František Šimko

Aydar Rakhmatullin

Michal Korenko

Catherine Bessada

Structural Correlations and Chemistry of the Na 3 AlF 6 -SiO 2 Melt as an Electrolyte for the Solar Grade Silicon (SOG-Si) Electrowinning

Keywords: solid grade silicon, high temperature NMR, Na 3 AlF 6, SiO 2, alumino-silicates

published or not. The documents may come

Structural correlations and chemistry of the Na3AlF6 -SiO2 melt as an electrolyte for the solar grade silicon (SOG -Si) electrowinning

Introduction

Solar power energy is the most prevalent form of a renewable energy. It is not yet apparent what portion of our energy needs will be ultimately based on the sunshine, although it has a potential to definitely far transcend the total energy demand of humankind on the globe. Over 90 % of today`s photovoltaic cells still use silicon as conversion material. The reason is its abundance (Si constitutes 27 mass % of earth's crust), non-toxicity, acceptable band gap and reasonable energy conversion efficiency (around 20 %) [START_REF]Technology Roadmap: Solar Photovoltaic energy, Energy Technology Perspectives[END_REF][START_REF] Chen | Influence of carbothermic reduction on submerged arc furnace energy efficiency during silicon production[END_REF][START_REF] Chen | Effect of raw materials on the production process of the silicon furnace[END_REF]. One of the current hurdles against solar energy becoming a major contributor to the energy basket is still its high cost. An increasing attention has been thus paid to the production of solar grade silicon (SOG-Si) at low cost.

The understanding of the relations between the structure and chemistry inside the molten electrolyte systems (nature of ionic electroactive species, product of thermal dissociation, coordination chemistry, etc.) and their physico-chemical properties (conductivity, viscosity, density, phase equilibria, etc.) is essential for the industrial application, yet necessary information in this area is still very limited. Some studies on electrochemistry of some fluoride and chloride systems have been published in the seventies and eighties of the 20 th century [START_REF] Boe | Electrolytic Deposition of Silicon and of Silicon Alloys Part II: Decomposition Voltages of Components and Current Efficiency in the Electrolysis of the Na 3 AlF 6 -Al 2 O 3 -SiO 2 Mixtures[END_REF][START_REF] Matiašovský | Specific electrical conductivity of molten flourides[END_REF][START_REF] Cohen | Some prospective applications of silicon electrodeposition from molten fluorides to solar cell fabrication[END_REF]. Also, in recent years, one can see an increasing interest in this field [START_REF] Oishi | Process for Solar Grade Silicon Production by Molten Salt Electrolysis Using Aluminium-Silicon Liquid Alloy[END_REF][START_REF] Famiyeh | Electrodeposition of Silicon in Fluoride Melts[END_REF][START_REF] Sokhanvaran | Charge transport properties of cryolite-silica melts[END_REF][START_REF] Cho | Formation of a silicon layer by electroreduction of SiO 2 nanoparticles in CaCl 2 molten salt[END_REF][START_REF] Bieber | Silicon electrodeposition in molten fluorides[END_REF][START_REF] Ergul | Electrochemical decomposition of SiO 2 pellets to form silicon in molten salts[END_REF][START_REF] Abbar | Electrodeposition of Silicon from Fluorosilicic Acid Produced in Iraqi Phosphate Fertilizer Plant[END_REF][START_REF] Zou | Direct Synthesis of High Purity Silicon Wires by Electrorefining in Molten KF-NaF Eutectic[END_REF][START_REF] Xu | Electrodeposition of Solar Cell Grade Silicon in High Temperature Molten Salts[END_REF][START_REF] Thomas | Study of Properties of Cryolite -Lithium Fluoride Melt containing Silica[END_REF][START_REF] Massot | Silicon recovery from silicon-iron alloys by electrorefining in molten fluorides[END_REF][START_REF] Li | Preparation of Solar Grade Silicon Precursors by Silicon Dioxide Electrolysis in Molten Salts, The Minerals[END_REF][START_REF] Korenko | Density, Viscosity and Electrical Conductivity of Molten Cryolite Electrolytes (Na 3 AlF 6 -SiO 2 ) for Solar Grade Silicon (Si-SoG) Electrowinning[END_REF][START_REF] Young | Solid Oxide Membrane (SOM) Process for Ytterbium and Silicon Production from their Oxides[END_REF][START_REF] Fray | Silicon Electrochemistry in Molten Salt[END_REF].

Previous screening in between the several molten salt electrolytes has pointed out that, with respect to the deposited material purity and process current efficiency, the cryolite-based melts are promising media for the electrowinning of silicon [START_REF] Monnier | Recherches sur le raffinage électrolytique du silicium[END_REF][START_REF] Monnier | Dual Cell Refining of Silicon and Germanium[END_REF]. The process has not yet been, however, successfully commercialized due to the rather high melting point of silicon (1412 °C), prohibiting the production of liquid primary silicon at the temperatures usual for cryolitic electrolytes (ca 1000 °C). In addition, an accurate comprehension of the physicochemical behavior and the structure of different cryolite-based electrolytes (including the knowledge of the electroactive species), what is vital for industrial application, is also very scarce [START_REF] Grjotheim | Electrolytic deposition of silicon and silicon alloys: Part I: Physicochemical properties of the Na 3 AlF 6 -Al 2 O 3 -SiO 2 mixtures[END_REF][START_REF] Grjotheim | The electrodeposition of silicon from cryolite melts[END_REF][START_REF] Belyaev | Physicochemical processes at electrolysis of aluminium[END_REF][START_REF] Sokhanvaran | Charge transport properties of cryolite-silica melts[END_REF][START_REF] Weill | The 1010 ° and 800 °C isothermal section in the system[END_REF].

Although physico-chemical behavior of the various molten cryolite systems is the subject of a longtime inquiry due to the Hall-Heroult technology, data regarding the physicochemical properties of the particular system Na 3 AlF 6 -SiO 2 are not only rather limited, but also available only for a small concentration range of silica.

Batashev and Zhurin [START_REF] Batashev | Teoreticeskoye Osnovy Elektrometallurgii Alyuminiya[END_REF] were the very first who investigated the molten system Na 3 AlF 6 -SiO 2 . These authors have found by visual observations the eutectic point in the system Na 3 AlF 6 -SiO 2 at approximately 3 wt. % SiO 2 (9.75 mole %) and 980 °C. Likewise, a narrow field of solid solution of SiO 2 in cryolite was postulated on the cryolite side of the binary phase diagram. On the SiO 2 side (beyond the eutectic point), an area of immiscibility of the two liquid phases was found. However, these results, according Grjotheim and Matiašovský [START_REF] Grjotheim | The electrodeposition of silicon from cryolite melts[END_REF], have to be considered just as preliminary, and still need to be verified.

The data related to the system Na 3 AlF 6 -SiO 2 was later reviewed by Grjotheim et al. [START_REF] Grjotheim | Electrolytic Preparation of the Al-Si Alloy[END_REF]. The authors concluded that silica reacts with cryolite (Na 3 AlF 6 ) or AlF 3 with the formation of volatile SiF 4 :

4Na 3 AlF 6 + 3SiO 2 → 3SiF 4 +12NaF + 2Al 2 O 3 (1)
or

Na 3 AlF 6 + SiO 2 → SiF 4 +12NaAlO 2 + 2NaF (2)
and

4AlF 3 + 3SiO 2 → 3SiF 4 +2Al 2 O 3 (3)
The rates of these reactions are based on the authors, however, rather slow, and thus the changes in chemical composition of the melts are almost negligible.

The phase equilibria in the isothermal section of the system Na 3 AlF 6 -Al 2 O 3 -SiO 2 at 1010 °C were investigated by Weill and Fyfe [START_REF] Weill | The 1010 ° and 800 °C isothermal section in the system[END_REF]. The authors have found that the solubility of SiO 2 , which is in pure Na 3 AlF 6 (1010 °C) less than 5 wt. % (15.53 mole %), increases with increased concentration of Al 2 O 3 in the melt. The paper has also reported that the changes in the composition of the melt, due to the formation of volatile SiF 4 , were negligible and did not significantly affect the final composition of the melt after precipitation. It should be pointed out that the experiments [START_REF] Weill | The 1010 ° and 800 °C isothermal section in the system[END_REF] were carried out in a closed system (Pt vial) where the reaction equilibrium likely shifted to the left. In the open systems SiF 4 can, on the other hand, escape away of the reaction vessel, and the losses of fluorides caused by the reactions (1 or 2) can be detected and can cause more significant change of the reactant`s composition.

Fellner and Matiašovský [START_REF] Fellner | Chemical reactions in molten Na 3 AlF 6 -SiO 2 -Al 2 O 3 -AlF 3 mixtures[END_REF] were determining the influence of the different melt compositions on the losses of SiO 2 (and subsequently on the losses of fluorine) in the Na 3 AlF 6 -SiO 2 melt. The change of Gibbs energy in the reaction (1) is positive (ΔG R 0 (1300 K) = 506.81 kJ/mol) so one can expect that the equilibrium of the reaction would be shifted to the left-hand side. The authors mentioned rather high losses of fluorides (in the open reaction systems) likely caused by the reaction (1 or 2 and 3). It was found that the components in the system react with the formation of volatile SiF 4 . The formation of SiF 4 was subsequently determined analytically [START_REF] Fellner | Chemical reactions in molten Na 3 AlF 6 -SiO 2 -Al 2 O 3 -AlF 3 mixtures[END_REF].

The main aim of this work is focused on the behavior of SiO 2 in molten Na 3 AlF 6 . Our goal is to find out the structure and the form of all entities; ionic, non-ionic, complex, or polymerized in molten cryolite-silica melts. High Temperature (HT) Nuclear Magnetic Resonance (NMR) provides direct information about the number and the nature of present ions in the melt as well as local symmetry of the present constituents [START_REF] Machado | Anionic Structure in Molten Cryolite-Alumina Systems[END_REF][START_REF] Rakhmatullin | Study of the NaF-ScF 3 system as a molten bath for production of Sc alloys: A combination of NMR and molecular dynamics simulations[END_REF][START_REF] Keppert | Multi-nuclear magnetic resonance study of Na 3 AlF 6 -AlPO 4 molten and solidified mixtures[END_REF][START_REF] Rakhmatullin | Bessada Aluminium phosphate behaviour in Na 3 AlF 6 -Al 2 O 3 melts: a new insight from in situ high temperature NMR measurements[END_REF]. Rapid Solidification Processing (RSP) allows us to prepare the solidified melt samples with an internal structure as close as possible to a liquid state. Such prepared samples can be then easily analyzed by a whole spectrum of conventional room temperature spectral techniques.

A frequent presence of different disordered solids is well known as a problem in resolving the structure of SiO 2 containing systems. To understand and to comprehend the structure of disordered solids is a difficult task taking into account a missing long-range periodicity and the impossibility to make use of standard diffraction techniques. One of the main experimental methods to determine short-range structures in glasses and amorphous materials is high resolution solid-state NMR spectroscopy.

Experimental

Chemicals and preparation of samples

Chemicals: The chemicals sodium hexafluoroaluminate (Na 3 AlF 6 ), and silicon dioxide (SiO 2 ) were analytical grade and purchased commercially. The CAS Registry Nos., suppliers, and mass fractions are listed in Table 1. The chemicals were stored in glove box Jacomex GP concept with autonomous purification system, at atmosphere of inert argon gas. All the chemicals were used directly for samples preparation. The weighing, homogenization in mortar and preparation of each individual sample were performed in a glovebox. For individual purpose (spontaneously cooled samples, rapid solidified samples, hightemperature NMR measurements), the mechanically homogenized powder mixtures of Na 3 AlF 6 and SiO 2 (in a mole content 0, 5, 25 and 50 mole % of SiO 2 ) were prepared in a glovebox, in an argon inert environment.

Preparation of spontaneously cooled samples: Individual samples were synthetized by direct reaction in molten state. 10.0000 grams of each mixture were individually placed in a Pt crucible and heated in a resistance furnace from room temperature up to 1025 o C at a heating rate of 5 K/min under 0.2 MPa of argon atmosphere. The holding time was 100 min. The temperature control and the data processing were performed using a computerized measuring device (multicomponent model for thermal analysis data collections National Instruments, where the data collections run online under Labview software). The temperature of the samples was controlled by a Pt-PtRh10 thermocouple, calibrated on the melting points of highly pure NaCl and NaF. The accuracy of the temperature difference measurement between the temperatures of primary crystallizations of the given mixtures was (±1 o C). After melting, the samples were then spontaneously cooled down to room temperature at a rate of 7 o C/min. The samples were then homogenized in glovebox and ready for analysis.

Preparation of rapid solidified (RSP) samples: For RSP experiments the samples with the same composition and were pressed into the form of tablets (30 grams). The RSP apparatus (more specifically for the melt spinning method) consisted of an induction heating coil and a rotating cooling Cu-wheel. The samples, in the form of pressed pellets, were placed in a graphite crucible glued into a quartz tube. At the bottom of the crucible there was a small orifice for the outflow of melt. The distance between the orifice and the rotating cylinder was approximately 0.2 mm. The quartz housing tube with the crucible and sample was filled with Ar, to ensure an inert atmosphere. The apparatus arrangement permitted the solidification of the individual melts, heated on 1025 o C, from the molten (above the melting point) to the solid state at a cooling rate of about 10 6 K s -1 . General details of the techniques may be found elsewhere [START_REF] Jacobson | Rapid solidification processing[END_REF][START_REF] Lavernia | The rapid solidification processing of materials: science, principles, technology, advances, and applications[END_REF].

High-temperature and Solid-state NMR analysis

The different mixtures of Na 3 AlF 6 and SiO 2 (α-quartz) were prepared in a glove box under dried argon atmosphere and mixed well. For HT NMR measurements, approximately 60 mg of the different mixtures were put into tightly closed high purity boron nitride (BN) crucibles to avoid any contamination [START_REF] Rakhmatullin | Study of the NaF-ScF 3 system as a molten bath for production of Sc alloys: A combination of NMR and molecular dynamics simulations[END_REF].

All NMR measurements have been carried out using Bruker Avance 400 (9.4 T) NMR spectrometer. The HT NMR spectra have been acquired using the laser-heated NMR system, developed in CEMHTI Orleans [START_REF] Rakhmatullin | Study of the NaF-ScF 3 system as a molten bath for production of Sc alloys: A combination of NMR and molecular dynamics simulations[END_REF]. The BN crucible containing the 100 mg of measuring sample is placed inside the radiofrequency coil into the NMR probe. To ensure a good homogeneous heating, the top and the bottom of the crucible are heated by a CO 2 laser (Coherent Diamond 250 W) passing axially through the NMR probe. The temperature is being controlled by laser power and during the experiment was kept on 1025 o C, for all measured salt mixture. The laser system was previously calibrated by a direct measurement of the temperature inside the NMR probe by a thermocouple. The melting point of the sample is clearly detected by the modification of the shape and width of the NMR line (Fig. 1), using single pulse excitation consisting of 20 μs pulses, recycle delays of 500 ms and 16 -256 scans to obtain a reliable signal-to-noise ratio. Fig. 1. 27 Al HT-NMR spectra of Na 3 AlF 6 measured after 1, 2, 2.5, and 3 minutes from the start of heating.

At room temperature, magic angle spinning (MAS) NMR spectra were acquired using MAS probes from Bruker. 27 Al, 23 Na, and 19 F spectra were collected with 2.5 mm diameter rotors at the rotor frequencies of 30 kHz and 29 Si spectra with 7 mm diameter rotors at the rotor frequencies of 6 kHz. In order to ensure good excitation conditions for both quadrupolar nuclei 27 Al, and 23 Na, very short pulses of 0.5 μs were used with recycle times of 500 ms. For 19 F and 29 Si, π/2 pulse widths were 1.0 μs and 4.1 μs, respectively, and recycle delay was 5×T 1 . Around 128 scans were acquired for 19 F experiments, and up to 1024 for 27 Al, 23 Na, and 29 Si. The reported chemical shifts are referenced to 1 M solutions of NaCl, Al(NO 3 ) 3 for 23 Na and 27 Al, respectively; TMS and CFCl 3 for 29 Si and 19 F, respectively. The NMR parameters (chemical shifts, line widths, quadrupolar coupling parameters) were fitted to the experimental spectra by means of a DMfit2013 program [START_REF] Massiot | Modelling one and two-dimensional solid-state NMR spectra[END_REF].

Weight-loss measurements

Weight-losses caused by the melting of the system were determined gravimetrically and by means of X-ray fluorescence analysis (XRF, ARL ADVANT´X 3600 W). The samples of the composition (Na 3 AlF 6x mole % SiO 2 , x = 0 -40) and weight (30.0 ± 0.01) g were in the first step heated in boron nitride crucible up to 1020 °C in an argon inert atmosphere. The heating rate was 8 -9 °C/min. After reaching the temperature, the samples were kept at this constant temperature for one hour and then spontaneously cooled at 7 °C/min to room temperature. The losses were ex-post recorded gravimetrically and the composition of the solidified samples was determined by XRF. The XRF device was firstly calibrated on the same system. The several solid samples have been prepared with the different composition of SiO 2 for the calibration beforehand. The uncertainty of the gravimetric weight-loss measurement was estimated as 0.1 %. The uncertainty of the XRF weight-loss measurement was estimated (based on the calibration) as 3 %.

X-ray measurements

All solidified samples were grounded to fine powders, and they were then mounted on foils (PANalytical B.V., X-ray film Polyimide 9430 500 21011). To collect the X-ray patterns, a transmission Stoe Stadi P diffractometer equipped with a linear PSD and a curved Ge(111) primary beam monochromator, was used. X-ray diffraction patterns were recorded within the interval of 10 °-80 ° in steps of 0.02° 2θ using Co Kα1 radiation. Phase analysis was performed using X'Pert HighScore Plus PANalytical software with the PDF2 2011 database.

Rapid solidified processing (RSP)

The rapidly solidified samples were prepared with a different amount of SiO 2 (5, 25 and 50 mole % of α-quartz). The RSP apparatus consisted from the inductive furnace and the rotating metal cylinder. Inside the inductive furnace was a quartz tube within the graphite crucible with the samples (30 g). At the bottom of the graphite crucible was a small hole for the outflow of the melt. The distance between the hole and the rotating cylinder was ca 1 millimeter. A nitrogen inert atmosphere was used inside the furnace. The apparatus arrangement permitted the solidification process (from 100 °C above the melting point to the solid state) by a cooling rate at the interval of 10 5 -10 6 °C/s. Further general details of the technique may be found elsewhere [START_REF] Jacobson | Rapid solidification processing[END_REF][START_REF] Lavernia | The rapid solidification processing of materials: science, principles, technology, advances, and applications[END_REF].

Results and Discussion

High temperature NMR analysis

The NMR spectra acquired in the molten state consist in a single Lorentzian line, characteristic of a rapid exchange at the timescale of NMR between the different atomic configurations around the observed nucleus. The measured chemical shift is thus the average of the individual chemical shifts of the different species.

Figure 2 shows an evolution of the shape of 27 Al spectra with the composition of silica. The evolution of the chemical shifts with silica content is reported for all nuclei 19 F, 23 Na, and 27 Al in Figure 3 and Table 2. The isotropic chemical shift of all three isotopes has a similar evolution with the increasing concentration of SiO 2 in melt. The whole spectra can be divided into two different parts. In the first part, one can see a continuous linear increasing of all three chemical shifts over the composition range from 0 to 32.5 mole % of SiO 2 . The typical line widths (full width at half maximum, FWHM) are similar of an order between 90 and 160 Hz. It can be seen, in chemical shift of all elements, a jump change of the slope at the concentration of SiO 2 around 32 mole %. In this second part, the chemical shift stabilized on a constant value and the signal broadened progressively (FWHM ≈ 320 Hz). Additionally, NMR line shape changes from Lorentzian to Gaussian. It means that the local structure of the melt has, at the concentration of 32 mole % SiO 2 , significantly changed. For the compounds that are tending to create glass phases, molecular motion (expressed by viscosity) is an important parameter. The width of the NMR peaks is one parameter that reflects that molecular motion. It is very sensitive to the rate of the molecular reorientation in liquid state [START_REF] Anderson | Nuclear Magnetic Resonance Spectroscopy in Environmental Chemistry[END_REF]. The broadening of NMR lines, observed in our experiment, can currently be caused by the reduction of a solute's molecular mobility, which relates with the increase of the solution`s viscosity.

These findings are in very good agreement with the pivotal work made in this topic by Batashev and Zhurin in 1933 [START_REF] Batashev | Teoreticeskoye Osnovy Elektrometallurgii Alyuminiya[END_REF]. The authors have for the first time reported the phase diagram of the system Na 3 AlF 6 -SiO 2 (in the concentration range of SiO 2 from 0 to 50 wt. %). A eutectic point (coordinates; 3 wt.(10 mole) % SiO 2 and 980 °C) and an immiscibility field (above 12 wt. (32 mole) % SiO 2 ) was identified. This immiscibility phenomenon may exactly be responsible for the jump of the chemical shift observed in our experiment. Very similar findings can be also find in the work of Korenko et al. [START_REF] Korenko | Density, Viscosity and Electrical Conductivity of Molten Cryolite Electrolytes (Na 3 AlF 6 -SiO 2 ) for Solar Grade Silicon (Si-SoG) Electrowinning[END_REF] where the investigation of the physico-chemical properties (density, viscosity and electrical conductivity) of the molten system Na 3 AlF 6 -SiO 2 can be found. The addition of silica to the molten cryolite had a big effect on the viscosity. The authors had assumed that a polymerized glassy-network formation in the melt is responsible for that behavior. Also, a sharp change in the excess molar volume and in the change of the trend of the electrical conductivity, detected at the concentration of SiO 2 very close to that reported by Batashev and Zhurin [START_REF] Batashev | Teoreticeskoye Osnovy Elektrometallurgii Alyuminiya[END_REF], were identified in the work of Korenko et al. [START_REF] Korenko | Density, Viscosity and Electrical Conductivity of Molten Cryolite Electrolytes (Na 3 AlF 6 -SiO 2 ) for Solar Grade Silicon (Si-SoG) Electrowinning[END_REF].

An increase of the chemical shift of 27 Al can be also interpreted as a decrease of the average coordination number of the aluminum atoms. It means, that the increase of the SiO 2 content in the melt is related to the formation of four-coordinated aluminum Al(O,F) 4 . A dissolution of alumina (Al 2 O 3 ) and phosphate (AlPO 4 ) in cryolite melts was being previously studied by high temperature NMR and by MD simulations with DFT calculations [START_REF] Machado | Anionic Structure in Molten Cryolite-Alumina Systems[END_REF][START_REF] Keppert | Multi-nuclear magnetic resonance study of Na 3 AlF 6 -AlPO 4 molten and solidified mixtures[END_REF][START_REF] Rakhmatullin | Bessada Aluminium phosphate behaviour in Na 3 AlF 6 -Al 2 O 3 melts: a new insight from in situ high temperature NMR measurements[END_REF]. The formation of fluoro-oxoaluminate and fluoro-aluminophosphate species, where aluminum atoms are connected by one or two Al-O-Al or P-O-Al bridges, was confirmed. Based on the similar chemical behavior of SiO 2 and AlPO 4 , the dissolution of SiO 2 in molten Na 3 AlF 6 could thus also be associated with the formation of oxygen containing bridges between aluminum and silicon Al-O-Si.

The fluorination of silica was more thoroughly assessed by Dolejš and Baker [START_REF] Dolejš | Thermodynamic analysis of the system Na 2 O-K 2 O-CaO-Al 2 O 3 -SiO 2 -H 2 O-F 2 O -1 : Stability of fluorine-bearing minerals in felsic igneous suites[END_REF]. A complex quaternary system of Na 2 O-Al 2 O 3 -SiO 2 -F 2 O -1 was investigated. In the binary Na 3 AlF 6 -SiO 2 space of this more complex system, a presence of the following chemical bonds and species were suggested: Al-O-Si (albite -NaAlSi 3 O 8 , nepheline -NaAlSiO 4 , Na 6 Si 8 O 19 ), Al-Si-O-F (topaz -Al 2 SiO 4 F 2 ), and Na-Si-F (NaF, Na 2 SiF 6 , SiF 4 (g)). The possible formation of Si-O-F bonds, similar to SiO 2 F 2 2-and Si 2 O 4 F 3

3-

, was latter predicted by thermodynamic modeling in the molten systems containing Na, O, Si, and F atoms [START_REF] Dolejš | Thermodynamic modeling of melts in the system Na 2 O-NaAlO 2 -SiO 2 -F 2 O -1[END_REF]. The presence of fluorine-containing alkali silicate glasses with Si-O-F tetrahedral is also reported in the following systems; MF-SiO 2 (M=alkali metals) and AlF 3 -SiO 2 [START_REF] Takusagawa | Infrared Absorption Spectra and Strucutre of Fluorine-Containing Alkali Silicate Glasses[END_REF][START_REF] Mysen | Interaction Between Fluorine and Silica in Quenched Melts on the Joins SiO 2 -AlF 3 and SiO 2 -NaF Determined by Raman Spectroscopy[END_REF]. A Si 4 O 7 F 2 -formation, was in these works, predicted as a reaction product.

In our measurements, the 19 F chemical shifts range from -191 to -198 ppm. This chemical shift, however, excludes the presence of Si-F, and Si-F-Na bounds groups in Na 3 AlF 6 -SiO 2 melts, since the 19 F chemical shift reported for Si-F-Na group (Na 2 SiF 6 ) is at -152 ppm [START_REF] Zeng | Fluoride sites in aluminosilicate glasses: High-resolution 19 F NMR results[END_REF][START_REF] Duncan | Study of Fluorine in Silicate Glass with 19 F Nuclear Magnetic Resonance Spectroscopy[END_REF]. These authors, at the same time, proposed that the SiO 4 -tetrahedron is preserved in the melt as a rigid structure entity. By the combination of the data, obtained for the different nuclei in our and previous works, we can propose that aluminium and silicon atoms in our melt would be connected by an Al-O-Si bridge.

A proper evidence for the previous statements can be seen when we look on Fig. ) is represent by AlF 5 2-as an average coordination form. Further, let us consider, that the atomic fractions in the cryolite-rich melts (i.e. the partitioning of Al, F, and Si different species) can be derived by using the Eqn. 1 and 2. Then, one should notice, that for eutectic concentration, the 27 Al chemical shift moves upward (to the values corresponding to the pure albite (δ( 27 Al) = 63.0ppm, for albite [START_REF] Stebbins | Nuclear Magnetic Resonance Spectroscopy of Silicates and Oxides in Geochemistry and Geophysics[END_REF])), while the 19 F chemical shift remains the same. It means that at the eutectic composition, the fluorine partitioning between the different species in the solid and liquid phase, remains uniform.

Weight loss analysis

The experimental results of the mass losses are depicted in Fig 4 . The mass loses were determined by weight analysis of the samples (after the melting and spontaneous cooling), as well as by X-ray fluorescence (XRF) analysis. The XRF analysis confirmed that the total weight losses are in the linear relationship with the specific Si-losses, which is an indication that the weight losses are due to the volatilization of Si-compound(s) from the melt (e.g. SiF 4 ). The similar behavior was also found in the previous works [START_REF] Fellner | Chemical reactions in molten Na 3 AlF 6 -SiO 2 -Al 2 O 3 -AlF 3 mixtures[END_REF][START_REF] Dolejš | Thermodynamic analysis of the system Na 2 O-K 2 O-CaO-Al 2 O 3 -SiO 2 -H 2 O-F 2 O -1 : Stability of fluorine-bearing minerals in felsic igneous suites[END_REF][START_REF] Kogarko | Experimental investigation of the effect of alkalinity of silicate melts on the separation of fluorine into the gas phase[END_REF][START_REF] Snow | Reactions in the cryolite-silica system[END_REF][START_REF] Siljan | Sodium aluminium fluoride attack on alumino-silicate refractorieschemical reactions and mineral formation[END_REF] where the authors have reported SiF 4 as predominant volatile product, upon the melting of the mixture of Na 3 AlF 6 and SiO 2 . The formation of the volatile product shifts the melt`s composition from a simple binary system to the ternary system Na 3 AlF 6 -SiO 2 -SiF 4 . The continuous evaporation of SiF 4 off the melt further increases the thermodynamic degree of freedom and the system can then be considered, based on the Dolejš and Baker [START_REF] Dolejš | Thermodynamic analysis of the system Na 2 O-K 2 O-CaO-Al 2 O 3 -SiO 2 -H 2 O-F 2 O -1 : Stability of fluorine-bearing minerals in felsic igneous suites[END_REF], as the quaternary Na 2 O-Al 2 O 3 -SiO 2 -F 2 O -1 (using the Dolejš and Baker's formulas, suitable for the geological description of granitic and rhyolitic magmas with the presence of fluorine). These authors also used a thermodynamic calculation to propose the following possible de-volatilization`s equilibria: To further zoom in the structural correlations in our molten system, especially at the melt/solid (glass) interphase, and to distinguish between the above-mentioned reaction paths, an application of a robust, cutting-edge approach was needed. A combined approach including the solid state NMR, XRD, and EDX analysis was applied. The solidified samples were prepared, either as spontaneously cooled, or as rapidly solidified (prepared by RSP).

Spontaneously solidified samples: X-ray and MAS NMR analysis

To be able to clarify an influence of the concentration of SiO 2 on the structure of the Na 3 AlF 6 -SiO 2 melt, a series of spontaneously solidified samples with different concentration of SiO 2 (5, 25 and 50 mole %) were prepared for a subsequent analysis.

An interesting phenomenon was visually observed when we looked at the solidified sample with the highest SiO 2 content (50 mole %). A formation of the two obviously separate and distinguish phases with different surface-look was visible. One phase looked like a "glass", while the other one had more "poly-crystalline" surface. Due to this fact, the sample with the content of SiO 2 50 mole % was analyzed by two ways: i) as one single homogenized sample and ii) as separated two phases, upper and lower layers.

The results from the first way of analysis are presented in this chapter 3.3. The results of the separated phases are reported in following chapter 3.4.

The Fig. 5 shows the results of the X-ray analysis of the spontaneously solidified samples. A MAS NMR ( 19 F, 23 Na, and 27 Al) analysis of those samples can be seen on the Fig. 6 and7. A similar analysis of the separated phases (come from the sample with 50 mole % of SiO 2 ) is shown on the Fig. 8 and9.

As it can be seen from the Fig. 5, two crystalline structures can be found in all spontaneously solidified samples of Na 3 AlF 6 -SiO 2. The first one is pure cryolite, the second one is NaF. A small part of NaF in the sample is from a well-known thermal dissociation of Na 3 AlF 6 [50][51][52] according the following reaction. The rest of the NaF presented in the samples, comes from different possible reaction between cryolite and silica (e.g., like was proposed in work [START_REF] Boe | Electrolytic Deposition of Silicon and of Silicon Alloys Part II: Decomposition Voltages of Components and Current Efficiency in the Electrolysis of the Na 3 AlF 6 -Al 2 O 3 -SiO 2 Mixtures[END_REF], and/or [START_REF] Dolejš | Thermodynamic analysis of the system Na 2 O-K 2 O-CaO-Al 2 O 3 -SiO 2 -H 2 O-F 2 O -1 : Stability of fluorine-bearing minerals in felsic igneous suites[END_REF]). Other products of the reactions can be in non-crystalline forms, or their patterns are covered by those of NaF. The non-crystalline forms were in fact detected in the sample with the higher concentration of silica (Fig. 5) where a typical background feature was observed in the range from 15 o to 40 o (2Θ). This background is typical for silicon glassy phases [START_REF] Hanawalt | Chemical Analysis by X-Ray Diffraction[END_REF].

The intensity of NaF peaks however increase with the concentration of SiO 2 , which means that the increasing presence of NaF in the samples can not only be a result of the thermal dissociation of cryolite. Some part of the newly formed NaF must be the product of the interaction between cryolite and silica. Another product(s) of the interaction between cryolite and silica ended up likely in outgoing vapors (like SiF 4 ), or in amorphous phase(s). Subsequent MAS NMR and SEM EDX analysis of the spontaneously and RSP rapidly solidified samples, was performed.

Figure 6 shows the high resolution 19 F, 23 Na, and 27 Al MAS NMR spectra of the spontaneously solidified samples. As it can be seen from the figure, the fluorine spectra Fig. 6. The comparison of 19 F, 23 Na, and 27 Al spectra (black lines) of the spontaneously solidified samples with different content of SiO 2 (A -5 mole %, B -25 mole % and C -50 mole %); *spinning side bands. Colored lines show the contributions of each fitting component. of all samples contained only two signals; one at -191 ppm and another at -223 ppm. The first signal is assigned to cryolite (Na 3 AlF 6 ), while the second signal to sodium fluoride (NaF). The intensity of the peak belongs to the NaF increases with the increasing concentration of SiO 2 in the samples. This observation is another evidence that the major amount of NaF in this system comes from the reaction between molten Na 3 AlF 6 and SiO 2 . The absence of other fluorine signals in samples also indicates that no other compounds, with the fluorine atom in their structure, are present in the melt. This finding is in agreement with the HT NMR results.

In the case of 27 Al NMR, the spectra of all samples contain a signal at 0 ppm corresponds to the aluminum in the octahedral structure of cryolite (Na 3 AlF 6 ). The spectra also contain a new signal at (δ iso = -56 ppm). The intensity of that signal is clearly increasing with the concentration of SiO 2 in the samples. But the shape of this peak indicates, that this compound is amorphous; hence, likely does not belong to any crystalline phase [START_REF] Smelik | A study of the thermal behavior of terrestrial tridymite by continuous X-ray diffraction[END_REF]. The 23 Na spectra contain peaks at 7 ppm and at 1.7 ppm, and one duplet at 7.8 ppm. The first peak ascribed to sodium in NaF, we can again see the increasing of its intensity with the increasing of the concentration of SiO 2 in the samples. Two other peaks correspond to the sodium, intercalated into two positions in the structure of cryolite (Na 3 AlF 6 ). An increase of the background of these spectra can be also seen, especially at the highest concentration of the SiO 2 , indicating a presence of a disordered compound, amorphous NaAlSi 3 O 8 [START_REF] Kogarko | Unmixing in fluorosilicate systems[END_REF]. This fact was the very reason why a convolution of the 23 Na spectra was subsequently performed (Fig. 7).

Based on what was already said above, we can conclude that the increasing of the concentration of SiO 2 brings about two major effects in the spontaneously solidified samples of the system Na 3 AlF 6 -SiO 2 . The first effect is related to the reaction between both components where one of the product is NaF (e.g. based on the reactions 1, 2 or 4). The second effect, especially pronounced at higher concentration of SiO 2 , is a presence of disordered amorphous compound/compounds. Both findings are in very good correlation with what was already observed in the X-ray analysis of this system.

X-ray and MAS NMR analysis of the sample with 50 mole % SiO 2

Figure 8 shows an X-ray diffraction of separable phases of the sample SiO 2 that was prepared with 50 mole %, as was mentioned above. The upper crystalline layer (Fig. 8 upper pattern) contains only NaF and cryolite. The lower polycrystalline layer (Fig. 8, lower pattern) contains only the diffractions of cryolite and the diffractions of tridymite and cristobalite. Tridymite is βform of SiO 2 , Fig. 8. X-ray pattern of the Na 3 AlF 6 mixture with 50 mole % of SiO 2 ; picture up -upper crystalline layer of the sample (*-NaF [START_REF] D' Espinose De Lacaillerie | MAS NMR spectra of quadrupolar nuclei in disordered solids: The Czjzek model[END_REF][START_REF] Schmelz | Gel synthesis of an albite (NaAlSi 3 O 8 ) glass: An NMR analysis[END_REF], other diffractions -Na 3 AlF 6 [START_REF] Mcmurdie | Standard X-Ray Diffraction Powder Patterns from the JCPDS Research Associateship[END_REF][START_REF] Mascolo | Thermal crystallization of ion-exchanged zeolite A[END_REF]); picture down -lower polycrystalline layer of the sample (X -SiO 2 (cristobalite form) [START_REF] Murdoch | High-resolution 29 Si NMR study of silicate and aluminosilicate glasses: the effect of network-modifying cations[END_REF], Y -SiO 2 (tridymite form) [START_REF] Kirkpatrick | High resolution solid-state sodium-23, aluminum-27, and silicon-29 nuclear magnetic resonance spectroscopic reconnaissance of alkali and plagioclase feldspars[END_REF]). while cristobalite is γform of this compound. These findings are in line with the work of [START_REF] Dolejš | Thermodynamic analysis of the system Na 2 O-K 2 O-CaO-Al 2 O 3 -SiO 2 -H 2 O-F 2 O -1 : Stability of fluorine-bearing minerals in felsic igneous suites[END_REF], where is reported the existence of a large stability fields of the silica polymorphs in the silica-fluoride systems. These structures of silica had been mostly identified on the typical non-crystalline background feature, observed in the range from 15 o to 40 o (2Θ). The feature in this range represents a wide interval of Gaussian distribution of bound distance between silicon and oxygen in the structure of SiO 2 . According to the diffraction pattern in this region (20° -40°, 2Θ), the new glassy phases in this system are probably based on cristobalite and tridymite (β-and γform of SiO 2 ). The spectrum of the lower layer also contains some minor diffractions of Na 3 AlF 6 and NaF.

The presence of the liquid-liquid immiscibility in molten fluoride-silicates has been a matter of a long discussion [START_REF] Grjotheim | Electrolytic deposition of silicon and silicon alloys: Part I: Physicochemical properties of the Na 3 AlF 6 -Al 2 O 3 -SiO 2 mixtures[END_REF][START_REF] Weill | The 1010 ° and 800 °C isothermal section in the system[END_REF][START_REF] Batashev | Teoreticeskoye Osnovy Elektrometallurgii Alyuminiya[END_REF]62]. The last investigations are indicating [START_REF] Dolejš | Thermodynamic analysis of the system Na 2 O-K 2 O-CaO-Al 2 O 3 -SiO 2 -H 2 O-F 2 O -1 : Stability of fluorine-bearing minerals in felsic igneous suites[END_REF] that the immiscibility phenomenon exists in these systems only at higher temperatures (1200 °C) and/or higher pressures (600 MPa). No immiscibility below 1100 °C was confirmed [START_REF] Dolejš | Thermodynamic analysis of the system Na 2 O-K 2 O-CaO-Al 2 O 3 -SiO 2 -H 2 O-F 2 O -1 : Stability of fluorine-bearing minerals in felsic igneous suites[END_REF]. To elucidate the structure of the amorphous phase/phases, identified by X-ray diffraction, a MAS NMR spectroscopy ( 27 Al, 19 F, 23 Na, and 29 Si) of the lower layer was performed, as well (Figure 9). As it can be seen in Fig. 9, the spectra of the 19 F and 23 Na isotopes contain peaks assigned to the crystal structure of Na 3 AlF 6 and NaF. The spectrum of the 27 Al isotope contains, beside a peak with δ iso = 0 ppm assigned to six-coordinated octahedral species (AlF 6 ) in the structure of Na 3 AlF 6 , also a broad peak at δ iso = 56 ppm assigned to tetrahedral framework of AlO 4 . If we compare the peak positions of the 27 Al, 23 Na, and 29 Si with the positions of those nuclei in one type of glass forming alumino-silicate, albite (NaAlSi 3 O 8 ), a very good correlation of the positions of those nuclei can be obtained. The presence of amorphous phase confirms also a relative width of the peaks of NaAlSi 3 O 8 which is due to a range of bond angles and bond distances around Al-O-Si sites [63,64]. The tetrahedral framework of AlO 4 , identified in the 27 Al spectrum (peak at δ iso = 0 ppm) is very likely related with albite as well. The 29 Si NMR spectra contains a broad peak assigned to NaAlSi 3 O 8 and a relatively sharp peak of SiO 2 in the mixed form of cristobalite and tridymite. The presence of these forms of SiO 2 in the samples was already confirmed by X-ray analysis. The 19 F spectrum contains, besides the peaks already assigned to Na 3 AlF 6 , only a small resonance of NaF. This fact indicates that the amorphous phase in the upper layer of the sample does not contain any species with fluorine.

Based what was found, it can be concluded that in molten system of Na 3 AlF 6 -SiO 2 , a reaction occurs between constituents. The products of the reaction between Na 3 AlF 6 and SiO 2 are NaF, NaAlSi 3 O 8 , and very likely (assuming atmospheric pressure) also vapors of SiF 4 .

These conclusions are in a good agreement with one of the thermodynamic models (Eqn. 4) proposed by Dolejš and Baker [START_REF] Dolejš | Thermodynamic analysis of the system Na 2 O-K 2 O-CaO-Al 2 O 3 -SiO 2 -H 2 O-F 2 O -1 : Stability of fluorine-bearing minerals in felsic igneous suites[END_REF].

Rapidly solidified samples -SEM and EDX analysis

In order further probe the structural correlations and the chemistry of the studied system of Na 3 AlF 6 -SiO 2 , a rapid solidification processing (RSP) was used to prepare deeply undercooled samples with 25 and 50 mole % of SiO 2 . Figure 10 shows a morphology of the surface, as well SEM EDX analysis on some identified spots on the surface of the under-cooled samples. As can be seen, the morphology of the samples is quite different from one another. The sample on the left side (25 mole % of SiO 2 ) consists of a uniform "spongy" morphology with hindered crystal growth. The morphology of the sample on the right side (50 mole % of SiO 2 ) is different, and two separable phases are clearly visible. All related elements (Na, Al, O, Si, and F), although in different concentration, was found to be present in all analyzed spots in both samples. However, the figure shows that the smooth phase in the sample on the right side (50 mole % of SiO 2 ) has somewhat higher concentration of oxygen, aluminum and silicon. The increased concentration of these elements may relate with the presence of NaAlSi 3 O 8 in this phase. On the other hand, the SEM EDX analysis of more rough phase (spots 2 and 3 on the left side and spot 3 on right side) shows a higher concentration of sodium and aluminum, which is probably related with the higher content of NaF and Na 3 AlF 6 .

The analysis of rapidly solidified sample with higher concentration of silica (50 mole %) proved what had been already indicated by previous analysis that the higher concentration of SiO 2 in Na 3 AlF 6 -SiO 2 system lead to polymerization of the melt and the formation of albite NaAlSi 3 O 8 .

Conclusion

NMR analysis of Na 3 AlF 6 -SiO 2 melts and solidified melts by means of the selective observation of the different nuclei involved in the system ( 19 F, 27 Al, 23 Na and 29 Si), and coupled with the side X-ray diffraction, showed to be a powerful tool for the phase/structural description of such a complex systems. We would like to stress that it was, to our knowledge, for the first time when NMR technique was used for the high temperature analysis of this rather complicated molten/crystallized (amorphous) Na 3 AlF 6 -SiO 2 system. It can be finally concluded, that in molten system of Na 3 AlF 6 -SiO 2 , a formation of NaF, NaAlSi 3 O 8 , and SiF 4 occurs. The silicon anion is incorporated into the melt structure by the Al-O-Si oxygen bridge. The high temperature reaction, which leads to this formation, can be formally described with the following scheme. The X-ray, SEM EDX analysis and MAS NMR analysis of the spontaneously and rapidly solidified samples also showed that the composition of the products on the right side of the reaction [START_REF] Oishi | Process for Solar Grade Silicon Production by Molten Salt Electrolysis Using Aluminium-Silicon Liquid Alloy[END_REF] does not change upon precipitation. The solidified samples retained the similar constituents like in the molten state: NaF, albite, cristobalite, trydimite and an amorphous phase(s) derived from the different modifications of SiO 2 .

Fig. 2 .

 2 Fig. 2. 27 Al HT-NMR spectra as a function of SiO 2 concentration, measured at 1025 °C.

Fig. 3 .

 3 Fig.3.27 Al,23 Na and19 F chemical shifts evolution for Na 3 AlF 6 -SiO 2 melts, at 1025 °C.

-

  3. Let us simplify, that in pure molten Na 3 AlF 6 , the fluoroaluminate species-distribution (AlF 4

Fig. 4 .

 4 Fig. 4. A weight loss analysis in the system Na 3 AlF 6 -SiO 2 . The amount of the samples: 30 g. Full circles: mass analysis after spontaneous cooling; open circles: SiF 4 losses determined by XRF analysis.

Na 3 6 )Fig. 5 .

 365 Fig. 5. The comparison of X-ray spectra of the spontaneously solidified samples with different content of SiO 2 (Apure Na 3 AlF 6 before melting [53, 54], Bpure Na 3 AlF 6 after melting, C -5 mole %, D -25 mole % and E -50 mole %); *position of NaF diffractions [55, 56].

Fig 7 .

 7 Fig 7. 23 Na MAS NMR spectrum of spontaneously solidified sample with 50 mole %. SiO 2 : black line experimental, red dotted line are fitted spectra, colored lines show the contributions of each fitting component.

Fig 9 .

 9 Fig 9. The fit of the MAS NMR ( 19 F, 27 Al, 23 Na and 29 Si) of the lower layer of the spontaneously solidified Na 3 AlF 6 mixture with 50 mole % of SiO 2 .

Fig. 10 .

 10 Fig. 10. SEM EDX analysis of the deeply under-cooled samples of Na 3 AlF 6 -SiO 2 system (25 and 50 mole % SiO 2 ) prepared by RSP. The left side: 25 mole % of SiO 2 . The right side: 50 mole % of SiO 2 .

Na 3

 3 AlF 6 (l) + 4 SiO 2 (diss) = 2 NaF(l) + NaAlSi 3 O 8 (l) + SiF 4 (g)[START_REF] Oishi | Process for Solar Grade Silicon Production by Molten Salt Electrolysis Using Aluminium-Silicon Liquid Alloy[END_REF]

Table 1 .

 1 CAS Registry Number, Mass Fraction and Purity of used Chemicals and materials.

	component	CAS Reg. No.	suppliers	purity
	Sodium hexafluoroaluminate	13775-53-	Alfa Aesar by Thermo	99.90%, powder
	Na 3 AlF 6	6	Fischer Scientific GmbH,
			Germany
	Silicon dioxide, SiO 2	7631-86-9	JMC (Johnson Matthey	99.90%, powder
			Chemicals Limited)
	BN crucible with lid, BN, for	10043-11-	P Vision-ABC France	99.99%, Crucible Ø 9,
	high-temperature NMR	5		hole Ø 2.5×7 mm deep
	measurements
	BN crucible for weight-loss	10043-11-	Saint-Gobain Construction	99.99%, Crucible Ø 30,
	measurements	5	Products, s.r.o., USA	hole Ø 25×70 mm deep
	Argon, Ar	7440-37-1	SIAD, Slovakia	99.999%, gas
	Platinum/10rhodium, PtRh10 11107-71-	Safina, Slovakia	90%Pt10%Rh, crucible
		4
	Sintered aluminium oxide,	1344-28-1 Morgan Advanced Materials	99.7%, sintered tubes
	Al 2 O 3		Haldenwanger GmbH,
			Germany
	Sodium chloride ultrapure,	7647-14-5	Alfa Aesar by Thermo	99.9%, powder
	NaCl		Fischer Scientific GmbH,
			Germany
	Sodium fluoride, NaF	7681-49-4	Alfa Aesar by Thermo	99.9%, powder
			Fischer Scientific GmbH,
			Germany

Table 2 .

 2 7 Al,23 Na and19 F experimental chemical shifts and FWHM for Na 3 AlF 6 -SiO 2 melts, at 1025 °C.

	Mole %	27 Al		23	Na	19 F
	SiO 2	δ iso / ppm	FWHM /	δ iso / ppm	FWHM /	δ iso / ppm	FWHM /
			Hz		Hz		Hz
	0	18.1	115	-8.9	82	-197.7	90
	5	18.6	114	-8.9	80	-197.3	91
	10	19.8	85	-8.3	86	-197.0	91
	15	21.7	102	-7.5	82	-196.4	97
	20	22.9	110	-7.2	97	-196.3	95
	25	23.8	159	-7.1	93	-196.0	107
	30	25.0	156	-6.5	90	-195.4	103
	32.5	26.8	323	-3.7	177	-191.0	217
	35	27.6	322	-3.7	163	-191.0	230
	40	27.1	314	-3.7	180	-190.6	342
	50	27.4	338	-3.6	176	-190.9	238
	Standard uncertainties u are u(δ) = ± 0.5 ppm, u(FWHM) = 10 Hz

Ackowledgement

This study was financially supported by the Slovak bilateral project (N° SK-FR-2013-0039), and Slovak Grant Agencies (VEGA-2/0060/18). The work performed within the ITMS project (with code 313021T081) supported by Research & Innovation Operational Programme funded by the ERDF.


Aydar Rakhmatullin

Maxim S Molokeev

Graham King

Ilya B Polovov

Konstantin V Maksimtsev

Erwan Chesneau

Emmanuelle Suard

Rinat Bakirov

František Šimko

Catherine Bessada

Mathieu Allix

Polymorphs of Rb 3 ScF 6 : X-ray and neutron diffraction, solidstate NMR, and DFT calculations study

Keywords: Rb 3 ScF 6, phase transitions, in-situ high-temperature solid-state NMR, synchrotron X-ray powder diffraction, neutron powder diffraction; structure determination, DFT-GIPAW

come

Introduction

Alkali metal fluoroscandates have recently attracted much attention due to their promising potential use in many areas such as fluorescent probes, solar cell, solid-state lasers, and other fields. [START_REF] Ai | Lanthanide-doped NaScF 4 nanoprobes: crystal structure, optical spectroscopy and biodetection[END_REF][START_REF] Yu | Controlled synthesis of high quality scandium-based nanocrystals as promising recyclable catalysts for silylcyanation reaction[END_REF][START_REF] Xiong | One-step surfactantfree synthesis of KSc 2 F 7 microcrystals: controllable phases, rich morphologies and multicolor down conversion luminescence properties[END_REF][START_REF] Zhang | The colour tuning of upconversion emission from green to red in NaScF 4 :Yb 3+ /Er 3+ nanocrystals by adjusting the reaction time[END_REF][START_REF] Tyagi | Syntheses and structures of Li 3 ScF 6 and high pressure LiScF 4 , luminescence properties of LiScF 4 , a new phase in the system LiF-ScF 3[END_REF] Due to their specific electronic configurations and the small ionic radius of scandium compared to other rare earth elements, fluoroscandates doped with Mn 4+ or Ln 3+ can generate interesting optical properties as recently demonstrated for NaScF 4 , [START_REF] Ai | Lanthanide-doped NaScF 4 nanoprobes: crystal structure, optical spectroscopy and biodetection[END_REF][START_REF] Yu | Controlled synthesis of high quality scandium-based nanocrystals as promising recyclable catalysts for silylcyanation reaction[END_REF] KSc 2 F 7 , [START_REF] Xiong | One-step surfactantfree synthesis of KSc 2 F 7 microcrystals: controllable phases, rich morphologies and multicolor down conversion luminescence properties[END_REF][START_REF] Chen | Simultaneous Tailoring of Dual-Phase Fluoride Precipitation and Dopant Distribution in Glass to Control Upconverting Luminescence[END_REF] and K 3 ScF 6 . [START_REF] Ming | Highly Regular, Uniform K 3 ScF 6 :Mn 4+ Phosphors: Facile Synthesis, Microstructures, Photoluminescence Properties, and Application in Light-Emitting Diode Devices[END_REF] Mn 4+ -doped K 3 AlF 6 has been latterly reported to show high color rendering properties. [START_REF] Song | Highly Efficient and Thermally Stable K 3 AlF 6 :Mn 4+ as a Red Phosphor for Ultra-High-Performance Warm White Light-Emitting Diodes[END_REF] As recently demonstrated, Rb 3 ScF 6 is isostructural with K 3 AlF 6 . [START_REF] Abakumov | The Crystal Structure of α-K 3 AlF 6 : Elpasolites and Double Perovskites with Broken Corner-Sharing Connectivity of the Octahedral Framework[END_REF][START_REF] King | The High-Temperature Polymorphs of K 3 AlF 6[END_REF] The specific crystal symmetry of the polymorphs, phase transitions, and associated physical properties of studied compound may be related to structural particularities of this class of compounds, which is named halide double perovskites (А 2 ВВ'Х 6 ). The double perovskite structure is so-called because the unit cell of double perovskite is twice as large as that of a simple ABX 3 perovskite. Moreover, K 3 AlF 6 exhibits superstructure polymorphs, which was attributed to the non-cooperative octahedral tilting. [START_REF] Abakumov | The Crystal Structure of α-K 3 AlF 6 : Elpasolites and Double Perovskites with Broken Corner-Sharing Connectivity of the Octahedral Framework[END_REF][START_REF] King | The High-Temperature Polymorphs of K 3 AlF 6[END_REF] Such structures are highly complex and difficult to study. Additionally, the dynamic motion of the AlF 6 octahedra in K 3 AlF 6 was established. An exact knowledge of the structure and dynamics of these various crystalline materials is required to understand their functionalities, and to further improve their properties to suit the above mentioned applications.

Structural studies on almost all reported lithium, potassium, and sodium fluoroscandates have been performed. Recently, the structure of two members of the CsF-ScF 3 system, CsScF 4 and CsSc 3 F 10 , has been reported. [START_REF] Krylov | Crystal structure and phase transitions of a layered perovskite-like CsScF 4 crystal[END_REF][START_REF] Rakhmatullin | Combining solid state NMR, powder X-ray diffraction, and DFT calculations for CsSc 3 F 10 structure determination[END_REF] However, rubidium containing fluoride compounds have been overlooked. Only the structure of the RT RbSc 3 F 10 polymorph has been reported to date. It is worth noting that this study was only published in a PhD manuscript and is not included in structural databases. [START_REF] Yin | New Solid-State Fluorides: Synthesis, Crystal Chemistry, and Optical Properties[END_REF] Regarding Rb 3 ScF 6 , Turrell et al. [START_REF] Turrell | Vibrational spectra, phase transitions and force-fields in crystalline scandium hexafluorides[END_REF] found that the compound undergoes two polymorphic transformations at 154 °C and 200 °C. From X-ray powder diffraction data, it was proposed that the room temperature and medium-temperature structures are tetragonal, with space group P4/mnc (Z= 128) at RT and the lattice parameters a = 6.419 Å, c = 9.154 Å and a = 6.467 Å, c = 9.222 Å at RT and 177 °C, respectively. The high-temperature structure was reported to be cubic, space group (Z= 4) with a = 9.214 Å at 250 °C. From variable temperature Raman spectroscopy experiments, the authors stated that all polymorphs contain isolated ScF 6 3-octahedra. However, only cell parameters and space groups were proposed for the three polymorphs and the crystalline structures have not been established.

In this paper, we used a combined approach including solid state NMR spectroscopy, transmission electron microscopy, and synchrotron, neutron powder diffraction to precisely determine the structure of three Rb 3 ScF 6 polymorphs between RT and high temperature. In addition, we employed in-situ high-temperature (HT) MAS NMR experiments to follow the structural transitions and dynamics. 2D MQMAS NMR methods enabled to enhance the spectral resolution by spreading signals in two spectral dimensions. High-temperature MAS NMR is an unusual method for structural characterization. Here, we show that the use of this technique can provide an accurate description of the phase transitions, as well as quantitative and qualitative information on structure and dynamics.

EXPERIMENTAL

Synthesis

Rubidium fluoride (Aldrich, 99.8 %) and scandium fluoride (JSC Dalur, >99 %) powder precursors were used for the synthesis of Rb 3 ScF 6 . The salts were first dried under vacuum at 150 °C for 6 h and then transferred to an argon filled glovebox. All the manipulations were performed in an argon-filled glovebox, unless mentioned otherwise. Both salts were then mixed and homogenized in an agate mortar in required proportions (5 grams of mixture; 3.7727 g of RbF and 1.2273 g of ScF 3 ) and placed into a nickel crucible covered with nickel lid. The synthesis was performed by solid state reaction inside the glovebox to exclude possible contamination by moisture and minimize the influence of oxygen. The crucibles were placed in the furnace, and the heating was performed at 840 °C for 6 h with a heating rate of 5 °C/min. The furnace was then cooled with a rate of 2 °C/min, and the crucibles were taken out and weighed. The changes of crucible's mass did not exceed 10 mg, and vapor deposition was not noticed. The resulting pale-white salt was extracted from the crucible outside the glovebox and homogenized.

Thermal analysis measurements

Differential scanning calorimetry (DSC) was used for following phase transformations taking place during both heating and cooling of Rb 3 ScF 6 . The measurements were performed with a Mettler Toledo STAR DSC823 calorimeter equipped with a FRS 5 sensor and 56 Au-Au/Pd thermocouples (working range of 10-700 °C, resolution <0.04 μW). The Rb 3 ScF 6 samples were loaded in a platinum crucibles and heated from 25 to 260 °C at 5 (heating) and 7 °C/min (cooling). Dry air flow through the furnace was maintained at 50 ml/s rate.

Electron diffraction

Selected area electron diffraction (SAED) patterns were collected on a Philips CM20 transmission electron microscope (TEM) fitted with an Oxford energy dispersive spectrometry (EDS) analyzer. The sample was first crushed in ethanol, and then a drop of the solution with the small crystallites in suspension was deposited onto a carbon-coated copper grid.

X-ray Powder Diffraction

High resolution synchrotron powder diffraction data were collected at the 11-BM beamline at the Advanced Photon Source (APS), Argonne National Laboratory using a wavelength of 0.457893 Å at RT and 0.457901 Å at 187 °C. The powder was packed into a kapton capillary with an outer diameter of 0.8 mm and spun during data acquisition from 0.5 to 50° (2 theta) using 0.001° steps.

High temperature X-Ray powder diffraction (XRPD) data were recorded on a Bragg Brentano D8 Advance Bruker diffractometer (CuK α radiation) equipped with a LynxEye XE detector over an angular range of 5°<2 <130°.

Rietveld refinements were performed using the Topas 4.2 [START_REF] Bruker | TOPAS 4.2. In User's Manual. General profile and structure analysis software for powder diffraction data[END_REF] and JANA2006 [START_REF] Petříček | Crystallographic Computing System JANA2006: General features[END_REF] software.

Neutron Powder Diffraction

Neutron powder diffraction (NPD) data were obtained at the Institute Laue Langevin (ILL, Grenoble, France) on the D2B diffractometer at room temperature using an 8 mm diameter vanadium tube. Data were collected with a wavelength of 1.59354 Å over a range of 0°<2 <160° with a 0.05° step size.

NMR spectroscopy

Room temperature solid-state MAS NMR spectra were recorded on a Bruker Avance III HD 17.6 and Avance NEO 20 T spectrometers using 1.3 and 2.5 mm resonance probes at MAS frequency of 60 or 30 kHz, respectively. [START_REF] Rakhmatullin | X-ray Diffraction, NMR Studies, and DFT Calculations of the Room and High Temperature Structures of Rubidium Cryolite, Rb 3 AlF 6[END_REF] F, 45 Sc, and 87 Rb RF strengths were 190, 464, and 83 kHz, respectively. 87 Rb MQMAS spectra were acquired by two different ways, i.e.

either with Z-filtering [START_REF] Massiot | Sensitivity and Lineshape Improvements of MQ-MAS by Rotor-Synchronized Data Acquisition[END_REF] and using RIACT excitation method. [START_REF] Wu | Quantitative Multiple-Quantum Magic-Angle-Spinning NMR Spectroscopy of Quadrupolar Nuclei in Solids[END_REF] The Z-filter experiment parameters were identical to the ones used in our previous study. [START_REF] Rakhmatullin | X-ray Diffraction, NMR Studies, and DFT Calculations of the Room and High Temperature Structures of Rubidium Cryolite, Rb 3 AlF 6[END_REF] RIACT MQMAS spectra were measured using the two pulse RIACT (II) sequence [START_REF] Angeli | Boron Speciation in Soda-Lime Borosilicate Glasses Containing Zirconium[END_REF] with pulse widths of 3.7 μs and 8 μs, at a RF field of ~150 kHz. The sweep widths were 500 kHz and 120 kHz (4ν r ) in the direct and indirect dimension. A recycle delay of 0.1 s has been used.

High temperature data were collected at 17.6 T using a MAS LASER probe with boron nitride crucibles contained in 7 mm zirconia bottom-less rotor spinning at 6 kHz. The diode laser beam (DILAS 200 W, 980 nm) is guided by fiber optics to the crucible.

Unfortunately, a significant temperature gradient was detected in the sample due to the heating of the container from bottom only. To decrease the temperature gradient inside the sample, only about 20 mg of powder was placed in the crucible.

In order to improve the resolution, two decoupling pulse schemes were applied: CW (10 kHz for [START_REF] Rakhmatullin | X-ray Diffraction, NMR Studies, and DFT Calculations of the Room and High Temperature Structures of Rubidium Cryolite, Rb 3 AlF 6[END_REF] F; 5 kHz for 45 Sc) in the case of HT experiments and PISSARRO 21 45 Sc and [START_REF] Rakhmatullin | X-ray Diffraction, NMR Studies, and DFT Calculations of the Room and High Temperature Structures of Rubidium Cryolite, Rb 3 AlF 6[END_REF] F in the case of MAS frequency of 30 or 60 kHz. [START_REF] Rakhmatullin | X-ray Diffraction, NMR Studies, and DFT Calculations of the Room and High Temperature Structures of Rubidium Cryolite, Rb 3 AlF 6[END_REF] F, 45 Sc, and 87 Rb chemical shifts are referenced to CFCl 3 , 0.11 M ScCl 3 solution in 0.05 M HCl, and 0.01 M RbNO 3 , respectively.

The NMR parameters (chemical shifts, line widths, and quadrupolar parameters) were fitted for several different rotation frequencies and for two magnetic fields to the experimental spectra by means of the DMfit program. [START_REF] Massiot | Modelling one and two-dimensional solid-state NMR spectra[END_REF] Additionally, the simulations of 1D and 2D

MQMAS and RIACT 87 Rb spectra were performed using a fNMR package implementing the method described in Reference 23.

DFT calculations

In the case of DFT calculations using the Perdew-Burke-Ernzerhof (PBE) functional [START_REF] Perdew | Generalized Gradient Approximation Made Simple[END_REF] for compounds containing Ca, Sc, and La atoms, there is an overestimation of the hybridization between the 2p anion (oxygen or fluorine) orbitals and the unoccupied 3d 0 and 4f 0 orbitals. As a consequence of this overestimation, the covalent character of a bond increases and the agreement between the experimental NMR data and theoretical predictions decreases. [START_REF] Profeta | First-Principles Calculation of the 17 O NMR Parameters in Ca Oxide and Ca Aluminosilicates: the Partially Covalent Nature of the Ca-O Bond, a Challenge for Density Functional Theory[END_REF][START_REF] Sadoc | NMR parameters in alkali, alkaline earth and rare earth fluorides from first principle calculations[END_REF] The DFT+U method,in which the artificial energy shift U of the 3d 0 states towards higher energy is inducing a decrease of bond covalency, is a suitable corrective approach on a practical level. [START_REF] Profeta | First-Principles Calculation of the 17 O NMR Parameters in Ca Oxide and Ca Aluminosilicates: the Partially Covalent Nature of the Ca-O Bond, a Challenge for Density Functional Theory[END_REF][START_REF] Sadoc | NMR parameters in alkali, alkaline earth and rare earth fluorides from first principle calculations[END_REF] The convenient value of U of the DFT+U method depends on the atomic species and surroundings of the atom. To determine suitable values of U, a series of calculations were performed using the CASTEP module [START_REF] Stewart | First principles methods using CASTEP[END_REF] implemented in the Materials Studio 7.0 software package. Different U values were used for previously studied fluoroscandates. [START_REF] Rakhmatullin | Combining solid state NMR, powder X-ray diffraction, and DFT calculations for CsSc 3 F 10 structure determination[END_REF][START_REF] Rakhmatullin | Combined Approach for the Structural Characterization of Alkali Fluoroscandates: Solid-State NMR, Powder X-ray Diffraction, and Density Functional Theory Calculations[END_REF] The correlations between calculated isotropic 45 Sc and [START_REF] Rakhmatullin | X-ray Diffraction, NMR Studies, and DFT Calculations of the Room and High Temperature Structures of Rubidium Cryolite, Rb 3 AlF 6[END_REF] F magnetic shielding constants (σ iso ) and experimentally determined isotropic (δ iso ) chemical shift values has been plotted and fitted by linear regressions (Figure S1). From these fits, R-squared values were obtained. The coefficient of determination should be close to 1. The relationship between R 2 and U perfectly fits with a parabolic curve with maximum at 0.051 and 0.059 Hartree for 45 Sc and [START_REF] Rakhmatullin | X-ray Diffraction, NMR Studies, and DFT Calculations of the Room and High Temperature Structures of Rubidium Cryolite, Rb 3 AlF 6[END_REF] F nuclei, respectively. Consequently, the value U = 0.055 Hartree was chosen for further calculations (Figure S1).

The cut-off energies were 780 eV and the k-point spacing of 0.04 Å -1 . The calculations were performed after a geometry optimization of all atomic positions, keeping the experimental cell parameters and symmetry constraints. The obtained relationship for 45 Sc and [START_REF] Rakhmatullin | X-ray Diffraction, NMR Studies, and DFT Calculations of the Room and High Temperature Structures of Rubidium Cryolite, Rb 3 AlF 6[END_REF] F at U = 0.055 Hartree are : δ iso = -0.8315×σ iso +671.7 and δ iso = -0.730×σ iso +70.17, respectively.

Results

The Rb 3 ScF 6 material was first checked at room temperature by X-ray powder diffraction. The data corresponds to those reported by Turrell et al. [START_REF] Turrell | Vibrational spectra, phase transitions and force-fields in crystalline scandium hexafluorides[END_REF] Then, the phase Hereafter, the three polymorph are labelled α (RT), β (medium-temperature), and γ (HT).

Structure from Powder Diffraction

We first investigated the structure of Rb 3 ScF 6 at high temperature, as it corresponds to the highest symmetry crystal structure. At 250 °C, all X-ray powder diffraction peaks of γ-Rb 3 ScF 6 were indexed with a cubic cell ( ) which parameters (a = 9.1944(1) Å) are close to the δ polymorph of K 3 AlF 6 . 2 Therefore this structure (2 Rb, 1 Sc, and 1 F sites) was used as a starting model for Rietveld refinements (Figure 1c). The K + site was replaced by Rb + and Al 3+ by Sc 3+ , respectively. The thermal parameters of the fluorine crystallographic site was refined anisotropically given the distortion around this anion. Rietveld refinements were stable and led to low R-factors (Table 1, Figure 1c). Atomic coordinates are provided in Table S1, anisotropic thermal parameters (large values, see discussion below) are presented in Table S2, and selected interatomic distances are shown in Table S3.

The powder diffraction pattern corresponding to β-Rb 3 ScF 6 and recorded at 187 °C can be indexed with a tetragonal cell (I4/m) and cell parameters (a = 14.4093(2) Å and c = 9.2015(1) Å) close to the ones of β-K 3 AlF 6 so that this latter structure was used as a starting model (4 Rb, 2 Sc, and 7 F sites). [START_REF] King | The High-Temperature Polymorphs of K 3 AlF 6[END_REF] The Rietveld refinement was stable and led to low Rfactors (Table 1, Figure 1b) proving that these two phases are isostructural. Coordinates of atoms and a selection of interatomic distances are shown in Table S4 and S5.

Both static or dynamic disorder influence atomic displacement parameter (ADP) values. Previously, large ADP values were observed for K 3 AlF 6 and Rb 3 AlF 6 , and were explained by significant rotations of AlF 6 octahedra. [START_REF] King | The High-Temperature Polymorphs of K 3 AlF 6[END_REF][START_REF] Rakhmatullin | X-ray Diffraction, NMR Studies, and DFT Calculations of the Room and High Temperature Structures of Rubidium Cryolite, Rb 3 AlF 6[END_REF] As it will be shown below from the analysis of HT NMR data, we observe the same dynamic behavior of ScF 6 octahedra, which leads to relatively large ADP values for β and γ polymorphs of Rb 3 ScF 6 , especially for fluorine atoms.

All synchrotron powder diffraction peaks of α-Rb 3 ScF 6 recorded at 22 °C can be indexed with a tetragonal cell (I4 1 /a) and cell parameters (a = 20.2561(4) Å and c = 36.5160(0) Å) which appears isostructural to α-K 3 AlF 6 . [START_REF] Abakumov | The Crystal Structure of α-K 3 AlF 6 : Elpasolites and Double Perovskites with Broken Corner-Sharing Connectivity of the Octahedral Framework[END_REF] This observation was further confirmed by electron diffraction data which showed similar patterns to α-K 3 AlF 6 (Figure 2).

Due to the large number of degrees of freedom for the atomic positions (>150), a joint synchrotron and neutron refinement was used to determine the structure of the α-phase. The structure of α-K 3 AlF 6 was used as a starting model. During the initial steps, all sites corresponding to the same element were constrained to have the same displacement parameter and soft distance constraints were used for the Sc-F bond length. For the final refinement, the distance constraints could be removed and each metal site was allowed its own isotropic displacement parameter while all F sites were constrained to have the same displacement parameter. Fourier difference maps did not show any residue in the background. The fits of the combined Rietveld refinement are shown in Figure 1a and S3. Atomic coordinates, thermal parameters, and Sc-F and Rb-F interatomic distances are gathered in Tables S6 andS7. It should also be noted that it might not be possible to synthesize good quality single crystals of Rb 3 ScF 6 for precise structural elucidation, due to the inevitable crystal twinning taking place during cooling in the synthesis process. [START_REF] Abakumov | Phase transitions in K 3 AlF 6[END_REF] Additional 23 laboratory X-ray powder diffraction patterns measured at different temperatures in the range of 30-250 °C were used to obtain the thermal dependence of the cell parameters (Figure 1d). As expected, the unit cell parameters expand nearly linearly with increasing temperature. All cell parameters were transformed to pseudo cubic in order to make comparison between the different polymorphs.

Similar to the K 3 AlF 6 polymorph structures described by Abakumov et al. [START_REF] Abakumov | The Crystal Structure of α-K 3 AlF 6 : Elpasolites and Double Perovskites with Broken Corner-Sharing Connectivity of the Octahedral Framework[END_REF] It should be pointed out that unlike K 3 AlF 6 but like K 3 GaF 6 , 30 β-Rb 3 ScF 6 transforms directly to cubic γ-phase without going through an intermediate γ-K 3 AlF 6 with Fddd (n°70) space group. Our results are partially consistent with the former research work from Turrell et al. [START_REF] Turrell | Vibrational spectra, phase transitions and force-fields in crystalline scandium hexafluorides[END_REF] in which isolated ScF 6 3-octahedra were observed for all polymorphs and the cell parameter for the cubic phase was reported as a = 9.214 Å at 250 °C.

It is worth noting that Rb 3 ScF 6 is another new member of a small family, but expanding in recent years, of double perovskite with non-cooperative octahedral tilting (NCOT). To the best of our knowledge, this group currently includes (K or Rb) 3 AlF 6 , 1, 2, 18 Sr 3 WO 6 , [START_REF] King | Crystal Structure and Phase Transitions in Sr 3 WO 6[END_REF] (Ba or Sr) 3 TeO 6 , [START_REF] Stöger | Sr 3 TeO 6 and Ba 3 TeO 6 : double perovskites with pronounced superstructures[END_REF] Rb 2 K(Cr or Ga)F 6 , 33 K 3 GaF 6 , [START_REF] King | New examples of non-cooperative octahedral tilting in a double perovskite: phase transitions in K 3 GaF 6[END_REF] (K or Rb) 3 MoO 3 F 3 , [START_REF] Fry | Structures of α-K 3 MoO 3 F 3 and α-Rb 3 MoO 3 F 3 : Ferroelectricity from Anion Ordering and Noncooperative Octahedral Tilting[END_REF] Rb 3 InCl 6 , [START_REF] Majher | Rb 3 InCl 6 : A Monoclinic Double Perovskite Derivative with Bright Sb 3+ -Activated Photoluminescence[END_REF] and Cs 1.17 In 0.81 Cl 3 . 36 For definition of R-factors see references 15 and 16.

Solid-state NMR

From our work on powder diffraction data, the crystal structure of α-Rb 3 ScF 6 contains five scandium sites in octahedral environments with the same multiplicities, along with 18 rubidium and 30 fluorine sites. All fluorine atoms are terminal, i.e. non-bridging.

45

Sc MAS NMR spectra recorded at 17.6 T and 20 T contain three signals (blue line Figure 5) which are reconstructed by four contributions with relative intensities 1:1:2:1 (Table 2; Figure 5 and S4). The line with higher integral intensity corresponds to two scandium sites.

The 45 Sc chemical shift values for six and seven coordinated scandium environments range from -32 to 14 ppm and from -67 to -40 ppm, respectively. [START_REF] Rakhmatullin | Combining solid state NMR, powder X-ray diffraction, and DFT calculations for CsSc 3 F 10 structure determination[END_REF][START_REF] Rakhmatullin | Combined Approach for the Structural Characterization of Alkali Fluoroscandates: Solid-State NMR, Powder X-ray Diffraction, and Density Functional Theory Calculations[END_REF] To the best of our knowledge, solid-state NMR data of eight coordination scandium environment were not previously reported in the literature. Therefore, from scandium NMR results, all Sc sites are six-fold coordinated. The assignment of lines to Sc sites from the integral intensities or the quadrupolar parameters cannot be provided. The line shapes were simulated using a mixed Lorentz/Gauss function. The intense resonance at an isotropic chemical shift δ iso of 14.4 ppm is assigned to the Sc site with the multiplicity of 8 (Sc2) and the small line at δ iso of 5.9 ppm to the Sc site with the multiplicity of 2 (Sc1) (Figure 7d). At the phase transition temperature, the coexistence of both polymorphs occurs.

Above 207 °C, only a singlet Lorentzian line (δ iso =11.9 ppm, FWHM =160 Hz at 235 °C), corresponding to the γ-phase, is observed. Thereby, 45 Sc MAS NMR observations agree well with the structural models of all polymorphs. The transition temperatures correlate well with the data obtained by DSC. The [START_REF] Rakhmatullin | X-ray Diffraction, NMR Studies, and DFT Calculations of the Room and High Temperature Structures of Rubidium Cryolite, Rb 3 AlF 6[END_REF] F NMR spectrum recorded at 20 T and 60 kHz (see Figure S5) consists of a broad envelope of signals in the -57 to -70 ppm range. The complete simulation of the spectrum using Lorentzian lines revealed a minimum of 8 signals (30 are expected). It was not possible to perform an assignment of the lines to the different F sites.

As in the case of 45 Sc NMR, a decrease of MAS rotation frequency from 30 kHz to 6 kHz induces a decrease in resolution of the [START_REF] Rakhmatullin | X-ray Diffraction, NMR Studies, and DFT Calculations of the Room and High Temperature Structures of Rubidium Cryolite, Rb 3 AlF 6[END_REF] F NMR spectrum, and upon heating up to 126 °C, the [START_REF] Rakhmatullin | X-ray Diffraction, NMR Studies, and DFT Calculations of the Room and High Temperature Structures of Rubidium Cryolite, Rb 3 AlF 6[END_REF] F lines sharpen up (Figure S6). After the α to β phase transition, the [START_REF] Rakhmatullin | X-ray Diffraction, NMR Studies, and DFT Calculations of the Room and High Temperature Structures of Rubidium Cryolite, Rb 3 AlF 6[END_REF] F MAS NMR spectrum of β-Rb 3 ScF 6 measured at 171 °C exhibits two peaks (Figure 7b). Accurate simulation of the spectrum, including all spinning sideband patterns, allowed to obtain the 1:4 integral intensity ratio for the resonances at -66.4 ppm and -64.1 ppm (FWHM of 910 Hz and 810 Hz), respectively (Table 3). The discrepancy between the expected seven signals and the observed two resonances can be explained in two possible different ways. The first "classic" interpretation is that the line with low intensity corresponds to two fluorine atoms with an occupation of 4 and 8, and the second intensive line corresponds to all the remaining fluorines, i.e. four sites with an occupation of 8

and one site with an occupation of 16. In this case, the chemical shifts of two fluorines for the first peak and five fluorines for the second must be very close. Another possible explanation of the discrepancy is related to the complex dynamics of the system, such as fast hoping of the fluorine on each position around one ScF 6 octahedron or, in other terms, to rotational disorder of ScF 6 octahedra. In that case, [START_REF] Rakhmatullin | X-ray Diffraction, NMR Studies, and DFT Calculations of the Room and High Temperature Structures of Rubidium Cryolite, Rb 3 AlF 6[END_REF] F δ iso appears as the barycenter of the individual δ iso values.

The multiplicities of Sc1:Sc2 sites are 2:8, and the expected integrated intensities ratio agrees well with the experimental value. Previous works showed that this behavior is frequently observed in fluorides. [START_REF] Rakhmatullin | X-ray Diffraction, NMR Studies, and DFT Calculations of the Room and High Temperature Structures of Rubidium Cryolite, Rb 3 AlF 6[END_REF][START_REF] Boča | The structure of the metastable K 18 Ta 5 Zr 5 F 63 phase[END_REF][START_REF] Smrčok | Polymorphism of K 2 ZrF 6[END_REF][START_REF] Boča | Differences in XPS and solid state NMR spectral data and thermo-chemical properties of iso-structural compounds in the series KTaF 6 , K 2 TaF 7 and K 3 TaF 8 and KNbF 6 , K 2 NbF 7 and K 3 NbF 8[END_REF] For example, the γ-K 3 AlF 6 2 and β-Rb 3 AlF 6 [START_REF] Wu | Quantitative Multiple-Quantum Magic-Angle-Spinning NMR Spectroscopy of Quadrupolar Nuclei in Solids[END_REF] polymorphs of the cryolite family contain eleven crystallographic inequivalent F sites and only four NMR lines can be observed in the experimental spectrum. Another example is the metastable K 18 Ta 5 Zr 5 F 63 compound, in which 7 fluorine sites and 5 signals were detected, corresponding to all five non-equivalent polyhedra. [START_REF] Boča | The structure of the metastable K 18 Ta 5 Zr 5 F 63 phase[END_REF] The dynamic of fluorine atoms in γ-K 3 AlF 6 and β-Rb 3 AlF 6 was more widely studied. [START_REF] Rakhmatullin | X-ray Diffraction, NMR Studies, and DFT Calculations of the Room and High Temperature Structures of Rubidium Cryolite, Rb 3 AlF 6[END_REF] It should also be noted that a similar rotational disorder of the (Mo or W)O 4 tetrahedra was observed in the (Ca or Sr or Ba)MoO 4 scheelite and NaRE((Mo or W)O 4 ) 2 scheelite-type compounds. [START_REF] Rabuffetti | Structural Disorder in AMoO 4 (A = Ca, Sr, Ba) Scheelite Nanocrystals[END_REF][START_REF] Culver | Thermally activated rotational disorder in CaMoO 4 nanocrystals[END_REF][START_REF] Amarasinghe | Rotational Disorder in Scheelite-Type NaRE(MO 4 ) 2 (RE = Rare-Earth, Y; M = Mo, W)[END_REF] To determine the correct explanation, we addressed GIPAW (Gauge Including Projector Augmented Waves) calculations of the NMR parameters. Figure S7 shows the [START_REF] Rakhmatullin | X-ray Diffraction, NMR Studies, and DFT Calculations of the Room and High Temperature Structures of Rubidium Cryolite, Rb 3 AlF 6[END_REF] F experimental and reconstructed spectra of β-Rb 3 ScF 6 . As evidenced from this figure, there is a large discrepancy between the two spectra. In order to calculate the [START_REF] Rakhmatullin | X-ray Diffraction, NMR Studies, and DFT Calculations of the Room and High Temperature Structures of Rubidium Cryolite, Rb 3 AlF 6[END_REF] F chemical shift values according to the second model, we averaged the calculated fluorine positions for each of the polyhedra: Sc2F3F4F5F6F7 2 and Sc1F1 4 F2 2 . Good overall agreement between obtained values and the experimental data was observed (Table 3). Thereby, the second assumption is acceptable and coherent with the proposed structural model and the first assumption is unlikely to take place in practice. Another confirmation of the proposed dynamic model is the absence of a quadrupole line shape in the scandium spectrum. GIPAW calculations lead to large quadrupolar constants of 13.3 and 5.9 MHz for Sc1 and Sc2 sites, respectively. In fact, as indicated above, the 45 Sc MAS NMR spectrum revealed two well-defined signals with a Gaussian/Lorentzian line shape, because of faster reorientation. It should be mentioned that calculated chemical shift values fit well with those observed (Table 4).

In the case of the 87 Rb spectrum recorded at RT, significant signal overlap is observed resulting from the large number of Rb sites (18) and their quadrupolar broadening (Figure S8). To overcome these limitations, we performed 2D MQMAS NMR experiments.

Because conventional Z-filtered MQMAS experiment at 17.6 T was unable to provide a sufficient signal-to-noise ratio for signals with a large value of quadrupole constants (even after four days of data accumulation), we turned to RIACT excitation method. RIACT method is recognized for improving the excitation of sites undergoing large quadrupolar couplings for I=3/2 nuclei, thus improving the sensitivity, at the cost of more complex line shape arising from non-uniform excitation. [START_REF] Wu | Quantitative Multiple-Quantum Magic-Angle-Spinning NMR Spectroscopy of Quadrupolar Nuclei in Solids[END_REF] MHz. The modeling of 1D spectra acquired at two different fields (17.6 and 20 T) while using the NMR parameters obtained from the fits of RIACT spectra further revealed a missing intensity in the 10-30 ppm chemical shift range. Therefore, we assumed that the 1D spectra contain a supplementary line with a quadrupole constant large enough to remain undetected even when using the RIACT excitation. 5. According to site multiplicities, line 1 can be assigned to the Rb1 (4d) site and line 2 to the sum of all others sites (16i, 2b, 8h), respectively. [START_REF] Rakhmatullin | X-ray Diffraction, NMR Studies, and DFT Calculations of the Room and High Temperature Structures of Rubidium Cryolite, Rb 3 AlF 6[END_REF] F and 87 Rb NMR spectra recorded at 207

°C clearly indicate the phase transition from β-Rb 3 ScF 6 to γ-Rb 3 ScF 6 . Each of the rubidium and fluorine NMR spectra was reconstructed using a single Lorentz line with a chemical shift at 2.2 ppm and -64.7 ppm at 235 °C; FWHM =156 Hz and 520 Hz, respectively. The resulting disagreement with the presence of two rubidium sites of 4b and 8c multiplicity in the structure can be explained by the presence of the two rubidium sites of γ-Rb 3 ScF 6 which are involved in the chemical exchange. It should be noted that the same exchange process was observed for β-Rb 3 AlF 6 . [START_REF] Rakhmatullin | X-ray Diffraction, NMR Studies, and DFT Calculations of the Room and High Temperature Structures of Rubidium Cryolite, Rb 3 AlF 6[END_REF] A good agreement between calculated [START_REF] Rakhmatullin | X-ray Diffraction, NMR Studies, and DFT Calculations of the Room and High Temperature Structures of Rubidium Cryolite, Rb 3 AlF 6[END_REF] F and 45 Sc shielding constants of γ-Rb 3 ScF 6 and the experimental chemical shifts was obtained (Tables 3 and4). The temperature dependence of all NMR spectra demonstrated overall reversibility of the spectral changes.

King et al. [START_REF] King | The High-Temperature Polymorphs of K 3 AlF 6[END_REF] observed the dynamic rotations of AlF 6 octahedra in δ-K 3 AlF 6 and they proposed that "such rotations could be occurring in some of the lower temperature phases as well." We also view this dynamic as a fast hoping mechanism of the fluorine on each position around one AlF 6 octahedron. [START_REF] Rakhmatullin | X-ray Diffraction, NMR Studies, and DFT Calculations of the Room and High Temperature Structures of Rubidium Cryolite, Rb 3 AlF 6[END_REF] This conjecture was confirmed by investigation of isostructural γ-K 3 AlF 6 and α-Rb 3 AlF 6 . In this study, we confirm this assumption for β-Rb 3 ScF 6 . Based on these findings, we revised the [START_REF] Rakhmatullin | X-ray Diffraction, NMR Studies, and DFT Calculations of the Room and High Temperature Structures of Rubidium Cryolite, Rb 3 AlF 6[END_REF] F MAS NMR spectrum of β-K 3 AlF 6 , which is isostructural with β-Rb 3 ScF 6 . It contains an asymmetrically broadened peak, which is reconstructed with two individual contributions. Unfortunately the lack of resolution of the spectrum does not allow to correctly and unequivocally measure the integrated intensity. The resulting 1:5 ratio is slightly higher than the expected one (1:4). Therefore it appears that the rotation of the AlF 6 octahedra is very likely to take place in β-K 3 AlF 6 . It is worth noting that no such rotation was observed in the alpha polymorphs of K 3 AlF 6 and Rb 3 ScF 6 . If there was a fast hoping mechanism of the fluorine on each position around one AlF 6 octahedron, only five lines would be observed in the fluorine spectrum, in agreement with the number of crystallographically nonequivalent aluminium/scandium sites.

The [START_REF] Rakhmatullin | X-ray Diffraction, NMR Studies, and DFT Calculations of the Room and High Temperature Structures of Rubidium Cryolite, Rb 3 AlF 6[END_REF] F line shapes of both β-Rb 3 ScF 6 and γ-Rb 3 ScF 6 spectra recorded without scandium decoupling can be ascribed as non-resolved multiplets (Figures 7a and7b). From the fitted spectrum, the coupling constant values are 1 J( 45 Sc, 19 F) 164, 167 Hz for βand 160

Hz for γ-phases. These values are in good agreement with previous results obtained for fluoroscandates. [START_REF] Rakhmatullin | Combined Approach for the Structural Characterization of Alkali Fluoroscandates: Solid-State NMR, Powder X-ray Diffraction, and Density Functional Theory Calculations[END_REF][START_REF] Pfadenhauer | Nuclear magnetic resonance of fluoroscandate anion, ScF 6 3-, in aqueous solution[END_REF]

Conclusions

In this work, the interplay between X-ray and neutron powder diffraction, solid state NMR, SAED, and theoretical calculations is exploited in order to achieve an accurate description of the structure of the three α-, β-, and γ-Rb 3 ScF 6 polymorphs. The structures, two tetragonal and one cubic forms, were determined from X-ray and neutron powder diffraction structural analysis based on isostructural K 3 AlF 6 models and these were further confirmed by solid state NMR and SAED methods. The structural correlation between the three polymorphs was also discussed. Two new examples of non-cooperative octahedral tilting are reported. High temperature MAS NMR appears as a powerful method that enables in-situ monitoring of the local dynamics of ScF 6 octahedra and phase transitions. A good agreement was achieved for observed and calculated NMR parameters. We expect this work to stimulate future opportunities in the synthesis and the investigation of Mn 4+ or lanthanide doped Rb 3 ScF 6 with interesting optical properties.

  transitions were analyzed by differential scanning calorimetry (DSC) method between 25 and 260 °C (FigureS2). The heating curve contains two well-separated peaks, at T onset = 137 °C and T onset = 200 °C. Both thermal effects represent solid-solid phase transitions characterized by symmetrical endothermic peaks during heating and symmetrical exothermic peaks during cooling. The cooling curve shows that these individual structural modifications are transformed reversibly, at T onset = 202 °C and T onset = 145 °C, respectively. The integral peak area of the thermal effects at cooling is directly proportional to the enthalpy of change during the phase transition. From that, the entropy of change of both transitions are about 0.29 J×mol -1 ×K -1 and 0.21 J×mol -1 ×K -1 , respectively. The measured transition temperatures are slightly different from the previously reported results of Turrell et al. (154 and 200 °C).[START_REF] Turrell | Vibrational spectra, phase transitions and force-fields in crystalline scandium hexafluorides[END_REF]

  and King et al.[START_REF] King | The High-Temperature Polymorphs of K 3 AlF 6[END_REF] , the β-Rb 3 ScF 6 structure derives from the cubic elpasolite structure of γ-Rb 3 ScF 6 by rotation of one-fifth of the ScF 6 octahedra with a 45° angle around the c-axis. Further 45° rotation of another one-fifth group of ScF 6 octahedra around the a or b-axis leads to the α-Rb 3 ScF 6 structure. This deformation of the cubic framework leads to changes in coordination environments for the rubidium atoms, while the coordination geometry around the scandium does not change and remains octahedral. In comparison with the six coordinated rubidium atoms in the γ-form (Figure3, right), four-fifths of these atoms in the β polymorph are in a seven coordinated pentagonal-bipyramidal environment, while the rest (one fifth) remain in octahedral symmetry (Figure3, left). A further symmetry decay via rotation of another onefifth group of ScF 6 octahedra results in a further increase in the coordination number of these rubidium atoms in the α phase: the three-fifths are in a seven coordinated and two-fifths are in an eight coordinated (a capped pentagonal bipyramid) (Figure4, right). The geometry of the cubic twelve coordinated rubidium sites is also undergoing modifications. Whereas the coordination environment around the Rb1(β) site remains unchanged, Rb2(β) is eleven coordinated by F atoms in the form of an irregular polyhedron. Further distortion of the ideal double perovskite structure in the α polymorph leads to the reduction of the coordination number of the Rb1(β) site from 12 to 9-11 for the atoms Rb1-7,11, 14, 16. Rb10, Rb15, and Rb17 retain a 12-fold coordination.

Figure 1 .

 1 Figure 1. Rietveld refinement of synchrotron and laboratory powder X-ray diffraction patterns of Rb 3 ScF 6 at: a) 22 °C; b) 187 °C; c) 250 °C. Black dots are the observed pattern, red dots are the calculated pattern, vertical green bars are the Bragg positions, and the grey line is the difference between observed and calculated patterns. (d) Temperature dependence of the unit cell parameters of the α, β, and γ phases: 1 -a of γ phase ( ), 2 -of β phase (I4/m), 3 -of β phase (I4/m), 4 -of α phase (I4 1 /a), 5 -c/4 of α phase (I4 1 /a).

Figure 2 .

 2 Figure 2. [001]*, [2-10]*, and [010]* selected are electron diffraction (SAED) patterns of α-Rb 3 ScF 6 . The indexation corresponds to the a = 20.25 Å, c = 36.5 Å cell with a I4 1 /a space group.

Figure 3 .

 3 Figure 3. Crystal structure of Rb 3 ScF 6 : on the left at 187 °C, β-phase and on the right at 250 °C, γ-phase.

Figure 4 .

 4 Figure 4. On the left: one unit cell of α-Rb 3 ScF 6 . Orange (Rb) and violet (Sc) polyhedra form network, gray is rubidium atoms in the cavities, and green is F. On the right: Single layer of Sc and Rb coordination polyhedra viewed down the c-axis of α-Rb 3 ScF 6 .

Figure 5 .

 5 Figure 5. 45 Sc MAS NMR experimental (black lines) spectrum of α-Rb 3 ScF 6 recorded at 17.6 T and at 30 kHz presented with its simulations (dashed red lines). Inserts show expanded 45 Sc MAS spectrum in the region of the central transition (left) and expanded satellite transition sidebands (right). Dashed color lines display the decomposition of the theoretical spectrum in its individual components.

Figure 6 .

 6 Figure 6. 45 Sc NMR spectra of Rb 3 ScF 6 acquired at 17.6 T and MAS 6 kHz as a function of temperature.

Figure 7 .

 7 Figure 7. Experimental (black) and simulated (red) 19 F (a, b), 87 Rb (c), and 45 Sc (d) NMR spectra at 17.6 T and MAS 6 kHz. (b) Insert shows 19 F spectrum and its simulation without 45 Sc decoupling. Colored dashed curves show the decomposition of the theoretical spectrum in its individual components.

Figures 8 ,

 8 S9, and S10 show RIACT and Z-filter MQMAS spectra recorded at 17.6 and 20 T with the same rotor. As expected, RIACT spectra demonstrate better signal-to-noise ratio. The 2D 87 Rb RIACT NMR spectrum recorded at 20 T reveals six resolved peaks with large quadrupole constant ranging between 5.7 and 8.7 MHz and eight lines close to the diagonal slope with small quadrupole splitting of the order of to 2

  Figure S8 depicts the simulated 1D spectra with fourteen lines obtained from 2D results and one additional line with C Q = 11.8 MHz, η Q = 0.5. It should be pointed out that the strong overlap of the 87 Rb resonances makes impossible to obtain unambiguous values of the integral intensities. While the NMR spectra allow to identify fifteen resolved contributions, the above described structure of α-Rb 3 ScF 6 features eighteen independent rubidium atomic positions. We propose to ascribe the group of high field peaks Rb sites with coordination number (CN) 7 and 8; the two sets of lines with the largest C Q being ascribed to rubidium sites with CN 9-11; and the small two 2D spots close to the diagonal slope can be assigned to Rb with CN 12. Thus, even though it remains impossible to perform an accurate spectral assignment of the 87 Rb NMR resonances with the crystallographic sites, our results allow to estimate the values of the 87 Rb NMR parameters and to propose line assignment.

Figure 8 .

 8 Figure 8. Experimental 87 Rb RIACT MQ MAS (left) NMR spectrum of Rb 3 ScF 6 at 20 T and spinning rate of 30 kHz and its simulation (right) with the parameters presented in Table5.

Table 1 .

 1 Crystallographic data for the polymorphs of Rb 3 ScF 6 from XRD and Neutron

	Rietveld refinement.
	Chemical formula	α-Rb 3 ScF 6		β-Rb 3 ScF 6	γ-Rb 3 ScF 6
	Source	Synchrotron	Neutron	Synchrotron	laboratory X-ray
	Formula weight (g.mol -1 )	415.35		415.35	415.35
	Temperature (°C)	22	23	187		250
	Wavelength (Å)	0.457893	1.59354	0.457901	1.5406
	Crystal system	Tetragonal	Tetragonal	cubic
	Space group	I4 1 /a (88)		I4/m (87)	-	(225)

Table 2 .

 2 45 Sc isotropic chemical shifts (δ iso ), quadrupolar constants (C Q ), asymmetry

	parameters (η Q ), and Integral intensities (I) obtained from the simulation of the 45 Sc MAS at
	17.6 T and 20 T.
	δ iso , ppm (±0.2ppm)	C Q , MHz (±0.1 MHz)	η Q (±0.1)	I, % (±2 %)
	19.2	2.3	0.7	21
	18.3	3.6	0.8	39
	8.1	2.2	0.95	18
	6.3	4.2	1	22

Table 3 .

 3 Experimental (isotropic chemical shifts δ iso , integral intensities I) and calculated (isotropic magnetic shielding σ iso and isotropic chemical shifts δ calciso )[START_REF] Rakhmatullin | X-ray Diffraction, NMR Studies, and DFT Calculations of the Room and High Temperature Structures of Rubidium Cryolite, Rb 3 AlF 6[END_REF] F NMR parameters of β-Rb 3 ScF 6 .

	Fluorine site	σ iso , ppm δ calciso , ppm <δ calciso >, ppm	(±0.1 ppm) δ iso , ppm	I, % (± 1%)
	F1	193.61	-71.52	-68.1
					-66.4	20
	F2	179.72	-61.38	(Sc1F1 4 F2 2 )
	F3	184.80	-65.09	-67.8	-64.1	80

Table 4 .

 4 45 Sc isotropic chemical shifts (δ iso ), and Integral intensities (I) obtained from the simulation of the 45 Sc MAS at 17.6 T and calculated isotropic magnetic shielding σ iso of βand γ-Rb 3 ScF 6 .

	polymorph	Atom	δ iso , ppm (±0.2 ppm)	I, % (± 1%)	σ iso , ppm	δ iso calc , ppm
	β	Sc1 Sc2	5.9 14.4	20 80	799.07 788.85	7.23 15.73
	γ	Sc1	11.90	100	791.06	13.89

Table 5 .

 5 87 Rb isotropic chemical shift (δ iso ), mean quadrupolar constants (C Q ), and relative intensities obtained from the simulation of the 87 Rb MAS and RIACT MQMAS at 17.6 T andThe temperature dependence of 87 Rb spectra exhibits similar variations as in the cases of variable temperature[START_REF] Rakhmatullin | X-ray Diffraction, NMR Studies, and DFT Calculations of the Room and High Temperature Structures of Rubidium Cryolite, Rb 3 AlF 6[END_REF] F and 45 Sc NMR measurements (FigureS11). At 148 °C, the spectrum contains a set of signals corresponding to α and β-polymorphs. The 87 Rb MAS NMR spectrum of β-Rb 3 ScF 6 at 171 °C presents two resonances at -21.7 and -2.6 ppm with relative intensities and line widths of 13 % / 2100 Hz and 87 % / 3500 Hz, respectively.

	20 T.
	δ iso , ppm (±0.2 ppm)	C Q , MHz (±0.4 MHz)	η Q (±0.2)
	-21.9	5.6	0.34

ACKNOWLEDGMENT

For DFT calculations, we thank the "Centre de Calcul Scientifique en region Centre" (Orléans, France). We acknowledge the ICMN (Orléans, France) for access to their Transmission Electron Microscope. Financial support from the IR-RMN-THC Fr3050 CNRS for conducting the research is gratefully acknowledged. This study was also financially supported by VEGA-2/0060/18 and ITMS project (code 313021T081, Research & Innovation Operational Programme funded by the ERDF). We thank also Dr. F.Vivet, Dr. F.Fayon, and Dr. D.Massiot for useful discussions.

ASSOCIATED CONTENT

Supporting Information

Tables of atomic coordinates and atomic displacement parameters; tables of bond distances; R 2 (U) and δ iso (σ iso ); DSC; Neutron diffraction data; 45 Sc, [START_REF] Rakhmatullin | X-ray Diffraction, NMR Studies, and DFT Calculations of the Room and High Temperature Structures of Rubidium Cryolite, Rb 3 AlF 6[END_REF] F, and 87 Rb MAS NMR; 87 Rb Zfilter and RIACT MQMAS (PDF); Crystallographic data (CIF). The Supporting Information is available free of charge on the ACS Publications website.

The crystallographic data are deposited in Cambridge Crystallographic Data Centre (CSD # 2062818, 2027066, and 2027067). The data can be downloaded from the site (www.ccdc.cam.ac.uk/data_request/cif).

AUTHOR INFORMATION