger and more distinct by higher temperature treatment.

Meanwhile, more grain shapes change to hexagonal from the treatment of 900℃, which infers that the grains belong to apatite-type LSO structure. The crystal grains significantly increase up from the nanometer scale (before sintering) to 1-3 µm and they get closely connected to each other, as well as in large scale shown in figure

IV.9(a). The sintering treatment obviously densifies the apatite materials which is beneficial in the prospect of SOFC electrolytes applications. The grains have the appearance of hexagons and one sees some of the boundary angles equaling 120 , which is congruent with the crystal structure of our previous discusses. As far as the calcination temperature is concerned, it seems that it does not affect significantly the grain size. Globally we can note that the sintered apatite materials, as characterized in this section, will be suitable candidates as electrolytes in SOFC.

IV.1.4 Electrical characterization

Before the electrical measurement, we have deposited a Pt collector by magnetron sputtering on each face of the sample to obtain a good current collector. The thickness of Pt coating is around 200 nm to avoid the Ostwald Ripening mechanism with the temperature. The experimental points were fitted by a least-squares procedure using an equivalent electrical circuit in order to extract the electrical features of the ceramic. The circuit consisted in one parallel (R//CPE) contributions to account for high and medium frequency processes (where R is a pure resistance and CPE is a Constant Phase Element ZCPE = 1/Y0(jω)p with Y0 the module of the CPE element and p a parameter taking into account the depressing of the semi-circle. The capacitive effect deduced from the R and CPE values is given by:

                   p 1 p p 1 CPE R C EQN. IV.3
The figure IV.10 shows a nyquist diagram of the sample registered at 500 o C, for our samples it's very difficult to distinguish the bulk and the grain boundary contributions. The resistance of the pellet increase with the calcination treatment, this result is very surprising because the increasing of the calcination temperature increase the density and the grain size of the pellets. This comportment is certainly induced by the presence of the impurity phase with the temperature.

The electrical conductivity of samples is presented in figure IV.11 in an Arrhenius plot. The ionic conductivity is relatively low between 0.06 to 7.73 mS.cm -1 at 675°C. The linear evolution of ionic conductivity indicate that the conductivity is thermally activate and the activation energy is respectively 1.04, 1.28, 0.98 eV for sample annealed at 800, 900 and 1000 o C. The value is relatively high in comparison with the literature data (0.5 to 0.9 eV without impurity phase) [2]. The capacity of the sample calcined at low temperature is close to 10 -10 /10 -9 F.cm -1 .

According to the work of Tao et al [3], the ionic conductivity is dominated by the grain In summary, the first attempt of a novel method, based on direct chemical reaction, is realized to synthesize apatite type lanthanum silicates as electrolyte in IT-SOFC. Suitable stoichiometric precursors are generated at the same time, and this is beneficial to the formation reaction of LSO. The apatite phase composition is obtained from quite moderate temperature of 700℃ for 6h. After the densification process of 1500℃ for 2h, the samples exhibit acceptable performance of ionic conductivity of 7.73 mS.cm -1 at 675°C. This novel method is worth to development due to it is facile to implement and low cost. The replacement of the chemicals in the reaction can satisfy some other synthesis requirements. It is noted that the impurity in the composition affects the conductivity performance, and it will be modified in future work by introducing different dispersants.

IV.2 Sr, Mn-doping LSO with co-precipitation method design IV.2.1 Sr-doping LSO In order to dope Sr into LSO composition, a new chemical reaction for co-precipitation is developed. The difficulty for Sr-doping is that Sr(OH)2 is highly soluble in water, thus we have to introduce new reactant oxalic acid H2C2O4. The solubility product constant Ks of SrC2O4 is as low as 5×10 -8 , meanwhile, the solubility of La2(C2O4)3 is 2.08mg/L, equals 3.8×10 -6 mol/L. The main reactions is as follows: Thus the obtained LSO has much impurity. The pH value is the key factor to affect the precipitation. The ammonium oxalate as an alternative can be employed to replace the oxalic acid-ammonia system. IV.2.2 Mn-doping LSO Manganese (Mn) doping in LSO composition can effectively improve its conductivity performance. [4] Mn ion has various valance of +2, +3, +4, +6, and +7 under certain condition. If the valence of Mn ion is +4, it will occupy Si site and the trivalent Mn prefers La site. The XRD pattern is used to identify the composition. Figure IV.17 shows the diffraction pattern of the product by molten NH4NO3 method. The resulting mixture is amorphous. At this stage, it has not been possible to state the reaction was taken place or not and further work would have been necessary. However, during the calcination, an intense emission of smoke was observed which led us to discard this method for environmental reason. indicates that the main part of the composition is the lanthanum oxychloride (LaOCl). This material has no ability to transfer oxygen ions. In addition, the properties determine the difficulty to remove it from the product: the low solubility in water or alcohol; its thermally stable properties at temperatures as high as 1000 °C [9]. By comparing different groups, higher abundance of LaOCl exists in the groups treated with higher temperature. It can be seen the apatite phase almost disappears at 1000℃ treatment, while the abundance of LSO phase has significant increase at 800℃. As for the 700℃ group, it is inferred the mixture is not completely melted by the experimental observation. Thus the formation of LSO is impeded.

To achieve pure phase LSO product, two ways are taken to solve the LaOCl problem: washing with citric acid solution and reduce the heating temperature. in the product and it is in higher abundance than LSO composition. Therefore, when using the sulfate path, the LSO phase can be found in the product but, at the same time, another impurity is also introduced. The solution gradually becomes alkaline with the CO2 being evolved outside the solution and ammonia being created. Therefore, lanthanum hydroxide can be deposited slowly and homogeneously on the silica gel particles and react with them. However, the formation reaction of LSO has not taken place in the process. ). This proves that the La2O3 got agglomerated during the deposition process. This agglomeration process is faster than the reaction with silica gel, which leads to an incomplete reaction to form apatite phase.

The hydrolysis process is still too fast in comparison with the La2O3-SiO2 reaction. Some dispersant or TEOS could be introduced in deposition process to prevent the agglomeration but this assumed relatively important further investigations. In this chapter, we have reported several preliminary attempts to prepare LSO with alternative chemical methods. The co-precipitation method proved to be the most effective since the apatite phase composition could be successfully obtained from quite moderate temperature of 700℃ for 6h. However after the sintering treatment of 1500℃ for 2h, the samples exhibit mediocre performance in terms of ionic conductivity (7.73 mS.cm -1 at 675°C). The other routes explored would need substantial improvements to become effective.

For these reasons, we finally selected the sol-gel method which gave high purity apatite samples with pretty good electric performances as developed in chapter V.

Chapter V Synthesis of Pure La 10-x Sr x Si 6 O 27-0.5x Apatites Using an Optimized Sol-Gel Process Lanthanum nitrate that had been previously studied by TGA in order to determine its hydration degree "x = 6" (shown in Figure V. 2), was dissolved in deionized water (solution A).

Alternatively, La2O3 was calcined at 800℃ and dissolved in dilute HNO3 to obtain a clear solution (solution B). Solutions A and B were used as La sources. Ethylene glycol (EG) and citric acid (CA) were added to the above solution yielding solution A1 or B1 in which the ratio between the (EG+CA) mixture (in 1:1 molar proportion) and the (La 3+ + Sr 2+ ) moles equaled one. TEOS and Sr(NO3)2 were mixed separately with deionized water leading to two mixtures; in step 1, this two mixtures were added into the solution A1 or B1 under mixing. After adjusting the pH with nitric acid or ammonia solution, the resulting solution was stirred for 3-4 h to form the sol (step 2), then the latter was dried in an oven at 80℃ yielding a dry gel (step 3). The dry gels were pressed under 200 MPa for 40s to form disks of 1.5cm diameter. Once the disks were obtained, they were calcined in air at 800℃, 900℃ and All the dry gels are amorphous. Indeed atoms of La, Si and Sr (when present) lie in quite close vicinity of each other in the gel which is conducive to the complete reaction in the sintering step and yields the apatite phase. The XRD patterns after calcination at 800℃ and sintering at 1500℃ show that the 2-Sr dope apatite group exhibits the highest crystallinity: as the doping ratio increases, the degree of crystallinity becomes higher with larger grains being formed. The undoped group shows major peaks of La2SiO5 which comes from a reaction between SiO2 and La2O3 in zones. The latter is locally in excess with a La2O3/SiO2 ratio higher than 5/6 which corresponds La10Si6O27 product. Based on the atoms balance, it can be inferred that some amorphous SiO2 is present in the undoped apatite. The addition of strontium atoms that compete with lanthanum in the reaction with silicon tends to alleviate this effect. Thus, the Sr-doping has a certain positive influence for obtaining pure apatite in our sol-gel process. There is still a small amount of La2SiO5 detected in "1-Sr doped" group which almost disappears in "2-Sr doped" group that exhibits narrow and sharp diffraction peaks. Neither Sr oxide nor silicate can be detected in the two groups of Sr doped apatite which indicated that Sr has been fully incorporated into the apatite structure. This positive effect of the Sr doping in the sol gel process is also probably due to the strong alkaline character of this metal that readily reacts with the silicate ion. Nevertheless, some very tiny secondary peaks persist even in the "2-Sr doped" group. In order to increase the purity, we decided to assess the effect of pH.

V.1.3 Study of the influence of pH

In this section, we prepared three reaction media having different pH:

-Solution A1 as such was taken as near-neutral medium (pH = 5. the most important process is the dissociation of citric acid into citrate anions which depends on the pH of the solution and plays a key role in chelation of the metals. The metal ions can be chelated by the citrate ions and other hydrophilic anions to form chains. In strongly acidic solutions, there is not enough citrate anions which results in a defective gelation process. At the same time, some condensation, hydrolysis and alcoholysis reactions of TEOS occurs via the hydroxyl groups of TEOS, H2O and EG respectively (step 2). The condensation reactions lead to the generation of siloxane bonds (Si-O-Si) (equation 3 of step 2). This formation of silicon chains is a kind of alcoholysis, and the hydroxyl group original from silanol, the product of previous hydrolysis reaction. This leads to form silicon-oxygen chains. There are unreacted hydroxyl group still at the ends of the chains, which keep the chains soluble in water. Thus, the solution contains both chelating metal ions chains and hydrophilic silicon chains that are intertwined due to Van der Waals attraction (dotted line in step 3). Such solution that contains randomly distributed ionic reagents favors an efficient gelation process, which prevents the formation of unwanted single oxide phases in the next calcination treatment.

Because the first solution is too acidic, the citric acid ionization is inhibited leading the chelation inoperative. Conversely, in the alkaline solution, the metal ions get preferentially associated with hydroxide ions, resulting in insoluble alkali hydroxide being precipitated without any gelation process leading to turbid solution: after 1h standing, the liquid appears stratified and the deposition can be found in bottom. The near-neutral group possess clear, stable and viscous solution. The acidic group exhibits not so clear, but stable solution. (alkaline pH) and optimized (near neutral pH) gelation conditions respectively. When using the "non optimized" gelation conditions, the agglomeration and crystallization of the precursors seem to start before the calcinations step: the micro-sized particles having regular shapes are probably separated La2O3 or SiO2 phases. However, with the optimized gelation conditions, the average size of the particles is in dozens nm: there is apparently neither partial crystallization nor agglomeration. The presence of such nano-particles is favorable for the formation of the apatite structure. In this section, we will focus on the undoped LSO obtained through "near-neutral solution" as it appears to be the most difficult apatite to synthesize. The investigated parameters were the calcination temperature and duration with the objective to identify the most suitable conditions.

Three calcination temperatures (800℃, 900℃ and 1000℃) and times (2h, 4h and 8h) have been explored. Firstly we noted that the formation of apatite is not satisfactory below 800℃. The The influence of the calcination duration is shown in the diagram (b): one does not see any significant effect of this parameter. We can conclude that, while the formation of the amorphous apatite molecule is a rather fast process which can be completed with an 800°C-2h calcination treatment, the crystallization process is a substantially activated process.

Therefore, besides a nearly neutral pH, the most favorable condition is a minimum calcination, temperature of 800℃ with a duration 2 hours being sufficient.

V. It can be seen that all powders obtained have the apatite structure even with a calcination temperature as low as 800℃. All the high-intensity reflections correspond accurately to the apatite phase La10Si6O27 (pdf ref.

code: 00-053-0291) composition and no secondary phases are detected, including Sr doping cases (groups 2 and 3). This indicates that pure apatite can be formed at 800℃ even for 2h. In addition the XRD patterns of group 2 and 3 do not show any peak pertaining to any Sr compound. Thus, it can be said that the Sr atoms have been well incorporated inside the apatite crystal structure. The reason of this very minor change in crystal geometry lies in the close ionic radii of Sr 2+

(1.32Å) and La 3+ (1.17Å).

The calcination temperatures slightly affect the lattice parameters as it can be seen in Figure V. 9 (b) which shows the diffraction patterns under different calcination temperatures at constant doping ratio. However, as expected, the diffraction intensity grows with the calcination temperature since the degree of crystallization increases. A close examination of these peaks shows average FWHM (width at half maximum) data ranging between 0.1181° and 0.2362°, which corresponds to rather small grains.

The microstructure of the LSO compounds impacts also on the ionic conductivity in SOFC applications. For example the degree of compactness of the bulk which reflects the crystallization degree, impacts the conductivity since the conductivity of the boundary zones is different from that of the crystal bulk. It also affects the isolation conditions of the gas fluxes, which is of prime importance within SOFC applications. there is a quite high gap with the theoretical value of 5.4 g•cm -3 (evaluated through simulation methods). It can be inferred that some micro-cracks exist in the synthesized compounds despite their high purity and crystallinity. Since it is not unfavorable for the flow isolation in a real SOFC, a further densification process based on a sintering at high temperature has to be applied. and they get closely connected to each other. The sintering treatment obviously densifies the apatite materials which is beneficial in the prospect of SOFC electrolytes applications. The grains have the appearance of hexagons and one sees some of the boundary angles equaling 120 , which is congruent with the crystal structure previously discusses. Specifically, a typical crystal grain exhibiting a regular hexagon shape is visible in the image of the 800-3 sample. As far as the calcination temperature is concerned, it seems that it does not affect significantly the grain size. Globally we can note that the sintered apatite materials, as characterized in this section, will be suitable candidates as electrolytes in SOFC. All the groups exhibit considerable ionic conductivities at intermediate temperature which make them fair candidates as electrolytes in IT-SOFC. The progressive change in conductivity with the temperature means that the synthesized apatites are suitable to work in a wide temperature range. From this figure, it can be found that Sr dopes affect the ionic conductivity more than the calcination temperature: while a Sr/La doping ratio of 1/9 (Group 2) is beneficial, the incorporation of more Sr (Sr/La = 2/8; Group 3) tends to decrease the conductivity. This non-trivial result is consistent with the findings of: (i) Zhang [6] who reported an improvement of the ionic conductivity from 4.3×10 -3 to 1.68×10 -2 S•cm -1 at 500℃ when passing from the La10Si6O27 to the La9SrSi6O26.5 apatite and (ii) A. Orera et al [7] who showed that the ionic conductivity decreases from 1×10 -2 to 2.6×10 -7 S•cm -1 at 800℃ when passing from the La9SrSi6O26.5 to the La8Sr2Si6O26 apatite. As for the calcination step, a high calcination temperature helps to improve the ionic conductivity, nevertheless this influence is not so marked. The best conductivity at intermediate temperature is obtained for the La9SrSi6O26.5 apatite formula with the calcination temperature of 1000℃, the corresponding conductivity (38.3 mS•cm -1 at 600℃) being significantly higher than the general conductivity levels reported in previous works using traditional synthesis methods [6,8]. This "medium Sr doped" LSO is therefore suitable for low temperature SOFC applications. Note worthily the undoped La10Si6O27 apatite have also a very high conductivity (45 mS•cm -1 ) at 800℃ which confirms the favorable effect of this sol gel synthesis method. The Sr doping ratios in LSO need to be investigated more deeply in the 0 and 2/8 range to accurately determine the best performance Sr/La ratio.

V.3 Summary

Lanthanum silicate oxides with and without Sr-doping have been synthesized using a facile, water-based sol-gel method for potential applications as oxygen ion conducting electrolytes in IT-SOFCs. The effects of various parameters, namely the pH value, the doping ratio, the calcination temperature and time have been investigated. We found that the most effective process to synthesize pure apatite consists in (i) a near-neutral medium for the gelation step and

(ii) a heat treatment at 800℃ for 2h for the calcination step. The Sr-doping proved helpful to complete the gelation and crystallization steps. The synthesized apatite samples have been characterized by XRD and its degree of crystallization has been studied in function of the calcinations temperature in the perspective of a real SOFC application.

A subsequent sintering heat treatment has been used to densify the samples, resulting in a highly crystallized variety of apatite that well fits the requirements of an SOFC application. The XRD, SEM and EDS results confirm that the compounds obtained are pure, well crystallized apatites and that Sr is well incorporated in the structure. Both the effects of the calcination temperature and Sr doping ratios have been investigated. The proposed synthesis method enables alleviating calcination and sintering conditions and provides fairly good SOFC electrolyte candidates even after calcination at 800℃ and sintering at 1500℃ for 2h. While a higher calcination temperature slightly improves the conduction performances, a medium Sr doping (Sr/La = 1/9) procures a substantial improvement. Indeed a remarkable, intermediate temperature conductivity of 38.3 mS•cm -1 is obtained at 600℃ with the La9SrSi6O26.5 formula, that represents therefore a suitable IT-SOFCs. The effects of various parameters, namely the pH value, the doping ratio, the calcination temperature and time have been investigated. We found that the most effective process to synthesize pure apatite consists in (i) a near-neutral medium for the gelation step and

(ii) a heat treatment at 800℃ for 2h for the calcination step. The Sr-doping proved helpful to complete the gelation and crystallization steps. The synthesized apatite samples have been characterized by XRD and its degree of crystallization has been studied in function of the calcinations temperature.

A subsequent sintering heat treatment has been used to densify the samples, resulting in a highly crystallized variety of apatite that well fits the requirements of an SOFC application. The XRD, SEM and EDS results confirm that the compounds obtained are pure, well crystallized apatites and that Sr is well incorporated in the structure. The proposed synthesis method enables alleviating calcination and sintering conditions and provides fairly good SOFC electrolyte candidates even after calcination at 800℃ and sintering at 1500℃ for 2h. While a higher calcination temperature slightly improves the conduction performances, a medium Sr doping (Sr/La = 1/9) procures a substantial improvement. Indeed a remarkable, intermediate temperature conductivity of 38.3 mS•cm -1 is obtained at 600℃ with the La9SrSi6O26.5 formula, that represents therefore a suitable candidate for low temperature SOFC applications.

Meanwhile, the non-doped La10Si6O27 exhibited an ionic conductivity of 45 mS•cm -1 at 800℃, which confirms the suitability of the optimized sol gel process for the synthesizing of LSO with and without Sr doping.

With the experimental results, Sr dopes affect the ionic conductivity more than the calcination temperature: while a Sr/La doping ratio of 1/9 (Group 2) is beneficial, the incorporation of more Sr (Sr/La = 2/8; Group 3) tends to decrease the conductivity. This non-trivial result is consistent with the findings of: (i) Zhang who reported an improvement of the ionic conductivity from 4.3×10 -3 to 1.68×10 -2 S•cm -1 at 500℃ when passing from the La10Si6O27 to the La9SrSi6O26.5

Figure I. 1 .

 1 Figure I. 1. William Grove's 1839 gas voltaic battery diagram, pioneer of modern fuel cell ................. Figure I. 2. Schematic diagram of the operation of a fuel cell (This work has been released into the public domain by its author, Sakurambo.) ............................................................................................. Figure I. 3. the input and output of the fuel cell .................................................................................... Figure I. 4. The energy and power properties of the fuel cell compared to other energy conversion devices (A. Comparison of the specific power between the present SOFC ~ 2W / cm 2 at 650℃ and multiple energy conversion devices as a function of the power density. B. Ragone plot, specific energy versus specific power, for various energy devices in relation to the present SOFC) [41]. ................... Figure I. 5. Changes in oxygen reduction activity plotted as a function of the oxygen binding energy [42] ........................................................................................................................................................ Figure I. 6. The types of oxygen adsorption process in the cathode ..................................................... Figure I. 7. The logarithm of the exchange current density (log i0) against the force of the metalhydrogen bond formed during the reaction itself. ................................................................................. Figure I. 8. Schematic of diffusion mechanisms in solid state structures: (a) vacancy diffusion; (b) Interstitial diffusion; (c) ions exchange-direct and circle. .................................................................... Figure I. 9. Schematic representation of the diffusion of an atom from its original position into another lattice site. Activation energy Em has to be supplied to the atom so that it could break inter-atomic bonds and to move into the new position. ............................................................................................. Figure I. 10. Arrhenius plot of lnD vs. 1/T with a slop of -Qd/R and an intercept of lnD0 ................... Figure I. 11. Cross-sectional views SEM micrographs of (a) a single cell, (b) the porous Ni-GDC (gadolinia-doped ceria) anode, (c) the dense GDC electrolyte, and (d) the porous SSC (Sm0.5Sr0.5CoO3) -GDC cathode. ...................................................................................................... Figure I. 12. A diagram of the reactions in the cathode of SOFC ......................................................... Figure I. 13. Schematic of the lattice structure of a perovskite-ABO3 ................................................ Figure I. 14. Variation of electrical conductivity (σ) of La1-xSrxMnO3-δ (x is 0 to 0.7) at different temperature (at pure oxygen PO2 = 1 bar). ............................................................................................. Figure I. 15. Schematic view of the crystal structures of: (a) Simple perovskite, (b) Double perovskite and (c) Ruddlesden-Popper K2NiF4 type phase. Sites for water insertion are shown: oxygen vacancies for the perovskites and interstitials for Ln2MO4+δ. ................................................................................ Figure I. 16. Transmission electron micrographs showing the anode (a) operated with hydrogen fuel (b) operated with syngas for 15min; (c) operated under same gas mixture for 2h (the ingredient of synthesis gas: CH4 23.64% ; CO 7.60% ; CO2 14.27% ; H2 49.48% ; H2O 5.00%) [64]. ..................... Figure I. 17. the three views of the pyrochlore structure A2B2O6O' (a) showing the relation between the structures of fluorite and pyrochlore in where an octant of the cell of the pyrochlore unit is represented by the large cube, (b) octahedral connectivity <BO6> units with A sites and O' anions as "extraframework ions," (c) the A sublattice as a network of corner-shared O'-centered tetrahedra, with B and O atoms omitted. A -purple, B -green, O -yellow and O' -orange ..................................................... Figure I. 18. Schematic diagram of the components of a planar cell to show the interconnect ............ Figure I. 19. Schematic showing selection of phases in Fe-Co-Ni based alloys as metallic interconnect materials [86] ......................................................................................................................................... Figure I. 20. Cubic fluorite structure of ceria ........................................................................................ Figure I. 21. Schematic of the δ-Bi2O3 polymorph crystal structures ................................................... Figure I. 22. Structures of pyrochlore -One eighth of the unit cell of the ordered pyrochlore structure showing specific positions of the cations and anions (B 4+ cation at the origin). [101].......................... Figure I. 23. Arrangement of B-O octahedra and tetrahedra in the ideal brownmillerite structure, A2B2O5 (A cations removed for clarity) ................................................................................................

Figure I. 24 .

 24 Figure I. 24. The apatite structure, A10(MO4)6X2±y, and alternative representation of the apatite structure: illustration of the "microporous" A4(MO4)6 framework: The cavities are where the remaining A6X2±y units would occupy. (original figure from ref [116]) ............................................... Figure I. 25. Schematic diagram of lanthanum-silicon apatite structure ............................................... Figure I. 26. Conductivities of selected electrolyte materials at intermediate temperature (LSO series lies at shaded part, original figure from ref [124]) ................................................................................ Figure I. 27. The interstitial oxygen site (brown sphere) at the periphery of the channels, and associated lattice relaxation (blue spheres = La, green spheres = Si) .................................................... Figure I. 28. 29 SiNMRspectra (left) and Raman spectra results (right) for (a) La8Sr2(SiO4)6O2, (b) La9Sr(SiO4)6O2.5, (c) deconvolution of the latter. [127, 128] ................................................................ Figure I. 29. O5 oxygen vacancy migration along the O5 oxide channel (a), and interstitial oxygen migration viewed perpendicular to the O5 channel, showing a non-linear (sinusoidal-like) pathway (b), suggested for La8Sr2(SiO4)6O2 and La9.33(SiO4)6O2 respectively........................................................... Figure I. 30. Proposed conduction pathway between adjacent oxide-ion channels via two "SN2"-type processes, with accompanying rotation of the silicate tetrahedra, obtained from computer simulation results of La9.33(SiO4)6O2. The incorporation of a periphery interstitial oxide-ion (yellow) (a) forces a silicate oxygen (orange) in between the two SiO4 units forming an Si2O9 unit (b), the top silicate unit rotates to form an Si2O9 unit with a neighboring silicate unit (c), and an oxygen on the top silicate unit (green) is released as an interstitial in a different channel (d). .............................................................. Figure I. 31. Comparison of the conductivities (500 °C) of oxygen stoichiometric samples with the same level of cation vacancies (a) and same level of oxygen excess -O2.5 (b) [116] ........................... Figure II. 1. A schematic diagram for showing dry pressing process, devices and the electrolyte obtained by this technique. .................................................................................................................... Figure II. 2. SEM micrographs of tape casting electrolyte using in SOFC and voltage-current, impedance spectrum characteristics of the cell operating at 800 °C. .................................................... Figure II. 3. (a) SEM micrographs of electrolyte layer on the left and porous Ni-YSZ cermet on the right. (b) Specific resistance at different temperatures in comparison with YSZ pellet. ....................... Figure II. 4. SEM micrographs of YSZ films grown by RMS (reactive magnetron sputtering) on (100) Si substrate at room temperature under 1 Pa: a) top view, b) cross-section. ......................................... Figure II. 5. Experimental setup of ultrasonic aerosol assisted chemical vapor deposition at atmospheric pressure and the morphology of as obtained electrolyte ................................................... Figure II. 6. Micrographs of fracture surface of the La10Si5.8Mg0.2O26.8 coating deposited by VLPPS (a) and APS (b). .......................................................................................................................................... Figure II. 7. A schematic diagram of sol-gel process and its application ways (https://str.llnl.gov/str/May05/Satcher.html) ......................................................................................... Figure II. 8. Flowchart of the process used in the preparation of doped and undoped lanthanum silicates. ................................................................................................................................................. Figure II. 9. Density and relative density of sintered samples at different temperatures [39] ............... Figure II. 10. Photography and X-ray diffraction mechanism of Bruker-AXS D8 FOCUS Advanced Bragg-Brentano X-ray Powder Diffractometer ..................................................................................... Figure II. 11. Stick pattern of high intensity diffraction for Lanthanum silicate (ref. 00-049-0443) .... Figure II. 12. JSM-7800F field emission scanning electron microscope .............................................. Figure II. 13. Diagram of the four-point method ................................................................................... Figure II. 14. Representation of an electric circuit impedance diagram. (a) Electrical circuit, (b)Complex impedance diagram corresponding to a Nyquist plot and (c) in a Bode plot. ................... Figure II. 15. Schematic of an impedance plot for an electroded polycrystalline sample with an analog equivalent electric circuit. ..................................................................................................................... Figure II. 16. Devices for measuring the conductivity (the inset is the structure of sample furnace) ... Figure II. 17. Schematic of DSC and TG technique .............................................................................. Figure II. 18. Schematic illustration of the simulation methods for different length and time scales ... Figure II. 19. Flowchart of a self-consistent calculation in a method based on the DFT calculation ...

  Figure I. 24. The apatite structure, A10(MO4)6X2±y, and alternative representation of the apatite structure: illustration of the "microporous" A4(MO4)6 framework: The cavities are where the remaining A6X2±y units would occupy. (original figure from ref [116]) ............................................... Figure I. 25. Schematic diagram of lanthanum-silicon apatite structure ............................................... Figure I. 26. Conductivities of selected electrolyte materials at intermediate temperature (LSO series lies at shaded part, original figure from ref [124]) ................................................................................ Figure I. 27. The interstitial oxygen site (brown sphere) at the periphery of the channels, and associated lattice relaxation (blue spheres = La, green spheres = Si) .................................................... Figure I. 28. 29 SiNMRspectra (left) and Raman spectra results (right) for (a) La8Sr2(SiO4)6O2, (b) La9Sr(SiO4)6O2.5, (c) deconvolution of the latter. [127, 128] ................................................................ Figure I. 29. O5 oxygen vacancy migration along the O5 oxide channel (a), and interstitial oxygen migration viewed perpendicular to the O5 channel, showing a non-linear (sinusoidal-like) pathway (b), suggested for La8Sr2(SiO4)6O2 and La9.33(SiO4)6O2 respectively........................................................... Figure I. 30. Proposed conduction pathway between adjacent oxide-ion channels via two "SN2"-type processes, with accompanying rotation of the silicate tetrahedra, obtained from computer simulation results of La9.33(SiO4)6O2. The incorporation of a periphery interstitial oxide-ion (yellow) (a) forces a silicate oxygen (orange) in between the two SiO4 units forming an Si2O9 unit (b), the top silicate unit rotates to form an Si2O9 unit with a neighboring silicate unit (c), and an oxygen on the top silicate unit (green) is released as an interstitial in a different channel (d). .............................................................. Figure I. 31. Comparison of the conductivities (500 °C) of oxygen stoichiometric samples with the same level of cation vacancies (a) and same level of oxygen excess -O2.5 (b) [116] ........................... Figure II. 1. A schematic diagram for showing dry pressing process, devices and the electrolyte obtained by this technique. .................................................................................................................... Figure II. 2. SEM micrographs of tape casting electrolyte using in SOFC and voltage-current, impedance spectrum characteristics of the cell operating at 800 °C. .................................................... Figure II. 3. (a) SEM micrographs of electrolyte layer on the left and porous Ni-YSZ cermet on the right. (b) Specific resistance at different temperatures in comparison with YSZ pellet. ....................... Figure II. 4. SEM micrographs of YSZ films grown by RMS (reactive magnetron sputtering) on (100) Si substrate at room temperature under 1 Pa: a) top view, b) cross-section. ......................................... Figure II. 5. Experimental setup of ultrasonic aerosol assisted chemical vapor deposition at atmospheric pressure and the morphology of as obtained electrolyte ................................................... Figure II. 6. Micrographs of fracture surface of the La10Si5.8Mg0.2O26.8 coating deposited by VLPPS (a) and APS (b). .......................................................................................................................................... Figure II. 7. A schematic diagram of sol-gel process and its application ways (https://str.llnl.gov/str/May05/Satcher.html) ......................................................................................... Figure II. 8. Flowchart of the process used in the preparation of doped and undoped lanthanum silicates. ................................................................................................................................................. Figure II. 9. Density and relative density of sintered samples at different temperatures [39] ............... Figure II. 10. Photography and X-ray diffraction mechanism of Bruker-AXS D8 FOCUS Advanced Bragg-Brentano X-ray Powder Diffractometer ..................................................................................... Figure II. 11. Stick pattern of high intensity diffraction for Lanthanum silicate (ref. 00-049-0443) .... Figure II. 12. JSM-7800F field emission scanning electron microscope .............................................. Figure II. 13. Diagram of the four-point method ................................................................................... Figure II. 14. Representation of an electric circuit impedance diagram. (a) Electrical circuit, (b)Complex impedance diagram corresponding to a Nyquist plot and (c) in a Bode plot. ................... Figure II. 15. Schematic of an impedance plot for an electroded polycrystalline sample with an analog equivalent electric circuit. ..................................................................................................................... Figure II. 16. Devices for measuring the conductivity (the inset is the structure of sample furnace) ... Figure II. 17. Schematic of DSC and TG technique .............................................................................. Figure II. 18. Schematic illustration of the simulation methods for different length and time scales ... Figure II. 19. Flowchart of a self-consistent calculation in a method based on the DFT calculation ...

Figure II. 20 .

 20 Figure II. 20. Material properties studies with DFT calculation ........................................................... Figure III. 1. Schematic diagram of the input files for VASP ............................................................. Figure III. 2. Schematic diagram of lanthanum-silicon apatite structure ............................................ Figure III. 3. Different Sr dopant ratio effects on the electronic properties compared to ionic conductivity ......................................................................................................................................... Figure III. 4. Effect of Sr dopant on the Fermi level ........................................................................... Figure III. 5. Total DOS (left) and partial DOS (right) of LSO with different Sr dopant ratios in (a) La:Sr = 10:0 (b) La:Sr = 9:1 (c) La:Sr = 8:2 ....................................................................................... Figure III. 6. Comparison among the different Sr-doping ratios ......................................................... Figure III. 7. PDOS curves analysis for different La and Sr doping ratios ......................................... Figure III. 8. Calculated band structure of La10Si6O27 ......................................................................... Figure III. 9. The DOS comparison between LSO and LGO .............................................................. Figure III. 10. The calculated electron density of LSO and LGO ....................................................... Figure III. 11. The calculated energy barriers along c-axis for activation energy of LSO with different Sr doping ratios and positions (a ~ b, La9SrSi6O26.5 with Sr position near to (a) and far from (b) migration channel; c ~ e, La8Sr2Si6O26 with two Sr positions near-near to (c), near-far from (d) and farfar from (e) migration channel; f, La10Si6O27) ..................................................................................... Figure III. 12. The calculated energy barriers along c-axis for activation energy of LGO (a) and the activation energy of each group (b). .................................................................................................... Figure III. 13. La10-xSrx(Si,Ge)6O27-0.5x XRD patterns: (a) modeled and (b) experimental, versus different doping ratios ......................................................................................................................... Figure IV. 1. co-precipitation reaction equipment design (Acid buretteleft; alkaline buretteright) ............................................................................................................................................................. Figure IV. 2. X-ray diffraction patterns of different groups of compounds synthesized with different calcination temperature ....................................................................................................................... Figure IV. 3. X-ray diffraction patterns the group of compounds synthesized with 1000℃ calcination temperature (the miller indices of lanthanum silicate is shown in the figure)..................................... Figure IV. 4. TG/DSC curves of precipitant to analyze the calcination process ................................. Figure IV. 5. The morphologies of samples with different calcination temperatures treatment by SEM analysis ................................................................................................................................................ Figure IV. 6. The grain sizes of samples treated with different temperatures by analyzing SEM photos ............................................................................................................................................................. Figure IV. 7. EDX analysis curve of the obtained sample in three different zones (1000℃ group as an example) .............................................................................................................................................. Figure IV. 8. X-ray diffraction patterns of different groups with further sintering treatment at 1500℃ for 2h ................................................................................................................................................... Figure IV. 9. Typical SEM micrographs of samples sintered at 1500℃ for 2h .................................. Figure IV. 10. Impedance diagram in Nyquist representation registered at 773 K under static air on apatite pellet. Frequency logarithms are represented .......................................................................... Figure IV. 11. Arrhenius plot of ionic conductivity ............................................................................ Figure IV. 12. Sr-doping LSO co-precipitation reaction equipment design........................................ Figure IV. 13. Experimental equipment and process of Mn-doping LSO with co-precipitation ........ Figure IV. 14. the phase diagram of the MnO-Mn2O3-MnO2 system[5] ............................................. Figure IV. 15. The XRD diffraction patterns of the powder before calcination and the sample after calcination (the inset shows the sample appearance) .......................................................................... Figure IV. 16. Flow chart of molten salt method for LSO synthesis .................................................. Figure IV. 17. XRD diffraction pattern of the composition synthesized by molten NH4NO3 method Figure IV. 18. The phase equilibrium diagram of the KCl-NaCl system ............................................ Figure IV. 19. XRD results of the product with NaCl-KCl eutectic method by multiple temperature Figure IV. 20. The diffraction pattern of the 850℃ group before and after the citric acid washing ... Figure IV. 21. The phase equilibrium diagram of the KCl-LiCl system .............................................

[ 8 ]Figure I. 1 .

 81 Figure I. 1. William Grove's 1839 gas voltaic battery diagram, pioneer of modern fuel cell

  Figure I.2 shows a schematic diagram of the solid oxide fuel cell in the planar form.

Figure I. 2 .

 2 Figure I. 2. Schematic diagram of the operation of a fuel cell (This work has been released into the public domain by its author, Sakurambo.)

Figure I. 3

 3 Figure I.3 sketches the input and output of the fuel cell. The voltage/intensity characteristics

Figure I. 3 .

 3 Figure I. 3. The input and output of the fuel cell To simplify the discussion, hydrogen and oxygen are chosen as an example for the reaction

Figure I. 4

 4 Figure I.4 shows the energy density and the power density of the fuel cell among the energy

Figure I. 4 .

 4 Figure I. 4. The energy and power properties of the fuel cell compared to other energy conversion devices (A. Comparison of the specific power between the present SOFC ~ 2W / cm 2 at 650℃ and multiple energy conversion devices as a function of the power density. B. Ragone plot, specific energy versus specific power, for various energy devices in relation to the present SOFC) [41].

Figure I. 5 .

 5 Figure I. 5. Changes in oxygen reduction activity plotted as a function of the oxygen binding energy [42]

Figure I. 6 .

 6 Figure I. 6. The types of oxygen adsorption process in the cathode

Figure I. 7 .

 7 Figure I. 7. The logarithm of the exchange current density (log i0) against the force of the metal-hydrogen bond formed during the reaction itself.

Figure I. 8

 8 gives some representative diffusion mechanisms for ion effective transmission. They have the potential to form an effective transportation.

Figure I. 8 .

 8 Figure I. 8. Schematic of diffusion mechanisms in solid state structures: (a) vacancy diffusion; (b) Interstitial diffusion; (c) ions exchange-direct and circle.

  Figure I.9 gives a schematic to represent the definition of activation energy.

Figure I. 9 .

 9 Figure I. 9. Schematic representation of the diffusion of an atom from its original position into another lattice site. Activation energy Em has to be supplied to the atom so that it could break inter-atomic bonds and to move into the new position.

  𝑄 𝑑 and pre-exponential 𝐷 0 , therefore, can be estimated by plotting ln𝐷 versus 1/T. Such plots are called Arrhenius plots, as shown in figure I.10.

Figure I. 10 .

 10 Figure I. 10. Arrhenius plot of lnD vs. 1/T with a slop of -Qd/R and an intercept of lnD0

I. 2

 2 Materials used in the SOFCsI.2.1 Cathode materialsThe oxygen reduction process occurs at the interface of electrode and electrolyte and the reaction is shown in Figure I.12. There are three ways to transfer oxygen and among them, TPB (triple phase boundary) is a very important reaction place[2, 51]. The cathode materials should have the properties: adsorption, catalytic cracking of oxygen, and conversion from the atoms to ions. Thus, the electro catalytic activity of the cathode material is a very important reference to evaluate the cathode performance.

Figure I. 12 .

 12 Figure I. 12. A diagram of the reactions in the cathode of SOFC

  Figure I.13 shows a schematic of the typical structure of perovskite.

Figure I. 13 .

 13 Figure I. 13. Schematic of the lattice structure of a perovskite-ABO3

  et al. and Li et al. have also reported an increase of the electric conductivity up to 200-485 S/cm (x = 0.5 at 1000 ℃). A plot of de log σT vs 1/T for La1-xSrxMnO3-δ in the condition of pure oxygen (PO2 = 1 bar) is shown in Figure I.14.

Figure I. 14 .

 14 Figure I. 14. Variation of electrical conductivity (σ) of La1-xSrxMnO3-δ (x is 0 to 0.7) atdifferent temperature (at pure oxygen PO2 = 1 bar).[57]

Figure I. 15 .

 15 Figure I. 15. Schematic view of the crystal structures of: (a) Simple perovskite, (b) Double perovskite and (c) Ruddlesden-Popper K2NiF4 type phase. Sites for water insertion are shown:oxygen vacancies for the perovskites and interstitials for Ln2MO4+δ.[59]

3 .[ 2 ]

 32 However, most of the reported performances vary tremendously because of several unknown variable factors during the operation/testing. The materials remain amount of work to clearly understand shortand long-term degradation problems with optimization and calculated predictions.

Fig. I. 16

 16 Fig. I.16 shows the carbon deposition on Ni-YSZ anode material with the cell of different work

Figure I. 16 .

 16 Figure I. 16. Transmission electron micrographs showing the anode (a) operated with hydrogen fuel (b) operated with syngas for 15min; (c) operated under same gas mixture for 2h(the ingredient of synthesis gas: CH4 23.64% ; CO 7.60% ; CO2 14.27% ; H2 49.48% ; H2O 5.00%)[START_REF] Chen | Evaluation of carbon deposition behavior on the nickel/yttrium-stabilized zirconia anode-supported fuel cell fueled with simulated syngas[END_REF].

  Fig. I.17 shows the three views of the typical structure of pyrochlore A2B2O6O' [80]. The crystal structure of these compounds can accommodate high oxygen content and allow flexible combinations of cations on the two sites A and B. This allows to make changes in the combination of cations A and B to adapt the stability and electrical properties from the structure, especially the stability at high temperatures to satisfy the practical requirements of SOFC.

Figure I. 17 .

 17 Figure I. 17. the three views of the pyrochlore structure A2B2O6O' (a) showing the relation between the structures of fluorite and pyrochlore in where an octant of the cell of the pyrochlore unit is represented by the large cube, (b) octahedral connectivity <BO6> units with A sites and O' anions as "extra-framework ions," (c) the A sublattice as a network of cornershared O'-centered tetrahedra, with B and O atoms omitted. A -purple, B -green, O -yellow and O' -orange [80]

  Figure I. 18 shows the position of interconnect in a fuel cell.

Figure I. 18 .

 18 Figure I. 18. Schematic diagram of the components of a planar cell to show the interconnect

Figure I. 19 .

 19 Figure I. 19. Schematic showing selection of phases in Fe-Co-Ni based alloys as metallicinterconnect materials[START_REF] Yang | Selection and evaluation of heat-resistant alloys for SOFC interconnect applications[END_REF]

Fluorite

  structure oxides belong to face centered of cubic lattice system. Figure I.20 exhibits a typical fluorite structure of ceria as an example. Generally, the fluorite structure has a common formula MO2, where M is high valence metal elements, for example CeO2, ZrO2, HfO2, and ThO2. There are still some special formulas, such as M2O3, which possess two oxygen defects in a single cell of fluorite structure. Among these oxides, only ZrO2, CeO2 and Bi2O3 have been of interest to researchers as an electrolyte material in SOFC.

Figure I. 20 .

 20 Figure I. 20. Cubic fluorite structure of ceria

Figure I. 21

 21 Figure I.21.

Figure I. 21 .

 21 Figure I. 21. Schematic of the δ-Bi2O3 polymorph crystal structures

271°C.[ 100 , 101 ]-

 100101 Pyrochlores based ceramicsPyrochlore structure with a general formula of A(III)2B(IV)2O7 structure have been actively investigated for ionic conduction for long time. Pyrochlore is a superstructure of fluorite structure (MO2) where A-and B-site cations are ordered and one eighth of the anions are missing (to form vacant sites as show in figure I.22[START_REF] Radhakrishnan | Influence of disorder-toorder transition on lattice thermal expansion and oxide ion conductivity in (Ca x Gd 1-x) 2 (Zr 1-x M x) 2 O 7 pyrochlore solid solutions[END_REF], the letter for showing position is called Wyckoff letter). It is reported that on reducing the size of A-site cations, pyrochlore to fluorite transition is favored (at elevated temperatures up to 1370-2227 ℃). On reducing the size of the cation, a structural transformation is induced from a fully ordered pyrochlore lattice A2B2O7 to a completely disordered anion deficient defective fluorite M4O7 (where M can be A or B).

Figure I. 22 .

 22 Figure I. 22. Structures of pyrochlore -One eighth of the unit cell of the ordered pyrochlore structure showing specific positions of the cations and anions (B 4+ cation at the origin). [102]

Figure I. 23 .

 23 Figure I. 23. Arrangement of B-O octahedra and tetrahedra in the ideal brownmillerite structure, A2B2O5 (A cations removed for clarity)

  Figure I.24 shows a schema of apatite structure: it consists of tetrahedron MO4, cation A and

Figure I. 24 .

 24 Figure I. 24. The apatite structure, A10(MO4)6X2±y, and alternative representation of the apatite structure: illustration of the "microporous" A4(MO4)6 framework:The cavities are where the remaining A6X2±y units would occupy.[START_REF] Kendrick | Developing apatites for solid oxide fuel cells: insight into structural, transport and doping properties[END_REF]

Figure I. 25 .

 25 Figure I. 25. Schematic diagram of lanthanum-silicon apatite structure

Figure I. 26

 26 Figure I.26 gives the ionic conductivity comparison of some selected typical electrolyte

Figure I. 26 .

 26 Figure I. 26. Conductivities of selected electrolyte materials at intermediate temperature (LSO series lies at shaded part, original figure from ref [125])

Figure I. 27 .

 27 Figure I. 27. The interstitial oxygen site (brown sphere) at the periphery of the channels, and associated lattice relaxation (blue spheres = La, green spheres = Si)

Figure I. 28 .

 28 Figure I. 28. 29 SiNMRspectra (left) and Raman spectra results (right) for (a) La8Sr2(SiO4)6O2, (b) La9Sr(SiO4)6O2.5, (c) deconvolution of the latter. [128, 129]

Figure I. 29 .

 29 Figure I. 29. O5 oxygen vacancy migration along the O5 oxide channel (a), and interstitial oxygen migration viewed perpendicular to the O5 channel, showing a non-linear (sinusoidallike) pathway (b), suggested for La8Sr2(SiO4)6O2 and La9.33(SiO4)6O2 respectively

Figure I. 30 .

 30 Figure I. 30. Proposed conduction pathway between adjacent oxide-ion channels via two "SN2"-type processes, with accompanying rotation of the silicate tetrahedra, obtained from computer simulation results of La9.33(SiO4)6O2. The incorporation of a periphery interstitial oxide-ion (yellow) (a) forces a silicate oxygen (orange) in between the two SiO4 units forming an Si2O9 unit (b), the top silicate unit rotates to form an Si2O9 unit with a neighboring silicate unit (c), and an oxygen on the top silicate unit (green) is released as an interstitial in a different channel (d).[START_REF] Kendrick | Developing apatites for solid oxide fuel cells: insight into structural, transport and doping properties[END_REF][START_REF] León-Reina | Interstitial oxygen conduction in lanthanum oxy-apatite electrolytes[END_REF]

  This doping influence has been reviewed by Emma Kendrick et al., as shown in Figure I.31.[117] They compare the influence in compounds with different interstitial oxygen ions. Elements doping in both cases have positive and negative effects.

Figure I. 31 .

 31 Figure I. 31. Comparison of the conductivities (500 °C) of oxygen stoichiometric samples with the same level of cation vacancies (a) and same level of oxygen excess -O2.5 (b)[START_REF] Kendrick | Developing apatites for solid oxide fuel cells: insight into structural, transport and doping properties[END_REF]

II. 1 .

 1 Synthesis methods II.1.1 Dry pressing Dry pressing is the technique of fabricating ceramic components by the compaction of flowable powders in a metal die set. This fabrication technology enables the manufacture of parts to accurate dimensional specifications and enables high volume production. There are three fundamental steps in dry pressing technology that include spray dried powder preparation, pressing and sintering. Dry pressing is simple, reproducible, and very cost-effective. Figure II.1gives a schema of the dry pressing technology and devices. Dense electrolyte can be obtained by this technique. Xia and Liu reported that GDC (Gd0.1Ce0.9O1.95) films were successfully fabricated by this dry-pressing process. SOFCs based on GDC films were tested having maximum power densities of 400 mW/cm 2 at 600°C[1, 2].

Figure II. 1 .

 1 Figure II. 1. A schematic diagram for showing dry pressing process, devices and the electrolyte obtained by this technique.

( 1 .

 1 76 A cm -2 and 425 mW cm -2 respectively), as shown in Figure II.2.

Figure II. 2 .

 2 Figure II. 2. SEM micrographs of tape casting electrolyte using in SOFC and voltage-current, impedance spectrum characteristics of the cell operating at 800 °C.

Figure II. 3 .

 3 Figure II. 3. (a) SEM micrographs of electrolyte layer on the left and porous Ni-YSZ cermet on the right. (b) Specific resistance at different temperatures in comparison with YSZ pellet.

Figure II. 4

 4 Figure II.4 by H. Hidalgo et al [19]. The dense, thin film is obtained with excellent electric

Figure II. 4 .

 4 Figure II. 4. SEM micrographs of YSZ films grown by RMS (reactive magnetron sputtering) on (100) Si substrate at room temperature under 1 Pa: a) top view, b) cross-section.

Figure II. 5 .

 5 Figure II. 5. Experimental setup of ultrasonic aerosol assisted chemical vapor deposition at atmospheric pressure and the morphology of as obtained electrolyte

  Figure II.6 shows the morphologies of the layer deposited by different types of thermal spray.

Figure II. 6 .

 6 Figure II. 6. Micrographs of fracture surface of the La10Si5.8Mg0.2O26.8 coating deposited by VLPPS (a) and APS (b).

Figure II. 7 .

 7 Figure II. 7. A schematic diagram of sol-gel process and its application ways (https://str.llnl.gov/str/May05/Satcher.html)

  8h), fast and user-friendly sol-gel processing technique. The flowchart of the sol-gel process is given in Figure II.8. Then, J. Zhou et al.[37] synthesized La9.67Si6-xAlxO26.5-x/2 electrolyte with multiple Al proportion, however La9.67Si6O26.5(x = 0) among the series exhibits the highest electrical conductivity. By viewing the reports, the synthesis process seriously affects the performance of the compounds. The improvement of sol-gel process is necessary to achieve pure phase, high crystalline compounds.

Figure II. 8 .

 8 Figure II. 8. Flowchart of the process used in the preparation of doped and undoped lanthanum silicates.

-

  Low cost of the equipment required; -Reaction complete; -High purity of products; -Fast preparation; -High efficiency and usage of raw-materials; II.2 Characterization II 2.1 Density Density is an important indicator to measure the performance of a sample. As electrolyte material in fuel cells, the samples should be as high as possible to isolate the gas flow between the two electrodes. The density of prepared samples is determined from measurements of the mass and volume, and calculated by the following equation. -the mass of sample; dthe diameter and ethe thickness.

Figure II. 9

 9 Figure II. 9. Density and relative density of sintered samples at different temperatures[39]

Figure II. 10

 10 Figure II.10 shows the equipment in which is the sample stage, and the detector / counter lies

Figure II. 10 .

 10 Figure II. 10. Photography and X-ray diffraction mechanism of Bruker-AXS D8 FOCUS Advanced Bragg-Brentano X-ray Powder Diffractometer

Figure II. 11 .

 11 Figure II. 11. Stick pattern of high intensity diffraction for Lanthanum silicate (ref. 00-049-0443)

A

  scanning electron microscope (SEM) is used in this study to determine the microstructure and the morphology of the obtained samples. It is a type of electron microscope that produces images of a sample by scanning it with a focused beam of electrons.

Figure II. 12 .

 12 Figure II. 12. JSM-7800F field emission scanning electron microscope

  electrolyte. It can be measured by the DC method. The principle and the measuring device are presented to define the electrical conductivity. The DC method of four points is used to measure the electrical conductivity of the sample as shown in Figure II .13.

Figure II. 13 .

 13 Figure II. 13. Diagram of the four-point method

5 Z[ 41 ]

 541 exp(𝑗𝜑) = 𝑍 0 𝑐𝑜𝑠𝜑 + 𝑗𝑍 0 𝑠𝑖𝑛𝜑 EQN II.' and Z" are employed to replace the real and imaginary parts to simplify the equation:𝑍(ω) = Re(𝑍) + 𝑗Im(𝑍) = 𝑍 ′ + 𝑍 ′′ EQN II.6The complex impedance is generally represented by Nyquist plot or Bode plot in measurement results. According to the results, the impedance can be fitted to a simple circuit. Figure II.14 shows an example of electrical circuit (a), corresponding Nyquist plot (b) and Bode plot (c). In the representation of the Nyquist plane, the real part and the imaginary part of the impedance (Z 'and Z ") are plotted respectively on the X and Y axis. Usually, electrochemistry takes the negative Y-axis to up as shown in Figure II. 14 (b). The impedances of low frequencies and high frequencies are located at right and left of the plot respectively. In the case of Bode plot, the logarithm of modulus | Z | and / or variation of the argument of the phase (φ) are represented as a function of logarithmic angular frequency [log (|Z|) = f (logω) or φ = f (logω)]. The advantage of such a representation (Figure II.14.c) is to identify directly the frequency spectrum corresponding to each measured result.

Figure II. 14 .

 14 Figure II. 14. Representation of an electric circuit impedance diagram. (a) Electrical circuit, (b)Complex impedance diagram corresponding to a Nyquist plot and (c) in a Bode plot.

Fig. II. 15 a

 15 Fig. II.15 a shows the schematic of an impedance plot of a polycrystalline sample with electrode

Figure II. 15 .

 15 Figure II. 15. Schematic of an impedance plot for an electroded polycrystalline sample with an analog equivalent electric circuit.

Figure II. 16 .

 16 Figure II.16. shows the ionic conductivity measurement device (a samples furnace equipped

Figure II. 16 .

 16 Figure II. 16. Devices for measuring the conductivity (the inset is the structure of sample furnace)

Figure II. 17 .

 17 Figure II. 17. Schematic of DSC and TG technique

  is one of the most commonly used quantum methods in the fields of solid state physics and quantum chemistry for determination of physical and quantum factors of systems. The objective of most ab initio approaches based on fundamental quantum theory is to calculate stationary states of electrons in the electrostatic field of atomic nuclei, i.e., the electronic structure. The energy of this ground state can then serve as a basis for investigation of displacements of the nuclei which leads to determination of many macroscopic properties important in technology. The calculation scale and time lies in an extremely small scale. It can deal with system of a single molecule, a group of molecules, a liquid or solid, as shown in Figure II.18 of the compassion of different simulation methods.

Figure II. 18 .

 18 Figure II. 18. Schematic illustration of the simulation methods for different length and time scales

  𝐸 = 𝐸 𝛼 (𝑅 ⃗⃗ ) + 𝐸 𝑒 (𝑅 ⃗⃗ ) EQN II.12 This approximation is known as the Born-Oppenheimer adiabatic approximation. The position of the nuclei in the field is supposedly fixed. The parameter of nuclei kinetic energies in Hamiltonian operator can be omitted. (𝑇 ̂𝑒 + 𝑉 ̂𝛼𝛼 + 𝑉 ̂𝛼𝑒 + 𝑉 ̂𝑒𝑒 )𝛹 𝑒 (𝑟 ⃗, 𝑅 ⃗⃗ ) = 𝐸 𝑒 (𝑅 ⃗⃗ )𝛹 𝑒 (𝑟 ⃗, 𝑅 ⃗⃗ ) EQN II.13

Theorem 1 :

 1 The electron density ρ(r) determines the external potential υext(r). The energy functional E[ρ(r)] alluded to in the first Hohenberg-Kohn theorem can be written in terms of the external potential υext(r) in the following way:𝐸[𝜌(𝑟 ⃗)] = 𝐹[𝜌(𝑟 ⃗)] + ∫ 𝜌(𝑟 ⃗)υ 𝑒𝑥𝑡 (𝑟 ⃗) 𝑑𝑟 ⃗ EQN II.14 Where ∫ 𝜌(𝑟 ⃗)υ 𝑒𝑥𝑡 (𝑟 ⃗) 𝑑𝑟 ⃗ represents the core-electron interaction. 𝐹[𝜌(𝑟 ⃗)] is a function of density 𝜌(𝑟 ⃗) independent of external potential υ 𝑒𝑥𝑡 (𝑟 ⃗); it contains the contributions of kinetic and coulomb energy: 𝐹[𝜌(𝑟 ⃗)] = 𝑇[𝜌(𝑟 ⃗)] + 𝑉 𝑒𝑒 [𝜌(𝑟 ⃗)] = 𝑇[𝜌(𝑟 ⃗)] + 𝐸 𝐻 [𝜌(𝑟 ⃗)] + 𝐸 𝑥𝑐 [𝜌(𝑟 ⃗)] EQN II.15 Where 𝑇[𝜌(𝑟 ⃗)] is the kinetic energy of the electron system and 𝑉 𝑒𝑒 [𝜌(𝑟 ⃗)] is the term electronelectron interaction that includes Hartree energy 𝐸 𝐻 [𝜌(𝑟 ⃗)] (the Coulomb repulsive of electronelectron) and the exchange and correlation energy 𝐸 𝑥𝑐 [𝜌(𝑟 ⃗)].

  ′ | 𝑑𝑟 ′ EQN II.18 and the exchange-correlation potential υ 𝑥𝑐 (r) υ 𝑥𝑐 (r) = 𝜕𝐸 𝑥𝑐 [𝜌(𝑟)] 𝜕𝜌(𝑟) EQN II.19

  Carlo simulations for the energy of the HEG have been performed for several intermediate values of the density, in turn providing accurate values of the correlation energy density 𝐸 𝑐 𝐿𝐷𝐴 [𝜌(𝑟 ⃗)]. The most popular LDA's to the correlation energy density interpolate these accurate values obtained from simulation while reproducing the exactly known limiting behavior. Various approaches, using different analytic forms for 𝐸 𝑐 𝐿𝐷𝐴 [𝜌(𝑟 ⃗)], have generated several LDA's for the correlation functional, including Vosko-

  𝐸 𝑥𝑐 𝐺𝐺𝐴 [𝜌(𝑟 ⃗)] = ∫ 𝜌(𝑟 ⃗)𝑓[𝜌(𝑟 ⃗), ∇𝜌(𝑟 ⃗)] 𝑑𝑟 ⃗ EQN II.25 Where, 𝑓[𝜌(𝑟 ⃗), ∇𝜌(𝑟 ⃗)] was the function of exchange energy and dependent correlation of the electron density and its gradient. There are several versions of GGA most frequently used which are introduced by Perdew and Wang (PW91), Perdew, Burke and Ernzerhof.

29 It works with three objects: 1 . 3 .

 2913 |𝜙 𝑝𝑠 ⟩𝑐 𝑖 𝑖 + ∑ |𝜙 𝑖 ⟩𝑐 𝑖 𝑖 EQN II.28 Where ∑ |𝜙 𝑝𝑠 ⟩𝑐 𝑖 𝑖 is the development of the base |𝜓 𝑝𝑠 ⟩ on a pseudo partial waves and ∑ |𝜙 𝑖 ⟩𝑐 𝑖 𝑖 is the development of |𝜓⟩ on a basis of partial waves, within the volume of spheres 𝛺 𝑅 ⃗⃗ around atomic sites indicated by 𝑅 ⃗⃗ . The coefficients 𝑐 𝑖 are scalar products of wave functions and pseudo-projection functions within the area 𝛺 𝑅 ⃗⃗ . 𝑐 𝑖 = ⟨𝑝 𝑖 |𝜙 𝑖 𝑝𝑠 ⟩ EQN II.Partial wave |𝜙 𝑖 ⟩ obtained by radial integration of the Schrödinger equation for atomic energy 𝜀 𝑖 which are orthogonal to the functions of the core; 2. The pseudo partial wave |𝜓 𝑝𝑠 ⟩ coincides with the exact partial wave to the outside of the core area; The projection function of each partial wave |𝑝 𝑖 ⟩, shown in region 𝛺 𝑅 ⃗⃗ which satisfies the relationship ⟨𝑝 𝑖 |𝜙 𝑖 𝑝𝑠 ⟩ = 𝛿 𝑖𝑗 .

  To start the calculation, four important input files are necessary: INCAR, POSCAR, POTCAR and KPOINTS. INCAR is the central input file which determines 'what to do and how to do it', and contains a relatively large number of parameters. POSCAR contains the lattice geometry and the ionic positions. POTCAR file contains the pseudopotential for each atomic species used in the calculation. KPOINTS must contain the k-point coordinates and weights or the mesh size for creating the k-point grid. A calculation period costs several hours to one or two days and the code VASP is run at the Mé socentre de calcul de Franche-Comté .

Figure III. 1 .

 1 Figure III. 1. Schematic diagram of the input files for VASP III.2.2 Structure properties

Figure III. 2

 2 Figure III.2 shows the LSO apatite structure and the oxygen migration channel. As it can be

Figure III. 2 .

 2 Figure III. 2. Schematic diagram of lanthanum-silicon apatite structure

Figure III. 3

 3 Figure III.3 shows the calculation results (including the Fermi level, total energy and formation

Figure III. 3 ,

 3 the less doping LSO has a lower formation energy. It can be deduced that the apatite would be more stable without doping.

Figure III. 3 .

 3 Figure III. 3. Different Sr dopant ratio effects on the electronic properties compared to ionic conductivity

Figure III. 4 .

 4 Figure III. 4. Effect of Sr dopant on the Fermi level

Figure III. 5 .

 5 Figure III. 5. Total DOS (left) and partial DOS (right) of LSO with different Sr dopant ratios in (a) La:Sr = 10:0 (b) La:Sr = 9:1 (c) La:Sr = 8:2

  the three Sr doping ratios DOS are plotted and shown in Figure III.6. With Sr doping, the states around Fermi energy has significant shifting toward higher energy, therefore the material has a wider energy gap.

Figure III. 6 .

 6 Figure III. 6. Comparison among the different Sr-doping ratios

Figure III. 7 .

 7 Figure III. 7. PDOS curves analysis for different La and Sr doping ratios

Figure III. 8 .

 8 Figure III. 8. Calculated band structure of La10Si6O27

  Firstly, the complete substitution of Ge at Si position is calculated to obtain the DOS. The DOS of LSO and La10Ge6O27 (LGO) are shown in Figure III.9. It is clear that the two curves overlap. It can be deduced that the Fermi levels of the two materials are almost the same as in our previous analysis. The bonding orbitals of Si and Ge are the same (3,4)s 2 (3,4)p 2 , hence it has little influence on DOS and electronic transitions with Ge substitution. In this case, the calculation of different Ge doping ratios is omitted.

Figure III. 9 .

 9 Figure III. 9. The DOS comparison between LSO and LGO

Figure III. 10 .

 10 Figure III. 10. The calculated electron density of LSO and LGO

Figure III. 11 .

 11 Figure III. 11. The calculated energy barriers along c-axis for activation energy of LSO with different Sr doping ratios and positions (a ~ b, La9SrSi6O26.5 with Sr position near to (a) and far from (b) migration channel; c ~ e, La8Sr2Si6O26 with two Sr positions near-near to (c), near-far from (d) and far-far from (e) migration channel; f, La10Si6O27)

Figure III. 13 .

 13 Figure III. 13. La10-xSrx(Si,Ge)6O27-0.5x XRD patterns: (a) modeled and (b) experimental, versus different doping ratios

2 A

 2 Figure IV.1 gives the schema of the equipment that the reaction takes place in ammonia solution

Figure IV. 3 .

 3 Figure IV. 3. X-ray diffraction patterns the group of compounds synthesized with 1000℃ calcination temperature (the miller indices of lanthanum silicate is shown in the figure)

Figure IV. 4 .

 4 Figure IV. 4. TG/DSC curves of precipitant to analyze the calcination process

Figure IV. 5 .

 5 Figure IV. 5. The morphologies of samples with different calcination temperatures treatment by SEM analysis

Figure IV. 6 .

 6 Figure IV. 6. The grain sizes of samples treated with different temperatures by analyzing SEM photos

Figure IV. 7 .

 7 Figure IV. 7. EDX analysis curve of the obtained sample in three different zones (1000℃ group as an example)

Figure IV. 8

 8 Figure IV. 8. X-ray diffraction patterns of different groups with further sintering treatment at 1500℃ for 2h

Figure IV. 9

 9 Figure IV.9 shows the SEM microstructure of some synthesized apatites after sintering.

Figure IV. 9 .

 9 Figure IV. 9. Typical SEM micrographs of samples sintered at 1500℃ for 2h

Figure IV. 11 .

 11 Figure IV. 11. Arrhenius plot of ionic conductivity

9La(NO3) 3 +

 3 Sr(NO3)2 + 6Na2SiO3 + 14.5H2C2O4 + 17NH3•H 2O → 4.5La2(C2O4)3↓+ Sr(C2O4)↓+ 6SiO2↓+ 12NaNO3 +17NH4NO3 +23H2O EQN IV.4 and 9.5La(NO3)3 + 0.5Sr(NO3)2 + 6Na2SiO3 + 14.75H2C2O4 + 18NH3•H 2O → 4.75La2(C2O4)3↓+ 0.5Sr(C2O4)↓+ 6SiO2↓+ 12NaNO3 +18NH4NO3 +23.75H2O EQN IV.5for different Sr doping ratios. Adding excess of ammonia solution to increase the PH, Sr(C2O4) precipitation reaction is more complete. However, it affects SiO2 precipitation. In this case, we have to keep the pH around 7, thus we choose CH3COONH4 (ammonium acetate) as a pH buffer.

Figure IV. 12

 12 Figure IV.12 gives the schema of the equipment that the reaction is taken place in ammonium

Figure IV. 12 .

 12 Figure IV. 12. Sr-doping LSO co-precipitation reaction equipment design

2 (

 2 Figure IV. 13. Experimental equipment and process of Mn-doping LSO with co-precipitation

Figure IV. 14 .

 14 Figure IV. 14. the phase diagram of the MnO-Mn2O3-MnO2 system[5]

Figure IV. 15 .

 15 Figure IV. 15. The XRD diffraction patterns of the powder before calcination and the sample after calcination (the inset shows the sample appearance)

Figure IV. 17 .

 17 Figure IV. 17. XRD diffraction pattern of the composition synthesized by molten NH4NO3 method

Figure IV. 18 .

 18 Figure IV. 18. The phase equilibrium diagram of the KCl-NaCl system

Figure IV. 19 .

 19 Figure IV. 19. XRD results of the product with NaCl-KCl eutectic method by multiple temperature

Figure IV. 20 .

 20 Figure IV. 20. The diffraction pattern of the 850℃ group before and after the citric acid washing

Figure IV. 21 .

 21 Figure IV. 21. The phase equilibrium diagram of the KCl-LiCl system

Figure IV. 23 .

 23 Figure IV. 23. The phase equilibrium diagram of the Li2SO4-K2SO4 system (data from FTsalt)

Figure IV. 24 .IV. 4

 244 Figure IV. 24. XRD results of the product with Li2SO4-K2SO4 eutectic method at 700℃ and 900℃

Figure IV. 25 .

 25 Figure IV. 25. Schematic diagram of homogeneous deposition precipitation method equipment for synthesizing LSO compounds

Figure IV. 26 .

 26 Figure IV. 26. XRD results of the product with HDP method with calcination temperature of 800℃ for 2h

Figure IV. 27 .

 27 Figure IV. 27. The morphologies of the powder with HDP method calcined at 800℃ for 2h by SEM analysis

Figure V. 2 .

 2 Figure V. 2. TG/DSC curves of La(NO3)3•xH2O as raw material to verify the number of crystal water in a molecular

2 )-

 2 Solution B1 adjusted to pH 0.2 with HNO3 was taken as acidic medium; -Solution A1 adjusted to pH 8.3 with NH3•H2O was taken as alkaline medium. The synthesis procedure was then conducted as shown in figure V.1. The bottom of Figure V. 4 shows the aspects of acidic, near-neutral and alkaline medium at the end of solution preparation. The statuses of this three solutions are turbid (stable), turbid (unstable) and clear (stable and viscous) respectively.

Figure V. 4 .

 4 Figure V. 4. The mechanism of lanthanum silicates sol-gel formation process (the features of the three obtained sols are shown by the inset)

Figure V. 5 (

 5 Figure V. 5 (a) and (b) show the morphologies of two dry gels, prepared with "non optimized"

Figure V. 5 .

 5 Figure V. 5. SEM figures or the morphologies of the obtained compounds with optimized process (a, dry gel before calcination with unsuitable pH; b, dry gel before calcination with optimized pH.)

  influence of the calcination parameters is visible in Figure V. 6 that shows the useful portion of the X-ray diffraction range. The calcination temperature has a much stronger effect on the crystallization process than the duration. As we can see in the diagram (a), the diffraction peaks become sharper and narrower when the temperature increases. The sample calcined at high temperature displays peaks with low FWHM (Full width at half maximum) data, which means that it contains bigger grains of greater crystallinity. In addition, the two overlapping peaks [Miller indices of (211) and[START_REF] Schober | Phase transition in the oxygen and proton conductor Ba 2 In 2 O 5 in humid atmospheres below 300[END_REF]] are increasingly separated when passing from 800 to 1000℃.

Figure V. 6 .

 6 Figure V. 6. Diffraction patterns of the obtained powders for the sintering time (a) and temperature (b) studies

Figure V. 7

 7 shows a typical XRD patterns for dry gels before calcination.

Figure V. 7 .

 7 Figure V. 7. Typical XRD pattern of a dry gel before calcination

Figure V. 8 .

 8 Figure V. 8. XRD patterns obtained with different calcination temperature and Sr doping (no sintering)

Figure V. 9

 9 Figure V. 9 shows the 30-40° portions of the XRD diagrams relating to different calcination

Figure V. 9 .

 9 Figure V. 9. Local XRD patterns corresponding to three Sr doping ratios (a) and three calcination temperatures (b) (no sintering)

  Figure V. 10 shows typical SEM microstructures of various synthesized apatites.

  Figure V. 10 (a) shows agglomerated blocks and some smaller, dispersed particles, the average size of the blocks being in the order of magnitude of 10~50µm.

Figure V. 10 .

 10 Figure V. 10. SEM micrographs of calcined (no sintering) samples (a, 900°C-3; b, 1000°C-3; c, 1000°C-3)

Figure V. 11 .

 11 Figure V. 11. The sample density of each group by the optimized process

Figure V. 12 .

 12 Figure V. 12. The size change of the sample before and after sintering at 1500℃

Figure V. 13 .

 13 Figure V. 13. XRD patterns of the sintered samples (groups 1 to 3 having different calcination temperatures and Sr doping)

Figure V. 14 .

 14 Figure V. 14. Local XRD patterns of the group 1 to 3 having different Sr doping proportion (a); influence of sintering temperature (b)

Figure V. 15 .

 15 Figure V. 15. SEM micrographs of samples sintered at 1500℃ for 2h The EDS analyses of various samples are shown in Figure V. 16. To check the composition

Figure V. 17

 17 Figure V. 17 shows the results of the measurement of the electrical conductivity for each group.

Figure V. 17 .

 17 Figure V. 17. Ionic conductivities of the groups obtained with different Sr dopings and precalcination temperatures

Figure V. 18 .

 18 Figure V. 18. Ionic conductivities for different Sr ratios, measured at 500℃ (a) and 600℃ (b)

Figure V. 19 .

 19 Figure V. 19. Arrhenius plots of samples calcined at three temperatures (La9Sr2Si6O27 as an example) (a) with different Sr doping ratios (1000-1: La10Si6O27, 1000-2: La9SrSi6O27 and 1000-3: La9Sr2Si6O27) (b)

Table I .

 I 1. The electromotive forces and the ideal efficiency of a fuel cell at different temperatures .. Table I. 2. The characteristics comparison of fuel cells classified according to the electrolyte ............ Table I. 3. Summary of the properties and performance of multiple cathode materials .......................

Table I. 4. Wyckoff Positions and symmetry sites of Group 176 (P63/m) (quote from the Bilbao Crystallographic Server) ........................................................................................................................ Table I. 5. The atoms coordinate of lanthanum-silicon apatite structure .............................................. X

Table I .

 I 6. The undoped ionic conductivities of lanthanum silicates reported in literature................... Table I. 7. The apatite type LSO electrical properties doped by various elements ............................... Table II. 1. The PDF files of the compounds involved in this work ..................................................... Table II. 2. Some elements' characteristic X-ray energy for EDX characterization ............................. Table III. 1. Experimental ionic conductivities and activation energy of Ge, Sr substitution LSO apatite. (La10-xSrx(Si,Ge)6 in the table represents La10-xSrx(Si,Ge)6O27-0.5x for short, similarly hereinafter) .......................................................................................................................................... Table III. 2. The atoms coordinate of lanthanum-silicon apatite structure .......................................... Table III.3. Calculated and experimental lattice constants and internal parameters of LSOs and LGO ............................................................................................................................................................. Table IV. 1. The pH and temperature values during the co-precipitation process .............................. Table V. 1. XRD analyses of powders obtained with different Sr doping ratios and calcination temperatures ........................................................................................................................................ Table V. 2. Composition estimates based on the results of EDS ........................................................ Table V. 3. Density and conductivity properties of the LSOs obtained after sintering .......................

  . 1. The electromotive forces and the ideal efficiency of a fuel cell at different temperatures

	The reaction in cells	E 0 (V)	298 K ηmax (%)	E 0 (V)	600 K ηmax (%)	E 0 (V)	1000 K ηmax (%)
	𝑯 𝟐 +	𝟏 𝟐	𝑶 𝟐 = 𝑯 𝟐 𝑶(𝒈)	1.18	94	1.11	88	1.00	78
	𝑪𝑯 𝟒 + 𝟐𝑶 𝟐 = 𝑪𝑶 𝟐 + 𝑯 𝟐 𝑶 (𝒈)	1.04	100	1.04	100	1.04	100
	𝑪𝑶 +	𝟏 𝟐	𝑶 𝟐 = 𝑪𝑶 𝟐	1.34	91	1.18	81	1.01	69
	𝑪 +	𝟏 𝟐	𝑶 𝟐 = 𝑪𝑶	0.74	124	0.86	148	1.02	178

Table I .

 I 2. The characteristics comparison of fuel cells classified according to the electrolyte

	Fuel cell type	AFC	PAFC	MCFC	SOFC	PEMFC
	Common electrolyte	KOH	H3PO4	Li2CO3-K2CO3	YSZ	PEM
	fuel	Hydrogen	Natural gas, methanol, gasoline	Natural gas, methanol, gasoline	Natural gas, methanol, gasoline	Hydrogen, methanol
	Operating temperature	90-100℃	150-200℃	600-700℃	700-1000℃	50-100℃
	Conductive ions	OH -	H +	CO3 2-	O 2-	H +
	Typical stack size	10-100kW	200-400kW	300-3000kW	1-2000kW	<1-100kW
	Life (h)	10000	15000	15000	7000	5000
	Efficiency	60%	40%	45-50%	60%	35%-60%
	Advantages	• Cathode reaction faster in alkaline electrolyte, leads to high performance • Low cost components	• Higher temperature enables CHP • Increased tolerance to fuel impurities	• High efficiency • Fuel flexibility • Can use a variety of catalysts • Suitable for CHP	• High efficiency • Fuel flexibility • Can use a variety of catalysts • Solid electrolyte • Suitable for CHP & CHHP • Hybrid/GT cycle	• Solid electrolyte reduces corrosion & electrolyte management problems • Low temperature • Quick start-up
					• High
				• High	temperature
				temperature	corrosion	• Expensive
	Disadvantages	• Sensitive to CO2 in fuel and air • Electrolyte management	• Pt catalyst • Long start up time • Low current and power	corrosion and breakdown of cell components • Long start up time	and breakdown of cell components • High temperature operation	catalysts • Sensitive to fuel impurities • Low temperature waste
				• Low power	requires long	heat
				density	start up
					time and limits
						• Backup power
	Application	• Military • Space	• Distributed generation	• Electric utility • Distributed generation	• Auxiliary power • Electric utility • Distributed generation	• Portable power • Distributed generation • Transportation • Specialty
						vehicles

.2 illustrates the comparison of fuel cell technologies.[50] They are Alkaline Fuel Cell (AFC), Phosphoric Acid Fuel Cell (PAFC), Molten Carbonate Fuel Cell (MCFC), Solid oxide Fuel Cell (SOFC) and Proton Exchange Methanol Fuel Cell (PEMFC). It is indicted that SOFC has many advantages for various application and most of the disadvantages is derived from the high operation temperature. The development of IT-SOFC is necessary to improve this situation.

* CHP-combined heat and power; CHHP-combined heat, hydrogen, and power

Table I .

 I 3. Summary of the properties and performance of multiple cathode materials

	composition	TEC (×10 -6 /K)	σe (S/cm)	σi (S/cm)	DO (cm 2 /s)	k (cm/s)	Temp.
			Non-ABO3 structure
	8YSZ	10.2-10.5	0.17	0.003-0.02			1000℃
	YSZ-40%wt. LSM			3×10 -3	1-6×10 -9	7-1×10 -7	900℃
	LSGM	10.4		0.08			700℃
	Pt				4.1×10 -6	5×10 -2 -1.6
			ABO3 structure
	A=La, B=Mn	11.33-12.4	40-485	poor	2.45×10 -13	7.45×10 -8	1000℃
	A=La, B=Co	20-22	50-201		5.31×10 -9	3.47×10 -7	900℃
	A=La, B=Fe				5.28×10 -12	1.67×10 -7	1000℃
			A1-xA ' xBO3
	A=La, A ' =Sr, B=Mn	12.4 (x=0.2)	200-485	5.76×10 -6	1.33×10 -11		1000℃
	A=La, A ' =Sr, B=Co	20 (x=0.4)	2000	1.2	1.4×10 -8	4×10 -4	900℃
	A=La, A ' =Sr, B=Fe	x=0.1-0.4		8.3×10 -4	2.65×10 -9	5×10 -4	800℃
	A=La, A ' =Ba, B=Fe	x=0.2		3.1×10 -4			800℃
	A=Y, A ' =Ca, B=Mn	7-12 (x=0.3)
	A=Y. A ' =Ca, B=Fe	x=0.1		3.9×10 -2			1000℃
	A=Pr, A ' =Sr, B=Co	18.3-29.6	1000	(x=0-0.5)
	A=Pr, A ' =Sr, B=Mn	12.2 (x=0.5)	250				600℃
	A=Sm, A ' =Ba,Sr, B=Co	20-25	1280,280	(50℃,900℃)
			AB1-yB ' yO3
	A=La, B=Ga, B ' =Co	15.5	←y=0.2	3.4×10 -3	←y=0.4		800℃
	A=La, B=Ni, B ' =Fe	11.4 (y=0.4)	580				800℃
	A=La, B=Ni, B ' =Co	11.9-14.3	1200-1500	←y=0.4-0.6			1000℃
	A=Sr, B=Co, B ' =Sb	y=0.1	300				400℃
	A1-

xA ' xB1-yB ' yO3

	LSCF	15,3 (x=0.4, y=0.8)	875 (y=0.2)	0.18 (x=0.4, y=0.2)	3×10 -7 y=0.2) (x=0.4,	4×10 -5 y=0.2) (x=0.4,	900 ℃
	LSCN	15.6	x=0.2, y=0.2	3.16	x=0.4, y=0.2		900℃
	LSCM	x=0.2, y=0.8			2×10 -7		900℃
	LSFN	12.8	x=0.2, y=0.2
	GSCM	24	x=0.2, y=0.1
	BSCF	x=0.5, y=0.2			1.3×10 -4 (900℃)	1×10 -6 (500℃)
	(L0.75S0.25)0.95Cr0.5M0.5				3×10 -8		1000℃

(L-La, S-Sr, C-Co, F-Fe, N-Ni, G-Gd, M-Mn, B-Ba)

Table I .

 I 5. The atoms coordinate of lanthanum-silicon apatite structure

	Coordinate	La1-6h	La2-4f	Si-6h	O1-6h	O2-6h	O3-12i	O4-2a
	x	0.2289	0.3333	0.4020	0.3224	0.5965	0.3443	0
	y	-0.0125	0.6667	0.3718	0.4847	0.4731	0.2549	0
	z	0.2500	-0.0007	0.2500	0.2500	0.2500	0.0701	0.2500
	I.4.2 Electrical properties

Ln9.33+x(SiO4)6O2+3x/2 (Ln = La, Pr and Nd) shows the high oxide ion conductivities by the initial work of Nakayama et al.

Table I .

 I 6. The undoped ionic conductivities of lanthanum silicates reported in literature

	Formula	La10(SiO4)6O3	La9.67(SiO4)6O2.5 La9.60(SiO4)6O2.4 La9.56(SiO4)6O2.34	La9.33(SiO4)6O2
	Conductivity	1.8×10 -4 S/cm	1.3×10 -3 S/cm	6×10 -4 S/cm	1.4×10 -3 S/cm	1.5×10 -4 S/cm

Table I .

 I 7. The apatite type LSO electrical properties doped by various elements

	Doping site	formulas	Activation energy	Ionic conductivity (500°C)
		La8.67Ba(SiO4)6O2	0.67	1.1×10 -4
		La8.67Sr(SiO4)6O2	0.87	8.3×10 -5
		La8.67Mg(SiO4)6O2	1.13	3.6×10 -6
	La site
		La8.33Mg1.5(SiO4)6O2	1.23	1.2×10 -6
		La8.67Ca(SiO4)6O2	0.86	5.8×10 -5
		La9Mg0.5Si6O26	0.98	2.1×10 -5
		La8.67Ga0.5Si5.5O26	0.67	4.6×10 -4
		La10GaSi5O26	0.70	2.4×10 -3
		La10BSi5O26.5	0.68	1.1×10 -3
	Si site	La9.67Si5.5Mg0.5O26	0.67	3.0×10 -3
		La9.60(GeO4)6O2.4	1.03	2.0×10 -3*
		La9.55(GeO4)6O2.32	0.99	1.6×10 -3*
		La9.33(GeO4)6O2	/	2.9×10 -3*
	La and Si site La9.33Mg0.5Si5.5Mg0.5O26	0.80	1.0×10 -4

  Table II.1.

	II 2.3 Microstructure
	Table II. 1. The PDF files of the compounds involved in this work
	Compounds	Formula	Ref. code
	Lanthanum silicate	La9.33Si6O26	00-049-0443
	Lanthanum silicate	La2SiO5	00-040-0234
	Lanthanum silicate	La10Si6O27	00-053-0291
	Lanthanum oxide	La2O3	00-022-0641
	Quartz	SiO2	01-080-2148

Table II

 II

	. 2. Some elements' characteristic X-ray energy for EDX characterization
	Elements	C	O	Si	Sr	La
	X-ray energy				Kα 14.140	Lα 4.650
		Kα 0.277	Kα 0.525	Kα 1.739
	(keV)				Lα 1.806	M 0.833
	II 2.4 Conductivity

  𝐻 ̂is the Hamiltonian operator, Ψ a wave function, and E the energy. The wave function C is a function of the electron and nuclear positions. As the name implies, this is the description of an electron as a wave. The Hamiltonian operator 𝐻 ̂ is, in general,

	where 𝐻 ̂= -∑	𝑁 𝛼=1	{ 2𝑀 𝛼 ℏ 2	∇ 𝛼 2 }	-∑ { 2𝑚 𝑖 ℏ 2 𝑛 𝑖=1	∇ 𝑖 2 }	-∑	𝛼,𝑖	𝑍 𝛼 𝑒 2 𝑟 𝑎𝑖	+ ∑	𝛼,𝛽≠𝛼	𝑍 𝛼 𝑍 𝛽 𝑒 2 𝑅 𝑎𝛽	+ ∑	𝑖,𝑗≠𝑖	𝑒 2 𝑟 𝑖𝑗	EQN II.9
	where ∇ 𝑖/𝛼 2 is the Laplacian operator acting on particles of electrons/nuclei. M/m is the mass of
	the particles.
	It can be simply expressed focusing on the expression of energy,
					𝐻 ̂= 𝑇 ̂𝛼 + 𝑇 ̂𝑒 + 𝑉 ̂𝛼𝛼 + 𝑉 ̂𝛼𝑒 + 𝑉 ̂𝑒𝑒				EQN II.10
	Where,
	The Schrödinger equation, shown in EQN II.8, was devised as an equivalent formulation of
	QM and it is the basis for nearly all computational chemistry methods.
							𝐻 ̂𝛹 = 𝐸𝛹						EQN II.8

𝑇 ̂𝛼, 𝑇 ̂𝑒 -Kinetic energies of the electrons and nuclei; 𝑉 ̂𝛼𝛼 , 𝑉 ̂𝛼𝑒 , 𝑉 ̂𝑒𝑒 -Potential energy of nuclei-nuclei, electrons-nuclei, electrons-electrons interaction;

  . 1. Experimental ionic conductivities and activation energy of Ge, Sr substitution LSO apatite. (La10-xSrx(Si,Ge)6 in the table represents La10-xSrx(Si,Ge)6O27-0.5x for short, similarly hereinafter)

Table III .

 III 2. The atoms coordinate of lanthanum-silicon apatite structure

	Coordinate	La1	La2/Sr	Si/Ge	O1	O2	O3	O4
	X	0.2289	0.3333	0.4020	0.3224	0.5965	0.3443	0
	Y	-0.0125	0.6667	0.3718	0.4847	0.4731	0.2549	0
	Z	0.2500	-0.0007	0.2500	0.2500	0.2500	0.0701	0.2500
	III.3 Sr-doped LSO study
	III.3.1 electronic properties

Table III

 III

	. 3. Calculated and experimental lattice constants and internal parameters of LSOs
				and LGO
		Experiment		This work	Previous calculations
		a/Å	c/Å	a/Å	c/Å	a/Å	c/Å
	(La10Sr0)Si6 9.7248/9.7173 7.1895/7.1800 9.6759 7.1889 9.7607 7.1189
	(La9Sr1)Si6	9.7072	7.1979	9.6924 7.1918 /	/
	(La8Sr2)Si6	9.7083	7.2377	9.6760 7.2341 9.8053 7.1558
	(La10Sr0)Ge6 9.910	7.270	9.9036 7.3420 /	/

Table V .

 V The ratio between the number of moles of the (EG+CA) mixture to that of (La 3+ + Sr 2+ ) equals one. TEOS is first added in a stirred solution of Sr(NO3)2 in deionized water and the mixture is added under stirring into the above (EG+CA) solution. During the process of sol formation, the pH value is controlled around 4~6 (we had studied the influence of pH value in previous work). The sols obtained are dried at 120-150°C, yielding dry gels. These are 1. XRD analyses of powders obtained with different Sr doping ratios and calcination temperatures

	2 Optimized synthesis study V.2.1 Calcination study Based on the discussion, the La10-xSrxSi6O27-0.5x (x=0, 1, 2) apatites are synthesized through the water-based sol-gel technique using La(NO3)3•6H2O, Sr(NO3)2 and TEOS (tetraethyl orthosilicate) as raw materials. Ethylene glycol (EG) and citric acid (CA) were used -in equimolar ratio -as they are reputed to generate good quality sols according to the Pechini 1000℃ for 2h with a heating rate of 10℃/min and are finally freely cooled. Table V.1 shows the XRD analyses of different "groups" of powders synthesized using different doping ratios and calcination temperatures. We call hereafter Group 1, Group 2 and Group 3 the synthesized LSO apatites having the respective molar Sr/La ratio of: 0, 1:9 and 2:8, each group comprising three "individual materials" that have been calcined at 800, 900 and 1000°C respectively. Solution status Expected products formulas Sintering parameters Tag in this study XRD analysis results Group 1 Clear and jelly-like La10Si6O27 800℃-2h 800-1 Apatite structure 900℃-2h 900-1 1000℃-2h 1000-1 Group 2 La9SrSi6O26.5 800℃-2h 800-2 900℃-2h 900-2 1000℃-2h 1000-2 Group 3 La8Sr2Si6O26 800℃-2h 800-3 900℃-2h 900-3 process. compacted at 200 MPa for 30s, calcined in air at different temperatures:800℃, 900℃ and 1000℃-2h 1000-3

Table V .

 V 2. Composition estimates based on the results of EDS

	Group 1	Series	unn. C [wt.%]	norm. C [wt.%]	Atom. C [at.%]	Approximated formula
	Oxygen (O)	K-series	18.13	18.88	57.85
	Silicon (Si) Lanthanum (La) L-series K-series	9.32 68.59	9.70 71.42	16.94 25.21	La10Si6.71O22.9
		Total	96.04	100.00	100.00
	Group 2	Series	unn. C [wt.%]	norm. C [wt.%]	Atom. C [at.%]	Approximated formula
	Oxygen (O)	K-series	20.74	21.42	61.18
	Silicon (Si)	K-series	9.37	9.68	15.75
	Strontium (Sr)	L-series	2.02	2.08	1.09	La9Sr0.45Si6.14O25.1
	Lanthanum (La) L-series	64.71	66.82	21.98
		Total	96.84	100.00	100.00
	Group 3	Series	unn. C [wt.%]	norm. C [wt.%]	Atom. C [at.%]	Approximated formula
	Oxygen (O)	K-series	15.47	15.61	51.01
	Silicon (Si)	K-series	10.97	11.07	20.60
	Strontium (Sr)	L-series	3.55	3.58	2.13	La8Sr0.65Si6.29O15.5
	Lanthanum (La) L-series	69.12	69.74	26.25
		Total	99.10	100.00	100.00
	V.2.3 Conductivity study

Table V .

 V 3. Density and conductivity properties of the LSOs obtained after sintering

	Samples	Calcination Temp.-time	Sintering Temp.-time	Density (g•cm -3 )	Conductivity (mS•cm -1 ) 400 600 800	Ea (eV)
	La10Si6O27 (Gtoup1)	800℃-2h 900℃-2h 1000℃-2h		3.44 3.51 4.20	0.0146 0.0128 0.0108	0.459 0.030 0.312	N/A 0.233 45.0	1.84 1.49 1.38
	La9Sr1Si6O26.5 (Gtoup2)	800℃-2h 900℃-2h 1000℃-2h	1500℃-2h	3.53 3.57 4.44	0.0026 0.0230 1.11	0.0146 0.068 38.3	0.095 1.04 N/A	1.41 1.46 1.49
	La8Sr2Si6O26 (Gtoup3)	800℃-2h 900℃-2h 1000℃-2h		4.62 4.79 4.89	4.35E-5 9.93E-4 6.13E-3 2.13 1.323E-4 3.01E-3 1.77E-2 1.81 6.67E-4 1.67E-2 0.115 1.43

xSrx(Si,Ge)6O27-0.5x in SOFC were investigated using DFT calculation. Sr-doping at La site has

II.3.2.6 Solving equations

To solve the equations of Kohn-Sham, a basic status has been chosen to represent the electron density ρ (r), the potential V (r) and Kohn Conveniently, the value of forces on the atoms can be get at the end of each self-consistent electronic cycle and use of conjugate gradient algorithms, for minimizing the energy and determining the optimum geometry or performing the calculations molecular dynamics.

II.3.3 The pseudopotentials

The pseudopotential is used as an approximation for the simplified description of complex systems. It is an attempt to replace the complicated effects of the motion of the core (i.e. non- The Vienna Ab initio Simulation Package (VASP) [57] is a computer program for atomic scale materials modelling, e.g. electronic structure calculations and quantum-mechanical molecular dynamics, from first principles. It computes an approximate solution to the many-body Schrödinger equation, either within density functional theory (DFT), solving the Kohn-Sham equations.

In our work, the VASP is adopted to study the structural and electronic properties, including the Fermi energy, the density of states, band structure etc., of the Sr, Ge doped apatite-type lanthanum silicates LSO. This code is known for good parallelization which authorizes the calculation on more than one hundred atoms systems. It provides accuracy and efficiency for computer simulation ab initio and for these reasons it has become a widely used code.

In this chapter, we present the ab-initio calculation on Sr, Ge-doped lanthanum silicates LSO.

The calculation is based on the density functional theory (DFT) with the code VASP. Two S.O.T. Ogaji et al [1] reported that both computation methods and novel approaches based on artificial intelligence techniques can provide similar accuracy in the modeling of a SOFC. The operating voltage, the operating efficiency, the power output and the temperature generated of fuel cells are evaluated with this simulation method. However the prediction of the materials characteristics with this method is relatively rare in the literatures.

Finite element methods [2] and finite volume methods [3] are employed to analyze thermal pressing, electrochemical oxidation of fuel composition and some output characteristics of a SOFC. It is demonstrated to be an efficient way to predict and evaluate the performance of a SOFC system. Molecular dynamic is a numerical simulation method for the physical/chemical phenomena in complex systems, which may involve thermal management, mass and charge transport, together

In addition, the activation energy of Ge substitution LGO apatite is calculated under the same conditions. Figure III.12 (a) shows the calculation results. Relatively high total energy is presented in this group which means that LGO structure has a lower stability compared to LSO.

The activation energies of each group are compared in Figure III.12 (b). The activation energy changes slightly when Ge totally substitutes Si positions. Thus, calculations for different Ge doping ratios are not useful. However, the Sr doping effect on the activation energy seems more significant. Indeed, more Sr doping ratio leads to higher activation energy, which is not suitable for electrolyte performances in SOFC. This phenomenon is also consistent with the experimental results (shown in Table III.1). It also can be noted that the doping effect is more significant for the substitution at La 6h position (near the migration channel) than that at La 4f position (far from the migration channel). The Sr doping actually affects the migration channel and the results depend on the distance to the channel. However, Ge effect, covered by Ge-O tetrahedron, is not obvious even all Si positions are substituted by Ge.

III.6 Influence of doping positions on lattice parameters

From the calculation results, the two doping positions show different effects on the ionic conductivity. Based on the structure optimization results, the atom positions of each material and lattice parameter are obtained. The modeling results of XRD patterns for different dopant been discussed and the calculation results are in good agreement with the experimental results.

The ionic conductivity has been correlated with the Fermi level. This latter decreased sharply as the Fermi level moves to lower energies with Sr substitution which is the main factor that affects ionic conductivity. The activation energy is also simulated by the energy barriers along the migration channel. The effect of Sr doping on the activation energy is clear and the decrease is more obvious while the doping position is near to the migration channel. As to Ge doping, the affects slightly both activation energy and DOS diagram.

stirring continuously. Once the reaction is completed, the suspension is filtrated to obtain the calcination precursors. The precursors are calcined with the temperature from 700℃ to 1100℃ for 6h. After the characterization to identify the product, they are sintered with 1500℃ for 2h to densify the samples for SOFC application.

IV.1.2 Co-precipitation process and calcination

The pH and temperature value is closely monitored during synthesis process. Table IV The temperature is controlled at about 40~60℃ to accelerate the reaction and it is also found that the pH value keeps little change during the reaction, thus the reaction is complete of each drop arrives the ammonia solution , meanwhile it takes place as planned. boundaries contributions. For the pellet annealed at 1000°C, the capacity is of the order 10 - 11 F.cm -1 , in this case the ionic conductivity is controlled by the grain contribution [3].

Nevertheless, this analysis indicates that the poor conductivity of the pellet most probably originates from an interfacial blocking effect and/or the presence of the impurity phase. This section presents the attempt to prepare LSO powders by molten salt method for solid electrolyte application. According to the report of Buyin LI et al., [6] the reactants in the molten salt have a high reactivity and mobility, and react easily and completely, which can greatly reduce the synthesis temperature. Moreover the product powders have a better uniformity and fewer agglomerates. They successfully synthesized LSO powders with pure apatite phase at relatively low temperature of 900℃.

In order to further reduce the synthesis temperature, multiple salts as flux are employed in our investigation.

-NH4NO3

Considering the low melting point of NH4NO3 (Tmp=140℃), it is adopted as flux of the first attempt. Figure IV.16 gives the flow chart of this molten salt method. In order to ensure all the precursor easy to melting, lanthanum nitrate (La(NO3)3• 6H2O) and metadisilicic acid [7] (SiO2• 0.5H2O) were employed in this method. The mixed salts were melted at 180℃ for 4h.

After washing, filtering, the residue is dried as the target product. In this chapter, the synthesis process of Sr-doped La10Si6O27 through optimizing a water-based sol-gel method is studied. The relevant synthesis parameters have been investigated to get pure, highly crystalline powders. The mechanisms occurring in the sol-gel reactions are discussed.

Pure apatite powders have been obtained by calcination from a temperature as low as 800℃ for 2h and they have considerable performance as electrolyte material in IT-SOFC.

V.1 Parameters investigation

The influences of multiple elements doping were studied to modify the apatite La10Si6O27 performance as an electrolyte. Generally elements Ge, Mn, Al, Fe, etc [1][2][3][4][5] are chosen to dope at Si site. Sr has been chosen as suitable element doping at La site due to the similar chemical properties with La.

V 1000℃, with a heating ramp of 10℃/min and then freely cooled (step4). A final sintering (step 5) was performed at a temperature up to 1500℃ for 2h in order to obtain densified LSO.

In this work, the doping ratios of Sr, which occupies some La sites, were set as Sr/La = 0/10, 1/9 and 2/8 by atom, leading to three distinct "groups" of apatites having the theoretical formulas: La10Si6O27 (undoped), La9SrSi6O26. The influence of different doping positions on the apatite materials La10-xSrx(Si,Ge)6O27-0.5x in SOFC were investigated using DFT calculation. Sr-doping at La site has been discussed and the calculation results are in good agreement with the experimental results. We firstly discussed the relationship between the microscopic electronic properties and macroscopic electric performances. The ionic conductivity has been correlated with the Fermi level. This conductivity decreased sharply as the Fermi level moves to lower energies with Sr substitution which is the main factor that affects ionic conductivity.

The activation energy is also simulated by the energy barriers along the migration channel. The effect of Sr doping on the activation energy is clear and the decrease is more obvious while the doping position is near to the migration channel. However, Ge doping affects deeply electrons distribution rather than both activation energy and DOS diagram.

Lanthanum silicate oxides with and without Sr-doping have been synthesized using a facile, water-based sol-gel method for potential applications as oxygen ion conducting electrolytes in apatite and (ii) A. Orera et al who showed that the ionic conductivity decreases from 1×10 -2 to 2.6×10 -7 S•cm -1 at 800℃ when passing from the La9SrSi6O26.5 to the La8Sr2Si6O26 apatite. As for the calcination step, a high calcination temperature helps to improve the ionic conductivity, nevertheless this influence is not so marked. Further work should be carried out to accurately identify the doping ratio that yields the best conduction performance.

In addition, alternatives synthesis routes have been investigated: molten salts, HDP and coprecipitation. While the molten salts route led to major difficulty resulting from the high reactivity of lanthanum with chloride and sulfate ions, the precipitation routes are proved more promising: the HDP (homogeneous deposition precipitation) method could be improved by using the extremely divided silica (e.g. colloidal SiO2 obtained by fresh precipitation) and the co-precipitation could be revisited while exploring the effect of temperature and pH. These alternatives synthesis ways are worth further experimental work.

For the co-precipitation method, the apatite phase composition is obtained from quite moderate temperature of 700℃ for 6h. After the densification process of 1500℃ for 2h, the samples exhibit acceptable performance of ionic conductivity of 7.73 mS.cm -1 at 675°C. This novel method is worth to development due to it is facile to implement and low cost.

In the meantime, there are several issues that are particularly interesting to the current study, which can be further investigated:

For the simulation work, the further work can focus on the molecular dynamic calculation to confirm the oxygen ion migration pathway in the crystal structure. At the same time, it can precise the DFT activation energy calculation. In addition, more elements doping can be applied in this simulation work to predict the electric performance which is possible to reduce the experimental cost.

It is worthy to assemble the electrodes to a complete cell for the Sr-doping LSO samples obtained by sol-gel method. The considerable conductivity performance makes them to be alternatives of the current commercial electrolytes.

The co-precipitation method for Sr, Mn doping LSO should be developed with the introduction of dispersant, which may effectively reduce the agglomeration rate in the precipitation process.

Thus, it is possible to acquire the pure phase, well doped LSO. This modification is possible to extend to the homogeneous deposition precipitation (HDP) method.

Annex

Abstract:

The Solid Oxide Fuel Cell (SOFC) defined by its ceramic and oxide electrolyte, is an electrochemical energy conversion device that produces electricity directly from the chemical reaction of fuel. Nowadays, apatite type rare earths silicates and germaniums attract many interests as the solid electrolyte due to the superior transport properties with high ionic conductivity and low activation energy. They can operate stably at intermediate temperature over a wide oxygen partial pressure range and maintain excellent performances, being considered as a candidate for IT-SOFC electrolytes. Among this series of conductors, the La-Si-O type has a higher conductivity and the performance would be modified by different doping elements.

The objective of this thesis is to study the effects of element substitution/doping and synthesis methods on the structural and conductivity properties of apatite type lanthanum silicates. In this study, we use a double approach: a simulation approach and an experimental approach to optimize the electrolyte materials purity and performance.

Using simulation approach, a first principle calculation based on DFT (Density Functional Theory) was carried out to investigate the effect on doping positions: Sr dopant at La position and Ge dopant at Si position. The calculation results give a connection to the ionic conductivity obtained by experiments.

With experimental approach, we present the synthesis and characterization of Sr-doped La10Si6O27 (LSO) prepared through an optimized water-based sol-gel process. The results show that the ionic conductivity is thermally activated and values lies between 4.5×10 -2 and 1×10 -6 Scm -1 at 873 K as a function of the composition and powder preparation conditions.

KEY WORDS: apatite type lanthanum silicates; sol-gel; co-precipitation; DFT calculation; SOFC; electrolyte

Ré sumé :

Les piles à combustibles à électrolyte solide de type SOFC permettent de transformer directement l'énergie de la réaction chimique de formation de l'eau à partir de l'hydrogène et de l'oxygène, en énergie é lectrique. De nos jours, les apatites de type silicates de terres rares présentent beaucoup d'intérêt comme électrolyte solide en raison de leurs propriétés de transport élevé es avec une forte conductivité ionique et une faible é nergie d'activation. Ils peuvent fonctionner de maniè re stable à une tempé rature intermé diaire sur une large plage de pression partielle d'oxygè ne en maintenant d'excellentes performances. Ils sont ainsi considé ré s comme de bons candidats pour les é lectrolytes de piles de type IT-SOFC. Parmi cette sé rie de conducteurs, le type La-Si-O possè de une conductivité plus é levé e et leur performance serait modifié e par diffé rents é lé ments dopants.

L'objectif de cette thè se est d'é tudier les effets des é lé ments de substitution / dopage ainsi que les mé thodes de synthè se sur les proprié té s structurales ainsi que sur la conductivité des apatites de type silicates de lanthane. Dans cette é tude, nous utilisons une double approche: une approche de simulation et une approche expé rimentale pour optimiser la pureté et les performances des maté riaux d'é lectrolyte.

Dans l'approche de simulation, le calcul basé sur la DFT (Thé orie de la fonctionnelle de la densité ) a é té ré alisé en vue d'étudier l'effet des positions de dopage: dopant Sr à La position de La et dopant Ge à la position de Si. Les ré sultats obtenus par le calcul concernant la conductivité ionique sont en bon accord avec ceux obtenus par l'expérience.

Avec l'approche expérimentale, nous présentons la synthèse et la caractérisation de La10Si6O27 (LSO) dopé par Sr et é laboré par des procé dé s sol-gel optimisé s. Les ré sultats montrent que la conductivité ionique est activé e thermiquement avec des valeurs comprises entre 4,5 × 10 -2 et 1 × 10 -6 S• cm -1 à 873 K et dépend des conditions d'élaboration et de la composition de la poudre.

Mots Clé s : apatite de type silicates de lanthane, procé dé s sol-gel, co-pré cipitation, DFT, pile SOFC, é lectrolyte.