Laura Lander

Gwenaëlle Rousse

Dmitry Batuk

Claire V Colin

Daniel Alves

Dalla Corte

Jean-Marie Tarascon
email: jean-marie.tarascon@college-de-france.fr

Synthesis, structure and electrochemical properties of K-based sulfates

Keywords: Langbeinite K2Fe2(SO4)3, sulfates, Cu-based polyanionic compounds, diffusion properties, K2Cu2(SO4)3, fedotovite K2Cu3O

teaching and research institutions in France or abroad, or from public or private research centers.

Introduction

Over the last few years, sustainability has become an overriding factor in the search for new electrode materials. The discovery of the electrochemical activity of LiFePO4 vs. Li + /Li° back in 1997 was an impetus to further explore polyanionic materials for battery applications. [START_REF] Padhi | Mapping of Transition Metal Redox Energies in Phosphates with NASICON Structure by Lithium Intercalation[END_REF][START_REF] Masquelier | Phosphates, Silicates, Sulfates) Frameworks as Electrode Materials for Rechargeable Li (or Na) Batteries[END_REF] In this context, the finding of tavorite and triplite LiFeSO4F with potentials of 3.6 V and 3.9 V vs. Li + /Li 0 was an important step forward. [START_REF] Barpanda | A 3.90 V Iron-Based Fluorosulphate Material for Lithium-Ion Batteries Crystallizing in the Triplite Structure[END_REF][START_REF] Ati | Understanding and Promoting the Rapid Preparation of the Triplite -Phase of LiFeSO4 F for Use as a Large-Potential Fe Cathode[END_REF][START_REF] Ati | Synthesis and Electrochemical Properties of Pure LiFeSO4F in the Triplite Structure[END_REF] Owing to the attractive electrochemical performances of the LiFeSO4F polymorphs further research efforts were undertaken to stabilize novel "FeSO4F" frameworks for Li + and Na + insertion. This led to the discovery of orthorhombic and monoclinic KFeSO4F, which form new polymorphic "FeSO4F" host structures upon K + extraction. [START_REF] Recham | Preparation and Characterization of a Stable FeSO4F-Based Framework for Alkali Ion Insertion Electrodes[END_REF][START_REF] Ling | Mechanistic Study of the Electrochemical Extraction of K + from KFeSO4F[END_REF][START_REF] Lander | Electrochemical and Magnetic Properties of a Novel KFeSO4F Polymorph[END_REF] Among them, the orthorhombic "FeSO4F" phase displayed appealing cycling behavior towards Li and Na. This approach was further extended to phosphate-based phases such as KVPO4F. [START_REF] Fedotov | A 4 V Cathode Material for High-Power Rechargeable Batteries[END_REF] Bearing this in mind, we embarked on the search of new sulfate-based host structures, which could uptake alkali cations. We focused our attention on various A2Fe2(SO4)3 phases with A=Li, Na, K that present polymorphic "Fe2(SO4)3" frameworks. Li2Fe2(SO4)3 crystallizes in the Nasicon and anti-Nasicon structures, both displaying a potential of 3.6 V vs. Li + /Li 0 , while Na2Fe2(SO4)3 presents the alluaudite-type structure with a potential of 3.8 V vs. Na + /Na 0 . [START_REF] Manthiram | Lithium Insertion into Fe2(SO4)3 Frameworks[END_REF][START_REF] Wu | New-Type Low-Cost Cathode Materials for Li-Ion Batteries: Mikasaite-Type Fe2(SO4)3[END_REF][START_REF] Barpanda | A 3.8-V Earth-Abundant Sodium Battery Electrode[END_REF][START_REF] Oyama | Sodium Intercalation Mechanism of 3.8 V Class Alluaudite Sodium Iron Sulfate[END_REF] Another "Fe2(SO4)3" framework is based on the family of the langbeinite phases having the general composition A2M2(SO4)3, with A = K, NH4, Rb, Tl and M = Mg, Mn, Ni, Zn, Ca, Fe, Cd and Co. The langbeinite compounds are derived from the mineral K2Mg2(SO4)3 and have been vastly studied for their physical properties including antiferromagnetic spin-ordering, electrooptical effects as well as ferroelectric and ferroelastic features. [START_REF] Zemann | Die Kristallstruktur von Langbeinit, K2Mg2(SO4)3[END_REF][START_REF] Oelkrug | The Magnetic Structure of the Langbeinite K2Mn2(SO4)3[END_REF][START_REF] Emmenegger | Crystal Growth and Electro-Optic Effect of Some Double Sulfates with the Langbeinite Structure[END_REF][START_REF] Hernández-Rodríguez | Optical Birefringence Imaging of the Phase Transition of K2Mn2(SO4)3[END_REF][START_REF] Speer | Phase Transitions in Langbeinites I: Crystal Chemistry and Structures of K-Double Sulfates of the Langbeinite Type M2 2+ K2(SO4)3, M 2+ = Mg, Ni, Co, Zn, Ca[END_REF][START_REF] Windhaus | Moessbauer Studies of Fe 2+ in Iron Langbeinites and Other Crystals with Langbeinite Structure[END_REF][START_REF] Abrahams | Piezoelectric Langbeinite-Type K2Cd2(SO4)3: Room Temperature Crystal Structure and Ferroelastic Transformation[END_REF][START_REF] Abrahams | Piezoelectric Langbeinite-Type K2Cd2(SO4)3 Structure at Four Temperatures below and One above the 432°K Ferroelastic-paraelastic Transition[END_REF] However, to the best of our knowledge, their electrochemical properties have not been reported so far. Hence our goal was to explore the feasibility of preparing a stable langbeinite "Fe2(SO4)3" framework upon K + extraction from K2Fe2(SO4)3. Moreover, through the investigation of other langbeinite A2M2(SO4)3 phases, we have isolated a new K2Cu2(SO4)3 member that presents a noticeably different crystal structure as compared to cubic K2Fe2(SO4)3. This phase shows limited electrochemical activity and transport properties. It is thermally unstable and decomposes to form the fedotovite oxysulfate K2Cu3O(SO4)3 above 320°C. Lastly, we examined the possibility of long range magnetic ordering of Cu 2+ in K2Cu2(SO4)3 and K2Cu3O(SO4)3 via low-temperature neutron diffraction experiments.

Experimental part

Laboratory X-ray diffraction (XRD) patterns were recorded with a Bruker D8 Advance diffractometer equipped with a copper source (λCu-Kα1 = 1.54056 Å, λCu-Kα2 = 1.54439 Å) and a LynxEye detector. For high temperature XRD experiments, the diffractometer was equipped with an Anton Paar HTK1200N furnace. Synchrotron X-ray diffraction patterns were measured in transmission mode (the powder was placed in a Ø=0.7 mm capillary sealed under argon), with a wavelength of =0.4141 Å at the 11BM beam line at Argonne National Lab. Neutron powder diffraction (NPD) experiments were performed on the D1B powder diffractometer at the Institut Laue Langevin, with a wavelength of 2.529 Å and with the powder placed in a Ø=6mm vanadium can. The recorded patterns were refined using the Rietveld [START_REF] Rietveld | A Profile Refinement Method for Nuclear and Magnetic Structures[END_REF] method as implemented in the FullProf 23,[START_REF] Rodriguez-Carvajal | Recent Advances in Magnetic Structure Determination by Neutron Powder Diffraction[END_REF] program. Bragg peak indexation and structure determination were performed with help of the Dicvol [START_REF] Boultif | History of the Dichotomy Method for Powder Pattern Indexing[END_REF][START_REF] Boultif | Indexing of Powder Diffraction Patterns for Low-Symmetry Lattices by the Successive Dichotomy Method[END_REF] and Fox [START_REF]Free Objects for Crystallography Wiki[END_REF][START_REF] Favre-Nicolin | free Objects for Crystallography': a Modular Approach to Ab Initio Structure Determination from Powder Diffraction[END_REF] programs.

For transmission electron microscopy measurements, a FEI Tecnai G2 electron microscope operated at 200 kV was used. For the measurement, the sample was prepared in an Ar-filled glove box by grinding the powder in a mortar in anhydrous hexane and depositing drops of suspension onto holey carbon grids. The sample was transported to the microscope column completely excluding contact with air.

Electrochemical tests were conducted in Swagelok-type cells assembled in an argon-filled glovebox and cycled in a galvanostatic operating mode using a VMP system (Biologic S.A., Claix, France). Lithium metal was used as the negative electrode and the working electrode consisted of a composite of the active material and Carbon SP (Csp) (80:20 wt %), prepared by ball-milling for 15 min in a Spex 8000 miller. The negative and the positive electrode were separated by a Whatman GF/D borosilicate glass fiber sheet saturated with 1 M LiPF6 in EC:DMC (1:1 weight ratio) (LP30).

A.c. impedance measurements were performed with a Bio-Logic MTZ-35 Impedance Analyzer, in a frequency range of 1 MHz to 0.1 Hz and with an excitation voltage of 100 mV. The measurements were done under argon at various stabilized temperatures ranging from 100 to 450°C.

Results

a) Synthesis and Electrochemistry of K2Fe2(SO4)3

In previous reports, langbeinite K2Fe2(SO4)3 was prepared from an aqueous solution of K2SO4 and FeSO4. [START_REF] Windhaus | Moessbauer Studies of Fe 2+ in Iron Langbeinites and Other Crystals with Langbeinite Structure[END_REF][START_REF] Gattow | Über Doppelsulfate Vom Langbeinit-Typ A2+B 2+ (SO4)3[END_REF] Herein, we simply prepared this phase by ball-milling stoichiometric amounts of K2SO4 and anhydrous FeSO4 with a Spex 8000 vibratory miller for 1 h. The powders were placed in a hermetic stainless-steel jar filled in an argon dry box. A ball-to-powder weight ratio of ~30 was used. Afterwards, the composite mixture was annealed at 400 °C for 7 h under argon atmosphere to produce a single phase powder as deduced by X-ray diffraction (XRD).

The Rietveld refinement [START_REF] Rietveld | A Profile Refinement Method for Nuclear and Magnetic Structures[END_REF][23][START_REF] Rodriguez-Carvajal | Recent Advances in Magnetic Structure Determination by Neutron Powder Diffraction[END_REF] of as-prepared K2Fe2(SO4)3 was performed with an initial structural model constructed from K2Mn2(SO4)3, [START_REF] Oelkrug | The Magnetic Structure of the Langbeinite K2Mn2(SO4)3[END_REF] where Mn was replaced by Fe, and all atoms were freely refined. The final refinement is shown in Figure 1a and indicates that K2Fe2(SO4)3 and K2Mn2(SO4)3 are isotructural. K2Fe2(SO4)3 crystallizes in a cubic unit cell with lattice parameter a = 10.00476(4) Å. The structure, described in space group P213, consists of isolated FeO6 octahedra (blue) that are connected to six SO4 tetrahedra (light blue) via their oxygen (grey) vertices (Figure 1b). The K1 and K2 atoms, which are eight-and six-fold coordinated, respectively, are located in the large cavities of the Fe2(SO4)3 framework. The structural data, including a bond valence sum analysis, [START_REF] Bronw | Bond-Valence Parameters Obtained from a Systematic Analysis of the Inorganic Crystal Structure Database[END_REF] is summarized in Table 1. Electrochemical tests were conducted in Swagelok-type cells with a lithium anode and a cycling regime of C/20 (1C equals the uptake or removal of 1 Li + in 1 h). A typical compositionvoltage trace is shown in Figure 2a. On charge, we observe a pseudo-plateau at around 3.9 V vs. Li + /Li 0 and a flat plateau at ~4.1 V vs. Li + /Li 0 , each accounting for approximately 0.2 K + . On discharge, however, only ~0.2 Li + can be reinserted resulting in merely 10 % of the theoretical capacity (129 mAh/g) of K2Fe2(SO4)3. Further optimization trials of the cathode material (e.g. longer ball-milling, higher Csp content) did not improve the electrochemical performance.

To further check the extend of potassium removal, we conducted chemical oxidation of K2Fe2(SO4)3 using NO2BF4 as oxidizing agent in acetonitrile under reflux (~ 80°C) for times ranging from 5 hours to 2 days. XRD of the resulting K2-xFe2(SO4)3 compound indicates a minor shift of the Bragg peaks (Figure 2b, blue pattern), as well as a tiny amount of KBF4 (peak marked with asterisk), resulting from the reaction of NO2BF4 with the extracted K + . However, its amount did not increase with increasing reaction time, thus confirming the difficulties of K + extraction encountered during the electrochemical cycling. Lastly, the neat superimposition of the XRD patterns of the K-deficient samples (Figure 2b) prepared by chemical and electrochemical oxidation indicates that the same amount of K + is extracted for both routes and it is limited to values lower than ~0.4 K + per formula unit (see voltage-composition trace, Figure 2a). In addition to the poor reversibility observed during the electrochemical discharge, the existence of large voltage polarization suggests sluggish diffusion kinetics. This does not come as a surprise given the high percolation energy of 7.8 eV as calculated by the Bond Valence Energy Landscape (BVEL) approach (described in detail in SI; Figure SI1a). 23,[START_REF] Adams | From Bond Valence Maps to Energy Landscapes for Mobile Ions in Ion-Conducting Solids[END_REF] This value exceeds by far the BVEL percolation energies of other sulfate-based materials (~0.5 -3 eV) [START_REF] Lander | Electrochemical and Magnetic Properties of a Novel KFeSO4F Polymorph[END_REF][START_REF] Sun | 2Cu2O(SO4)2: A Possible Electrode for Sustainable Li-Based Batteries Showing a 4.7 V Redox Activity vs Li + /Li 0[END_REF][START_REF] Lander | Unveiling the Electrochemical Mechanisms of the Li2Fe(SO4)2 Polymorphs by Neutron Diffraction and Density Functional Theory Calculations[END_REF] , hence indicating a hampered K + diffusion. Problems during K + extraction were previously assessed for langbeinite K2TiV(PO4)3, where chemical oxidation failed to remove K + . [START_REF] Rangan | New Titanium-Vanadium Phosphates of Nasicon and Langbeinite Structures, and Differences between the Two Structures toward Deintercalation of Alkali Metal[END_REF] Moreover, it was reported that Li + and Na + are too small to generate a stable langbeinite framework. [START_REF] Gattow | Über Doppelsulfate Vom Langbeinit-Typ A2+B 2+ (SO4)3[END_REF] This statement is also confirmed by our unsuccessful trials to prepare langbeinite A2Fe2(SO4)3 with A=Li or Na using a variety of precursors and methods as well as ionic substitution of K2Fe2(SO4)3 with LiNO3 and NaNO3. In short, these results show that K2Fe2(SO4)3 is not a suitable electrode material. Aside from Fe-based sulfate compounds, we recently demonstrated the feasibility to achieve high redox potentials (> 4.6 V vs. Li + /Li 0 ) in Cu-based sulfates/oxysulfates such as Li2Cu2O(SO4)2. [START_REF] Adams | From Bond Valence Maps to Energy Landscapes for Mobile Ions in Ion-Conducting Solids[END_REF] Interestingly, Gattow et al. [START_REF] Gattow | Über Doppelsulfate Vom Langbeinit-Typ A2+B 2+ (SO4)3[END_REF] predicted that the Cu-based homologue of K2Fe2(SO4)3 might present a different crystal structure due to the preferential square-planar coordination of the Jahn-Teller active Cu 2+ . All together this prompted us to explore the possibility of stabilizing K2Cu2(SO4)3 and study its properties.

Phase-pure K2Cu2(SO4)3 was successfully prepared by a two-steps solid-state route. First, stoichiometric amounts of K2SO4 and anhydrous CuSO4 (Alfa Aesar, Reagent Grade), which has been dried under vacuum at 260 °C for 24 h, were ball milled for 4 h in an Ar-filled ball-mill jar

K + extraction Li + insertion a) b)
with a Spex 8000 vibratory miller with a ball-to-powder weight ratio of 25. The obtained mixture was then pressed to a pellet and heated at 300 °C for 20 h under constant argon flow.

The resulting powder consists of particles in the sub-micrometer range (Figure SI2). It is worth mentioning at this point that like most of the alkali-based 3d metal sulfates, K2Cu2(SO4)3 is highly moisture sensitive and decomposes into K2Cu(SO4)2•6H2O and CuSO4•5H2O after solely 8 h of air exposure (Figure SI3). It is therefore important to synthesize and handle K2Cu2(SO4)3

under air-and moisture-free conditions.

In the absence of single crystals, the crystal structure of K2Cu2(SO4 . This cell can accommodate four formulae units (Z = 4). We obtained in total 17 possible space groups that could index the observed reflections. Since no structural model was known for this compound, we performed ab initio structural determination methods for all possible space groups using the Fox [START_REF]Free Objects for Crystallography Wiki[END_REF][START_REF] Favre-Nicolin | free Objects for Crystallography': a Modular Approach to Ab Initio Structure Determination from Powder Diffraction[END_REF] program and compared the obtained structural models to the experimental SXRD data. During this process, the SO4 tetrahedra were treated as rigid groups. Besides the many possible space groups, the large number of atoms further complicated the search for the correct structural model. The only space group, which indexed all the Bragg peaks obtained by SXRD and resulted in a meaningful structure, was P212121. Furthermore, this symmetry is corroborated by the electron diffraction data (collected on an FEI Tecnai G2 microscope). The observed reflection conditions h00: h = 2n; 0k0: k = 2n; 00l: l = 2n are consistent only with the space group P212121 (Figure 3a). The final refinement of K2Cu2(SO4)3 with all atoms freely refined using the Rietveld method as implemented in the FullProf 23,[START_REF] Rodriguez-Carvajal | Recent Advances in Magnetic Structure Determination by Neutron Powder Diffraction[END_REF] program is shown in Figure 3b. The structural data deduced from this refinement are summarized in Table 2. Moreover, for a more accurate refinement of the O positions, we performed neutron powder diffraction on the D1B powder diffractometer, with a wavelength of 2.529 Å. The Rietveld refinement conducted on the NPD pattern is shown in Figure 3b and fully validates the structural model. 5a) presents a limited electrochemical activity (x ~ 0.1) being far from reaching the theoretical capacity of 124 mAh/g. The redox process proceeds via one plateau at 3.4 V vs. Li + /Li 0 and two minor sloping contributions at 3.75 V vs. Li + /Li 0 on charge and between 2.5-2.8 V vs. Li + /Li 0 on discharge that can be also seen on the dx/dV derivative curve (Figure 5b). We observed that charging the Li/K2Cu2(SO4)3 to higher potentials such as 5 V vs. Li + /Li 0 leads to a decomposition of the active material as deduced from traces of elemental copper on the separator of disassembled cells. We further attempted to chemically remove K + from K2Cu2(SO4)3 by oxidation using an excess of NO2BF4 in acetonitrile. Figure 6 compares the XRD patterns of samples recovered from electrochemical cells, which were stopped on charge (purple pattern) and discharge (maroon pattern), respectively, with the pattern of the chemically oxidized (blue pattern) and the pristine (orange pattern) samples. They all look alike with no noticeable shift of the Bragg peaks. However, we observe the formation of KBF4 (peaks marked with asterisk) for the chemically oxidized sample. From a Rietveld refinement (shown in Figure SI4), we could estimate the amount of KBF4 to be 10(4) %, hence implying that ~10 % of K + was extracted, in good agreement with the electrochemical data. To rationalize the poor removal of K + , we calculated the K + diffusion pathways via the Bond Valence Energy Landscape (BVEL) approach (Figure SI1b) and deduced an anisotropic diffusion of K + in this material with percolation energies of 1.59, 2.78 and 6.38 eV along the [100], [010] and [001] directions, respectively. To provide a real meaning to these values, temperaturedependent a.c. conductivity was measured on a sintered K2Cu2(SO4)3 pellet (Ø 10 mm, compactness 82%) between ionically blocking gold electrodes (Figure 7a). The measurements were done under argon at various stabilized temperatures ranging from 100 to 450°C in a frequency range of 1 MHz to 0.1 Hz and with an excitation voltage of 100 mV. A typical collected impedance spectrum (see inset Figure 7a) consists of a low frequency tail indicating that the conductivity is mainly ionic with in addition the presence of two semi-circles corresponding to the bulk contribution (high frequency) and the grain boundary (medium frequency). K2Cu2(SO4)3 presents an activation energy of 1.49 eV as deduced by fitting the a.c. data with the Arrhenius law and an extrapolated room temperature a.c. conductivity of RT = 10 -13 S/cm. Compared to other polyanionic cathode materials such as LiFePO4 and triplite LiFeSO4F, which show activation energies of 0.6 eV and 0.79 eV, respectively, 35,[START_REF] Sun | A Fully Ordered Triplite[END_REF] K2Cu2(SO4)3 presents rather mediocre conductivity in agreement with the observed electrochemical performances. Note the sudden drop of conductivity of K2Cu2(SO4)3 upon heating at around 380 °C suggesting a possible phase transition (Figure 7b). To get more insight into this possible phase transformation, we performed high-temperature in situ XRD measurements (Figure 8), where K2Cu2(SO4)3 was heated under a steady nitrogen flow from 50 °C to 620 °C in 20 °C steps and with a ramp of 5 °C/min and cooled down to 100 °C again. The temperature was held constant at each step during the recording of the XRD pattern (1h). Pristine K2Cu2(SO4)3 is stable until 400 °C and presents only a thermal expansion of the structure. From 420 °C onwards a new peak appears at ~12°, which can be assigned to the mineral fedotovite K2Cu3O(SO4)3. The phase transformation from K2Cu2(SO4)3 to K2Cu3O(SO4)3 is completed at 500 °C, before the irreversible decomposition of K2Cu3O(SO4)3 at 560 °C. The slightly different transition temperatures seen from impedance measurements and in situ XRD are due to differences in heating ramps and heating dwells. The phase transformation, also confirmed by DSC measurements, can be directly visualized through a colour change from light blue for K2Cu2(SO4)3 to dark green for K2Cu3O(SO4)3 (Figure SI5).

c) Synthesis and Structure of K2Cu3O(SO4)3

Fedotovite K2Cu3O(SO4)3 is a volcanic mineral, which was first discovered in Kamchatka, Russia, after a volcano eruption in 1975/1976. [START_REF] Starova | The Crystal Structure of Fedotovite, K2Cu3O(SO4)3[END_REF] It has only been characterized as a natural mineral, but, to the best of our knowledge, has never been obtained synthetically. We thus report here for the first time its synthesis protocol. For the preparation of K2Cu3O(SO4)3, we started either from K2Cu2(SO4)3, which was ball milled for 30 min with an excess of CuO (10 %) (Equation 1), or from the precursors K2SO4, CuSO4 and CuO (Equation 2), which were ballmilled for 45 min. The mixtures were heated at 500 °C for 30-48 h under argon atmosphere.

K 2 Cu 2 (SO 4 ) 3 + CuO → K 2 Cu 3 O(SO 4 ) 3 (1) K 2 SO 4 + CuSO 4 + CuO → K 2 Cu 3 O(SO 4 ) 3 (2)
XRD experiments confirmed the purity of the sample. Rietveld refinements of the SXRD and neutron patterns of synthetically prepared K2Cu3O(SO4)3 were performed using the monoclinic C2/c structural model previously reported by Starova et al. [START_REF] Starova | The Crystal Structure of Fedotovite, K2Cu3O(SO4)3[END_REF] (Figure 9). The obtained structural data is given in Table 3. The slight differences of the lattice parameters of our prepared fedotovite phase (a = 19.09059( 5 Unfortunately, our trials to remove K + from K2Cu3O(SO4)3 (theoretical capacity: 109 mAh/g) failed, regardless of the route (chemical or electrochemical) and conditions we tried.

Nevertheless, since both K2Cu2(SO4)3 and K2Cu3O(SO4)3 compounds are part of the family of S = 1/2 systems, which have been intensively studied for magnetic properties, we wanted to check for a possible transition into a magnetically ordered state. We therefore recorded neutron powder diffraction patterns at temperatures ranging from 1.6 K to 290 K (Figure SI6).

All NPD patterns are superimposable over the whole temperature range (expect for a small shift of peaks resulting from a cell contraction on cooling) implying the absence of magnetic long range ordering. Moreover, the unchanged background at low temperature suggests the absence also of short range correlations. This does not come as a surprise since the topology of the two compounds reveal rather isolated Cu 2+ atoms. Further studies on the magnetic behaviors of these compounds are desirable.

Conclusions

In previous reports, new polyanionic host structures for Li + and Na + insertion have been stabilized through K + extraction from their mother phase. We have here reported an extension of this concept to the langbeinite K2Fe2(SO4)3 phase, which shows, however, poor electrochemical activity owing to its structural instabilities upon K + extraction. Further exploring the A2M2(SO4)3 family, we synthesized a novel K2Cu2(SO4)3 member via a solid state

Figure 1 :

 1 Figure 1: Rietveld refinement of the X-ray diffraction pattern of K2Fe2(SO4)3. The red crosses, black line, and green line represent the observed, calculated and difference patterns, respectively. The positions of the Bragg reflections are shown as vertical blue bars. b) Structure of K2Fe2(SO4)3, where the FeO6 octahedra and SO4 tetrahedra are shown in blue and light blue, respectively. O and K atoms are illustrated as grey and orange spheres.

Figure 2 :

 2 Figure 2: a) Voltage-composition trace of cubic K2Fe2(SO4)3. A in A2Fe2(SO4)3 corresponds to K + in the first charge and to Li + onwards. b) XRD pattern of pristine K2Fe2(SO4)3 (orange), chemically oxidized K2-xFe2(SO4)3 (blue), electrochemically charged K2-xFe2(SO4)3 (purple) and discharged (K,Li)2Fe2(SO4)3 (maroon). The asterisk marks the peak attributed to KBF4.

  )3 was solved by combined synchrotron X-ray and neutron powder diffraction. With help of the Dicvol 25,26 program, the Bragg peaks in the synchrotron XRD patterns could be indexed in an orthorhombic unit cell with the lattice parameters a = 4.81065(1) Å, b = 11.91795(3) Å and c = 18.67516(4) Å and a volume of V = 1070.704(4) Å 3

Figure 3 :

 3 Figure 3: a) Electron diffraction data for K2Cu2(SO4)3. In the patterns taken along the main zone axis (square patterns), reflections violating h00: h=2n; 0k0: k=2n; 00l: l=2n extinction conditions reappear owing to the dynamical effects. The reflection conditions are unambiguously observed when the crystal is tilted away from the zone axis, so that only a single row of reflections fulfills the diffraction conditions (rectangular patterns). b) Rietveld refinement of the synchrotron XRD and neutron powder diffraction patterns of K2Cu2(SO4)3. The red crosses, black line, and green line represent the observed, calculated and difference patterns, respectively. The positions of the Bragg reflections are shown as vertical blue bars. The second phase in the neutron diffraction pattern stems from the vanadium can.

Figure 4 :Figure 5

 45 Figure 4: a) Structure of orthorhombic K2Cu2(SO4)3 shown along the [100] axis. The CuOx polyhedra and SO4 tetrahedra are shown in blue and red, respectively, with the oxygen atoms in grey. The potassium atoms are represented as yellow balls. b) Connectivity of the CuOx polyhedra and SO4 tetrahedra in K2Cu2(SO4)3. c) Local coordination of K1 and K2 with the respective K-O bond lengths.

Figure 5 :

 5 Figure 5: Voltage-composition trace of K2Cu2(SO4)3 cycled at C/50 started in oxidation (orange arrow) (a) and its derivative curve (b).

Figure 6 :

 6 Figure 6: XRD patterns of pristine K2Cu2(SO4)3 (orange) and chemically oxidized K2Cu2(SO4)3 using NO2BF4 (blue pattern). The purple and red XRD patterns were recorded ex situ after charge and discharge of K2Cu2(SO4)3. The peak marked with * corresponds to KBF4.

Figure 7 :

 7 Figure 7: Temperature dependence of the a.c. conductivity of K2Cu2(SO4)3 and its activation energy Ea deduced from the Arrhenius equation (a). These activation energies are physically not related to the percolation energies deduced from BVEL. The inset shows the measured impedance spectrum at 363 °C and the circuit used for the fit. The observed drop of conductivity around 380 °C suggests a phase transformation (b).

Figure 8 :

 8 Figure 8: High-temperature in situ XRD experiment on K2Cu2(SO4)3, which was heated from 50 °C to 620 °C and cooled down to 100 °C under nitrogen flow. The blue, green and purple pattern correspond to the pristine K2Cu2(SO4)3, the transition range (biphasic domain) and to fedotovite K2Cu3O(SO4)3 respectively. The grey patterns correspond to decomposition products.

  ) Å, b = 9.52853(2) Å, c = 14.18650(3) Å,  = 110.63109(19)° and V = 2415.100(9) Å 3 ) as compared to the one reported by Starova et al. (a = 19.037(6) Å, b = 9.479(2) Å, c = 14.231(5) Å,  = 111.04(3)°, corresponding to a unit cell volume of V = 2396.8(3) Å 3 ) 37 might be related to the fact that their structure was solved on the mineral, which might contain impurities that influence the lattice size.

Figure 9 :

 9 Figure 9: Rietveld refinement of the synchrotron X-ray powder diffraction (top) and neutron powder diffraction (bottom) of fedotovite K2Cu3O(SO4)3. Red, black and green lines represent the experimental, calculated and difference patterns, respectively. Bragg positions are shown as blue bars. The second phase in the neutron diffraction pattern stems from the vanadium can.

Figure 10 :

 10 Figure 10: a) Structure of K2Cu3O(SO4)3, which adopts a layered-like structure as shown along the b-axis. The Cu-based polyhedra (CuO5 and CuO4) and SO4 tetrahedra are shown in blue and light blue, respectively. Oxygen and potassium atoms are illustrated as grey and orange spheres. b) Local coordination of Cu-based polyhedra in K2Cu3O(SO4)3 and K2Cu2(SO4)3.

Table 1 : Crystallographic data and atomic positions of K2Fe2(SO4)3 deduced from Rietveld refinements of its X- ray powder diffraction pattern. The isotropic temperature values (Biso) and the results from Bond Valence Sum (BVS) analyses are listed in last two columns. Cubic K2Fe2(SO4)3

 1

	Space group P213			RBragg = 3.42 %		χ 2 = 1.50
	a = 10.00478(3) Å		V = 1001.433(6) Å 3
	Atom	Wyckoff position	x	y	z	Occupancy	Biso (Å 2 )	BVS
	K1	4a	0.8135(3)	0.8135(3)	0.8135(3)	1	2.21(7)	1.14(1)
	K2	4a	0.0502(3)	0.0502(3)	0.0502(3)	1	2.21(7)	1.00(1)
	Fe1	4a	0.3350(2)	0.3350(2)	0.3350(2)	1	1.39(4)	2.19(2)
	Fe2	4a	0.59432(17) 0.59432(17) 0.59432(17)	1	1.39(4)	1.93(2)
	S1	12b	0.2210(3)	0.3760(5)	0.0174(4)	1	1.41(6)	6.41(8)
	O1	12b	0.3108(8)	0.2798(8)	0.9597(7)	1	2.59(9)	2.18(4)
	O2	12b	0.0845(8)	0.3244(9)	0.0066(7)	1	2.59(9)	2.06(4)
	O3	12b	0.2353(7)	0.4970(10)	0.9388(11)	1	2.59(9)	2.14(5)
	O4	12b	0.2540(6)	0.4088(7)	0.1541(9)	1	2.59(9)	2.12(4)

Table 2 : Crystallographic data and atomic positions of K2Cu2(SO4)3 determined from Rietveld refinements of its synchrotron X-ray powder diffraction pattern. The isotropic temperature values (Biso) and the results from Bond Valence Sum (BVS) analyses are listed in last two columns. Orthorhombic K2Cu2(SO4)3

 2

	Space group P212121			RBragg = 4.84 %		χ 2 = 1.05
	a = 4.81065(1)Å	b = 11.91795(3) Å	c = 18.67516(4) Å		V = 1070.704(4) Å 3
	Atom	Wyckoff position	x	y		z	Occupancy	Biso (Å 2 )	BVS
	K1	4a	0.18250(32)	0.13076(11)	0.40811(7)	1	1.914(39)	1.05(1)
	K2	4a	0.69591(38)	0.32848(11)	0.18436(7)	1	1.519(40)	1.30(1)
	Cu1	4a	0.24424(32)	0.48396(5)	0.34274(4)	1	1.330(17)	1.87(1)
	Cu2	4a	0.24010(22)	0.11442(7)	0.05180(3)	1	1.085(15)	1.94(1)
	S1	4a	0.24667(54)	0.11663(12)	0.21865(7)	1	0.797(28)	5.82(3)
	O1	4a	0.16573(91)	0.03348(30)	0.27297(21)	1	1.520(108)	1.93(2)
	O2	4a	0.07946(73)	0.08287(30)	0.15149(23)	1	0.498(95)	2.08(2)
	O3	4a	0.20298(113)	0.23147(33)	0.23780(17)	1	1.765(103)	1.98(2)
	O4	4a	0.54695(74)	0.11448(35)	0.19594(19)	1	0.592(95)	2.05(2)
	S2	4a	0.20980(42)	0.38040(14)	0.04783(8)	1	1.027(32)	5.96(3)
	O5	4a	0.19490(104)	0.60269(34)	0.47395(17)	1	1.552(102)	1.80(2)
	O6	4a	0.31752(84)	0.27285(33)	0.07609(16)	1	0.582(92)	2.08(2)
	O7	4a	0.89854(76)	0.37610(36)	0.04664(21)	1	1.073(106)	2.05(2)
	O8	4a	0.29464(111)	0.46651(27)	0.09906(19)	1	1.109(96)	1.80(2)
	S3	4a	0.23111(46)	0.14077(12)	0.59875(8)	1	0.864(32)	5.94(3)
	O9	4a	0.06258(72)	0.11974(37)	0.66422(19)	1	0.544(89)	2.00(2)
	O10	4a	0.18384(109)	0.05074(29)	0.54712(20)	1	1.538(119)	2.15(2)
	O11	4a	0.16777(78)	0.24878(39)	0.56824(17)	1	0.844(92)	1.99(2)
	O12	4a	0.03586(73)	0.35793(32)	0.37840(20)	1	0.509(90)	1.96(2)

Table 3 : Crystallographic data and atomic positions of K2Cu3O(SO4)3 determined from the Rietveld refinement of its synchrotron XRD pattern. The isotropic temperature values (Biso) were constrained identical for a same chemical species. Results from Bond Valence Sum (BVS) analyses are listed in last column. Monoclinic fedotovite K2Cu3O(SO4)3

 3

	Space group C2/c	RBragg = 2.45 %

Acknowledgements

We thank Matthieu Courty for performing TGA/DSC measurements. Use of the 11-BM mail service of the APS at Argonne National Laboratory was supported by the U.S. Department of Energy under Contract DE-AC02-06CH11357 and is acknowledged. The French CRG D1B is acknowledged for allocating neutron beamtime. L.L. thanks the ANR "Hipolite" for the PhD funding.

approach that crystallizes in an orthorhombic unit cell (space group P212121) different from the one of the langbeinite phases. K2Cu2(SO4)3, which presents moderate electrochemical properties, is shown to transform upon heating to the naturally occurring mineral fedotovite K2Cu3O(SO4)3, which is prepared for the first time synthetically. In light of these findings, we can conclude that although the approach of stabilizing new host structures from K-based polyanionic materials is highly interesting, it cannot be fully generalized. Lastly, even though K2Cu2(SO4)3 nor K2Cu3O(SO4)3 are suitable as cathode materials, both compounds present a S=1/2 system and therefore might display interesting magnetic properties.

Supporting Information

Details on Bond Valence Energy Landscape (BVEL) calculations and resulting BVELs of K2Fe2(SO4)3 and K2Cu2(SO4)3; low magnification HAADF-STEM image of K2Cu2(SO4)3 particles; Rietveld refinement of chemically oxidized K2Cu2(SO4)3; pictures of K2Cu2(SO4)3 and K2Cu3O(SO4)3 powders; neutron powder patterns of K2Cu2(SO4)3 and K2Cu3O(SO4)3. CIF files of K2Fe2(SO4)3, K2Cu2(SO4)3 and K2Cu3O(SO4)3.

Author Information Notes

* Corresponding author: jean-marie.tarascon@college-de-france.fr

For Table of Contents Only

The possibility of extracting K to re-insert Li from langbeinite K2Fe2(SO4)3 is evaluated. A new copper-based compound K2Cu2(SO4)3 is reported for the first time and its structure determined. The electrochemical behavior of K2Cu2(SO4)3 against Li is explored, and its relation to fedotovite K2Cu3O(SO4)3 revealed.


Louisiane Verger

Olivier Dargaud

Nicolas Menguy

David Troadec

Laurent Cormier

Interaction between Cr-bearing pigments and transparent glaze: a transmission electron microscopy study

Keywords: electron microscopy, pigments, glaze, color alteration, chromium oxides

Spinel ZnAl2O4 and corundum Al2O3 doped with chromium are used as pink pigments in porcelain glazes. However, alteration of the color can occur during firing, and the resulting glaze appears brown and green respectively, instead of the expected pink. To investigate the mechanism of color change, electron transparent sections were prepared by Focused Ion Beam (FIB) at the interface between pigment and glaze. Observations under a transmission electron microscope (TEM) reveal a common mechanism for both systems. Al migration from the pigment toward the silicate melt results in alteration of the grain of pigments, and formation of a Cr enriched phase, with the same crystalline structure than the initial pigment.

Furthermore, the formation of anorthite is reported, due to the increase of the local concentration of Al in the melt. The different morphologies of altered grains of pigment encountered in the glaze are discussed base on the TEM observations.

Introduction

The stability of chromium-bearing crystals in glasses, slags or melts has been the subject of several studies. The dissolution/crystallization behavior is an important process to understand aggressive attack of refractory materials by molten metallurgical slags and melts [START_REF] Cooper | Dissolution in Ceramic Systems: I, Molecular Diffusion, Natural Convection, and Forced Convection Studies of Sapphire Dissolution in Calcium Aluminum Silicate[END_REF], crystal/melt partition in igneous processes [START_REF] Roeder | Crystallization of Chromite and Chromium Solubility in Basaltic Melts[END_REF][START_REF] Irving | A review of experimental studies of crystal/liquid trace element partitioning[END_REF] or the possibility of high chromium loading in nuclear glass wastes [START_REF] Hrma | Chromium phase behavior in a multi-component borosilicate glass melt[END_REF]. Chromium is also used in glaze coatings, painted tiles or porcelain stonewares as sub-microcrystallites that can influence the color or macrocrystallites for aesthetic ornaments (crystalline glazes) [START_REF] Martos | Towards more ecological ceramic pigments: Study of the influence of glass composition on the colour stability of a pink chromium-doped ceramic pigment[END_REF][START_REF] Mestre | Interaction of the chromiumiron black pigment with porcelanised stoneware[END_REF][START_REF] Murdock | The interaction of ceramic pigments with glazes[END_REF]. Though chromium was isolated only in 1797 by Nicolas Louis Vauquelin in France [START_REF] Vauquelin | Mémoire sur la découverte d'un nouveau métal à l'état d'acide et d'oxide dans le plomb rouge de Sibérie, le rubis et l'émeraude, et d'une nouvelle terre dans l'émeraude et le béril[END_REF], it was rapidly used to color ceramics, especially at the French Manufacture of Sèvres (Sèvres factory of porcelains) under the leadership of its director Alexandre Brongniart, a former collaborator of Vauquelin [START_REF] Brongniart | Traité des arts céramiques ou des poteries: considérées dans leur histoire, leur pratique et leur théorie[END_REF]. Indeed Cr-bearing crystals produce a richness of colors that was not available before the discovery of this element. A wide range of Cr-bearing pigments was developed yielding to various colorations: pink, red, reddish brown or green [START_REF] Cordoncillo | Influence of some mineralizers in the synthesis of sphene-pink pigments[END_REF]. To obtain a glaze, the crystalline pigments are dispersed in a uncolored frit and after firing, the color of the crystal is imparted to the glaze.

The color property strongly depends on the nature of crystal structure incorporating chromium, but it is also altered by possible reactions during firing between the starting pigment and the corrosive silicate melts, i.e. the glazes and frits, as noticed in previous investigations [START_REF] Martos | Towards more ecological ceramic pigments: Study of the influence of glass composition on the colour stability of a pink chromium-doped ceramic pigment[END_REF][START_REF] Mestre | Interaction of the chromiumiron black pigment with porcelanised stoneware[END_REF][START_REF] Murdock | The interaction of ceramic pigments with glazes[END_REF][START_REF] Yurdakul | The mechanism for the colour change of iron chromium black pigments in glazes through transmission electron microscopy techniques[END_REF][START_REF] Ozel | Production and characterisation of iron-chromium pigments and their interactions with transparent glazes[END_REF][START_REF] Ahmadi | Synthesis of Y(Al,Cr)O3 red pigments by coprecipitation method and their interactions with glazes[END_REF][START_REF] Eppler | The relative stability of ceramic pigments[END_REF][START_REF] Harisanov | Influence of crystallinity on chromatic parameters of enamels coloured with malayaite pink pigments[END_REF][START_REF] Verger | The stability of gahnite doped with chromium pigments in glazes from the French manufacture of Sèvres[END_REF]. These works conclude that reactions during firing are most likely due to the dissolution of pigment through chemical attacks. However, the main challenge is still to understand the possible interactions occurring between pigments and ceramic-matrices resulting in a color change after firing.

Previous works were essentially focused on the color change of iron-chromium pigments composed of (Cr,Fe)2O3 in zinc-based and zinc-free glazes [START_REF] Mestre | Interaction of the chromiumiron black pigment with porcelanised stoneware[END_REF][START_REF] Murdock | The interaction of ceramic pigments with glazes[END_REF][START_REF] Yurdakul | The mechanism for the colour change of iron chromium black pigments in glazes through transmission electron microscopy techniques[END_REF][START_REF] Ozel | Production and characterisation of iron-chromium pigments and their interactions with transparent glazes[END_REF][START_REF] Eppler | The relative stability of ceramic pigments[END_REF]. They reveal the importance of the glass matrix composition, the outward diffusion of Fe into the glaze, and the formation of spinel (Zn,Fe)(Cr,Fe)2O4 in zinc-based glazes. For the malayaite pink pigments (CaSnSiO5:Cr) used in different glazes, a drastic change of the color also occurs towards paler shades or in the appearance of a bluish hue, attributed to the formation of BaSnSi3O9 [START_REF] Harisanov | Influence of crystallinity on chromatic parameters of enamels coloured with malayaite pink pigments[END_REF][START_REF] Byrne | How glaze composition affects chrome-tin pinks[END_REF].

At the Sèvres factory, almost 60% of pigments composed of chromium oxides are spinels, synthesized in its laboratory. However, they undergo a change of color in a commonly used uncolored frit. It is a mixture of feldspar, kaolin, quartz and chalk (in proportion specific to Sèvres' porcelain) that vitrifies during the firing process. In this particular decoration, the pink color of spinel and corundum doped with chromium pigments is not stable: the resulting spinel and corundum glazes appear respectively brown and green.

In our previous investigation on a spinel pigment mainly composed of ZnAl1.59Cr0.41O4 [START_REF] Verger | The stability of gahnite doped with chromium pigments in glazes from the French manufacture of Sèvres[END_REF][START_REF] Verger | Spectroscopic properties of Cr 3+ in the spinel solid solution ZnAl2-xCrxO4[END_REF], we showed that the color change is caused by a modification of the Cr content in the spinel phase. It was evidenced that the initial pigment ZnAl1.59Cr0.41O4 gradually dissolves in favor of a Cr-enriched phase ZnAl0.54Cr1.46O4. This behavior is somewhat related to the peraluminosity of the frit/glaze defined as:

R = nAl2O3 / (nNa2O + nMgO + nK2O + nCaO)
with nAl2O3 and (nNa2O + nMgO + nK2O + nCaO) the molar content in alumina and alkali and alkaline-earth oxides in the specimen, respectively. When R<1, the glass is peralkaline and when R>1, the glass is peraluminous. The starting frit has a low peraluminosity of 0.50. When Al2O3 content is increased in the uncolored frit, i.e. the peraluminosity increases, the dissolution of the pigment was found to be reduced. It was conclude that the enrichment in Cr of the spinel after firing results from the gradual migration of Al from the pigment to the glaze, without changing the nature of the crystalline phase.

The color change occurring with corundum doped with chromium pigment was also observed by Martos et al. [START_REF] Martos | Towards more ecological ceramic pigments: Study of the influence of glass composition on the colour stability of a pink chromium-doped ceramic pigment[END_REF] It was found that the presence of ZnO was required for stabilizing the pink coloration in the glaze. However, the mechanism that underlies this change of color is still not known.

In this paper we will examine several examples of interaction between chromium pink pigments and the frit glass matrix. We will focus on the Al diffusion by analyzing the interface between the pigment and the surrounding glass. Focused Ion Beam (FIB) crosssection are used for analyses by transmission electron microscope (TEM), revealing a common dissolution mechanism and reaction at the pigment/glaze interface for Cr-doped spinel and corundum pigments.

Materials and methods

Two pigments containing Cr were selected for this study. They are historically synthesized at the Sèvres factory and named 10045 and 10059. Pigment 10045 is mainly composed of a spinel phase ZnAl1.59Cr0.41O4, characterized in our previous investigation [START_REF] Verger | The stability of gahnite doped with chromium pigments in glazes from the French manufacture of Sèvres[END_REF]. Pigment 10059 is composed of a corundum phase, Al1.9Cr0.1O3. Its composition was determined by Rietveld refinement, using the linear regression from Rossi et al. [START_REF] Rossi | Elastic Properties of Oxide Solid Solutions: The System Al2O3-Cr2O3[END_REF] that relates the cell parameters (a and c) to the Cr concentration x in Al2-xCrxO3 following Vegard's law. Glazes are obtained by mixing 0.5 g of pigment with 4.5 g of an uncolored crystallized frit named CI. The frit is composed of feldspar, kaolin, quartz and chalk in proportions specific to the porcelain of Sèvres. The mixture was not ground in order to observe larger grains of pigment and characterize the interface between the crystal and the uncolored glass. The mixture of the pigment and the frit is painted on a round porcelain mount, which is then fired. The heat treatment is the one used for firing porcelain artifacts at the manufacture: 1000°C is reached in ten hours, then 1280°C is reached in 5h30. Once 1280°C is reached, the oven is immediately turned off and slowly cooled down to room temperature. The atmosphere of the oven is not controlled for the preparation of this kind of decoration. Glazes composed of pigment 10045 and pigment 10059 are respectively called g-spinel and g-corundum.

Cross sections were cut from the porcelain shard with the glaze on the top. The fragment was embedded in a resin block, polished using diamond pastes down to 3μm and carbon coated.

Scanning Electron Microscopy (SEM) analyses were carried out with a Zeiss Ultra55, using an acceleration voltage of 15 kV, a working distance of 7.5 mm and a backscattered electrons detector, associated to an X-ray Energy Dispersive Spectroscopy (XEDS) microprobe.

Electron transparent foils were prepared using Focused Ion Beam (FIB) on a FEI STRATA DB235 instrument. Sections were analyzed with a JEOL 2100F microscope operating at 200 kV. This microscope was equipped with a field emission gun, an ultra-high resolution (UHR) pole piece and a scanning TEM (STEM) device, which allowed Z-contrast imaging in the high angle annular dark field (STEM-HAADF) mode. Chemical analyses were performed using a JEOL detector with an ultrathin window by XEDS elemental mapping in the STEM-XEDS mode. Selecting area electron diffraction (SAED) patterns were acquired along two or three zone axis to identify unambiguously the structure of the crystal (only one axis is shown in figures).

X-ray diffraction (XRD) pattern of g-corundum was collected directly on the glaze without specific preparation, using a PANalytical X'Pert PRO diffractometer with Cu Kα radiations (λCu,Kα1 = 1.54056 Å, λCu,Kα2 = 1.54439 Å) operating under 40kV and 40mA, in the 10° 2θ to 130° 2θ range, with 0.0167° 2θ steps and a counting time of 550 s per step.

Results

Morphological aspect of the spinel pigment grains in the glaze

The g-spinel glaze is composed of crystalline grains embedded in a glass that results from the melting of the uncolored frit. The grains correspond to the initial pigment, partially altered by reactions with the silicate melt during the heat treatment [START_REF] Verger | The stability of gahnite doped with chromium pigments in glazes from the French manufacture of Sèvres[END_REF]. We previously showed that the initial pigment has the spinel phase composition ZnAl1.59Cr0.41O4 (spinel-Cr0.41). This pigment is not stable during firing, leading to the formation of a Cr-enriched spinel ZnAl0.54Cr1.46O4 (spinel-Cr1.46) [START_REF] Verger | The stability of gahnite doped with chromium pigments in glazes from the French manufacture of Sèvres[END_REF]. Three grain populations in the same glaze can be distinguished. Fig. 1a shows homogeneous aggregated grains composed of spinel-Cr1.46.

Their diameter is typically below 1 μm. Their chemical composition (determined by SEM analysis associated with EDX measurements) indicates that those grains results from complete alteration of the initial phase that is not observed. Fig. 1b shows grains that are partially altered: the center has the composition of the initial spinel-Cr0.41 while the periphery corresponds to the spinel-Cr1.46. Their size is typically around 10 μm. The third example (Fig. 1c) shows also the presence of the initial pigment spinel-Cr0.41 and the new phase spinel-Cr1.46, but additional phases pointed out by arrows are present. It seems to diffuse from the pigment grain to the glass. From the backscattered electron imaging contrast of Fig. 1c, this phase seems to be devoid of Cr and Zn and is observed around grains of large size (> The change in the composition of spinel is at the origin of the color change between the initial pigment (pink) and the glaze (brown), in agreement with a colorimetric analysis of the spinel solid solution ZnAl2-xCrxO4 [START_REF] Verger | Spectroscopic properties of Cr 3+ in the spinel solid solution ZnAl2-xCrxO4[END_REF].

Interface between spinel grain and the glass

In order to get more information on (i) possible crystallographic relationship between the two spinel phases (i.e. the parent spinel-Cr0.41 and the new phase spinel-Cr1.46) and (ii) to investigate the crystalline nature of the additional phase, a TEM thin foil was obtained using FIB method from an area exhibiting all the phases aforementioned. Fig. 2a-e corresponds to STEM-XEDS elemental mapping achieved using Si-K, Al-K, Ca-K, Cr-K, Zn-K lines. As shown on the composite image (Fig. 2f), four different phases can be distinguished from the compositional criterion. Areas appearing in orange and green in Fig. 2f are related to the spinel phases previously observed by SEM: the undissolved initial pigment (spinel-Cr0.41) rich in Al and Zn (Fig. 2b,e) correspond to the orange zone and is surrounded by smaller grains of spinel-Cr1.46 rich in Cr and Zn (Fig. 2d,e) that coincide with green areas. SAED patterns acquired on initial pigment (Fig. 3b) and grains of spinel-Cr1.46 (Fig. 3c) confirm that the grains have the spinel structure. Moreover, SAED patterns indicate also that both Al-rich and Cr-rich crystals are orientated along almost the same direction suggesting a possible solid state transformation i.e. without a dissolutionreprecipitation process. From STEM-XEDS elemental mapping (Fig. 2a) and SAED observations (data not shown), areas appearing in blue in Fig. 2f and Fig. 3a correspond to amorphous SiO2-rich phase resulting from the vitrification of the uncolored frit. Finally, magenta areas in Fig. 2f and Fig. 3a are related to phases spreading out from the grain of pigment to the glass (they are only observed at close proximity of the initial grain pigment). The chemical composition deduced from XEDS measurements and SAED analysis (Fig. 4c) strongly suggests the presence of anorthite CaAl2Si2O8. This corresponds to the meta-aluminosilicate join, i.e. a peraluminosity of 1. HREM images (Fig. 4d) acquired on these phases reveal the presence of planar stacking fault and (010) twinning planes typical for anorthite, as reported by Xu et al. [START_REF] Xu | Twinning in synthetic anorthite; a transmission electron microscopy investigation[END_REF].

Interface between the Al2O3:Cr 3+ corundum pigment and the glass

In order to investigate the impact of the crystalline structure of the pigment on its reactivity, pigment 10059 composed of corundum Al1.9Cr0.1O3 was studied. The pink color of the pigment is modified during firing, and the glaze presents a green hue. Contrary to pigment 10045, no further crystalline phase composed of chromium was detected by XRD in the glaze.

However, the formation of anorthite with trace of sodium is detected by XRD on this sample (Fig. 5).

SEM observations on a cross section of the glaze was particularly challenging because the contrast between the grains of pigment and the glassy matrix was not good enough from the different images (secondary or backscattered electrons) to distinguish them. Grains of pigments can only be identified from XEDS elemental mapping of Al. Heterogeneity in Cr concentration was observed on XEDS mapping, but the spatial resolution was not sufficient enough to relate them to a crystalline phase. Therefore, in order to understand the mechanism of color change in this case, a TEM analysis was carried out on a thin foil prepared using the FIB method at the interface between a grain of pigment and the glass. From XEDS elemental maps and SAED analyses shown on Fig. 6, four main areas can be distinguished, similarly to the g-spinel glaze.

The orange area seen on the elemental composite image (Fig. 6f) corresponds to a crystalline phase with a corundum structure whose chemical composition determined by XEDS analysis, and despite small variations on the Cr-content (Fig. 6d), is close to the one of the initial pigment Al1.9Cr0.1O3. From SAED patterns (only one zone axis is shown in Fig. 6g) acquired in different areas of this phase, it appears that all the sub-grains have the same orientation with very minor deviations. From these observations, it can be inferred that this area corresponds to an unaltered grain of the initial pigment. The Cr-bearing corundum crystal is surrounded by a Ca-rich crystalline phase (Fig. 6c) that is shown to be anorthite from SAED pattern (Fig. 6h) and XEDS measurements of the composition. Si-and K-rich area labeled (i) on Fig. 5f corresponds to the glass resulting from the vitrification of the uncolored frit.

At the periphery of the Al1.9Cr0.1O3 crystal, small Cr-rich crystals are present and are visible on the STEM-HAADF image presented on Fig. 7a. As shown on Fig. 7b, their size is around 50 nm x 50 nm and they are dispersed in the anorthite phase closely to the Al1.9Cr0.1O3 crystal.

From HREM observations and subsequent Fourier transform analysis (Fig. 7c,d), it can be concluded that these crystals exhibit the corundum structure as well, which indicates that they are grains of eskolaite Cr2O3. Their presence reveals that the Al1.9Cr0.1O3 initial grain of pigment reacts during firing, leading to the formation of Cr2O3. Eskolaite Cr2O3 is green, thereby its formation explains the color change between the pigment (pink) and the glaze (green). Contrary to g-spinel, the size and quantity of chromium oxide crystallites formed are certainly too low to be detected by XRD.

Discussion

The alteration of pigments can affect the resulting color of porcelain glazes through three mechanisms: reaction between a pigment and a glaze to form a different crystal with different color properties, extraction of an element from the pigment giving a crystal with different color properties, substitution of one element for another improving the stability of the crystal and, possibly, altering the color. [START_REF] Eppler | The relative stability of ceramic pigments[END_REF] For the g-spinel and g-corundum, color alteration can be related to the second case: the extraction of Al from the pigment to the silicate melt, leaving Cr-enriched phases, ZnAl0.54Cr1.46O4 for g-spinel and Cr2O3 for g-corundum. It explains the color change from pink to brown (g-spinel) or green (g-corundum).

The mobility of Al is promoted by the chemical composition of the melt. The initial uncolored frit gives mainly a calcium aluminosilicate melt/glass after melting. In this type of glass, calcium cations ensure charge compensation of (AlO4) -tetrahedra. The migration of Al from the grain of pigment to the melt is favored by the large amount of alkali or alkaline-earth cations in the melt, which are available for charge compensation. Indeed, the peraluminosity of the uncolored frit before the thermal treatment is equal to 0.50, meaning that half of the alkali or alkaline-earth cations (mainly Ca 2+ ) can be used to stabilize Al in tetrahedral environment. For g-corundum, there is a clear correlation between Al and Ca elemental maps in Fig. 6 indicating that the outward diffusion of Al into the glaze is due to the high Ca mobility towards the interface to provide charge compensation for Al 3+ . The crystal dissolution is then due to two processes: reaction at the melt/pigment interface to allow the release of Al cations and diffusion of Ca 2+ cations in the melt towards the interface. Usually, diffusion is the rate-determining parameter controlling the crystal dissolution.

The migration of Al from the pigment to the melt increases locally its concentration around the pigment. As a consequence of the Al rich layer near the melt/pigment interface, the system can pass through the stability field of anorthite in the ternary SiO2-Al2O3-CaO [START_REF] Levin | Phase diagrams for ceramists[END_REF][START_REF] Richet | Glass formation in silicates: Insights from composition[END_REF]. Furthermore, anorthite is known to crystallize without nucleating agent in SiO2-Al2O3-CaO-MgO glass system [START_REF] Lo | Low temperature sintering and crystallisation behaviour of low loss anorthite-based glass-ceramics[END_REF][START_REF] Leonelli | Crystallization of some anorthite-diopside glass precursors[END_REF]. Al saturation concentration around some grains of pigment enables the formation of anorthite as firing at 1280°C is close to the maximum of crystal growth rate [START_REF] Klein | Crystallization behavior of anorthite[END_REF].

The formation of eskolaite in g-corundum indicates the poor solubility of Cr 3+ for this melt composition and at this temperature. This is also consistent with large difference in solubility of Cr in chromian spinel and coexisting basaltic lavas [START_REF] Barnes | The Range of Spinel Compositions in Terrestrial Mafic and Ultramafic Rocks[END_REF][START_REF] Wijbrans | Experimental determination of trace element partition coefficients between spinel and silicate melt: the influence of chemical composition and oxygen fugacity[END_REF]. We can propose that the Al compositional difference between the initial pigment and the melt can act as a driving force for Al diffusion. This is consistent with the fact that the dissolution of pigments is lower if the compositional difference is lower [START_REF] Verger | The stability of gahnite doped with chromium pigments in glazes from the French manufacture of Sèvres[END_REF]. In g-spinel, this driving force is still present. However, we can note a lower Zn-diffusion towards the glaze than for Al. This is consistent with the final spinel composition ZnAl0.54Cr1.46O4, which implies a larger extraction of Al 3+ cations than Zn 2+ cations from the pigment to the silicate melt. It can be explained by the difference in the stability of various cations in the sites of the spinel lattice. Indeed, Zn is known to be the most stable of all ions in tetrahedral site in spinels [START_REF] Miller | Distribution of Cations in Spinels[END_REF]. Conversely, the octahedral sitepreference is higher for Cr 3+ than for Al 3+ . As shown in Fig. 3, for g-spinel, the parent spinel-Cr0.41 grain and the new Cr-enriched phase spinel-Cr1.46 crystal exhibit the same crystallographic orientation. Therefore, the orientation of the crystals remains the same when Al migrates in the silicate melt. This result is consistent with the fact that spinel-Cr1.46 originates from the same grain of pigment. While all aluminium cations migrate in the melt for g-corundum, only 66% of the Al initial amount present in the grain of pigment migrates in the melt for g-spinel (calculated using the chemical composition of the initial and final phases in g-spinel, respectively ZnAl1.59Cr0.41O4 and ZnAl0.54Cr1.46O4). Al migration is then limited by the presence of Zn and/or the crystalline structure. Firstly, this difference has an impact on the size of the resulting phases: sizes of ZnAl0.54Cr1.46O4 grains distribute between 200 nm and 1 μm, while the size of Cr2O3 is about corundum than in glaze g-spinel. Indeed, while anorthite is forming a continuous layer between the pigment and the glass in g-corundum, it only crystallizes in particular directions in g-spinel.

Every grains of pigment react during firing. However, they do not all have the same aspect in the resulting glaze (Fig. 1). Indeed, while some grains are completely altered (Fig. 1a), others still contain the initial phase (Fig. 1b). This observation shows that the alteration process rate, and therefore the diffusion rate of Al, is not the same for every grain of pigment. Al diffusion is strongly dependent on the initial grain size and on possible aggregation of grains (such as Fig. 1c). As the convection is limited into the glaze, which can be deduced from the important presence of bubbles [START_REF] Verger | The stability of gahnite doped with chromium pigments in glazes from the French manufacture of Sèvres[END_REF], a local saturation composition of Al occurs preventing further outward diffusion of Al from the pigment, which in turn limit the pigment dissolution rate.

Diffusion affecting the interface composition is again controlling the dissolution process.

Based on the different observations made, we try to reconstruct the sequence of alteration of different grains of pigment, explaining the variety of morphology encountered (Fig. 8). When Al migration is favored, the grain of pigment completely reacts with the silicate melt and is totally replaced by the Cr-enriched phase (sequence A2 to A4 in Fig. 8). When Al diffusion is limited, the duration of firing of the glaze does not allow the alteration process to reach the center of the grain (sequence B2 and B3 in Fig. 8). When the silicate melt around the pigment is saturated in Al, crystallization of anorthite occurs, when the glaze is cooling down (scenario (i)), or when the glaze in heating up (scenario (ii)). Both scenarios result in the presence of partially reacted grains of pigment, surrounded by anorthite (step C4 in Fig. 8). The presence of anorthite is not important for coloration but implies an Al boundary rich layer that can prevent the crystal dissolution and thus the color change.

Al diffusion appears to be a key parameter to understand the three different kind of population in glaze g-spinel. It is most likely that the three same populations can be observed under a SEM in glaze g-corrundum if the chemical contrast between the pigment and the uncolored frit was not too low. The three kind of grain observed (A, B and C) can be seen at different step of the alteration of the pigment. When 1280°C is maintained during 20 hours, every grains of pigment have the aspect of grain A in the glaze. This means that eventually, B and C evolve towards A if the firing process is long enough to complete the alteration of the pigment.

Conclusion

To better identify the sequence of reactions leading to the alteration of the color of two pigments (spinel ZnAl1.59Cr0.41O4 and corundum Al0.9Cr0.1O3) during firing of glazes, samples were analyzed down to the nanoscale. A common mechanism explains the color change, occurring as a result of the formation of a Cr-enriched phase with the same crystalline structure than the initial pigment. The Cr-enriched phase results from gradual diffusion of Al from the pigment toward the silicate melt during firing. The diffusion's rate of Al in the silicate melt is not the same for every grain of pigment and strongly depends on the environment of the grain. The crystallization of anorthite confirms the hypothesis that Al migrates from the grain of pigment to the silicate melt.

Fig. 1 .

 1 Fig.1. SEM images of three different grains of pigments in g-spinel glaze, illustrating

Fig. 2 :

 2 Fig.2: elemental XEDS maps of g-spinel sample. (a-e) STEM-XEDS elemental mapping

Fig. 3 :

 3 Fig.3: Orientational relationships between spinel-Cr0.4 and spinel-Cr1.46. (a) STEM-

Fig. 4 :

 4 Fig.4: analyses of Si-rich phases. (a) composite image build with Al, Cr and Si elemental

Fig. 5 :

 5 Fig.5: XRD pattern of the sample g-corundum. Quartz SiO2 and (Ca,Na)(Si,Al)4O8 were

Figure 6 :

 6 Figure 6: elemental XEDS maps of g-corundum sample. (a-e) STEM-XEDS elemental

Fig. 7 :

 7 Fig. 7: identification of small Cr2O3 crystals

Fig. 8 :

 8 Fig.8: Proposed model for the reactivity of ZnAl2-xCrxO4 type pigment in silicate melt with

Acknowledgements

This work was supported by the Réseau Francilien sur les oxydes fonctionnels (DIM Oxymore) and the Région Ile-de-France. L. Verger acknowledges C. Bouttaz for her expertise in the preparation of the samples. The purchase of the Scanning Electron Microscope (SEM) facility of the Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie (IMPMC) was supported by Région Ile de France grant SESAME 2006 n°I-07-593/R, INSU-CNRS, INP-CNRS, University Pierre et Marie Curie -Paris 6, and by the French National Research Agency (ANR) grant no. ANR-07-BLAN-0124-01.