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X‑ray Diffraction, NMR Studies, and DFT Calculations of the Room

and High Temperature Structures of Rubidium Cryolite, Rb3AlF6
Aydar Rakhmatullin,* František Š imko,* Emmanuel Veŕ on, Mathieu Allix, Charlotte Martineau-Corcos,
Andy Fitch, Franck Fayon, Roman A. Shakhovoy, Kirill Okhotnikov, Vincent Sarou-Kanian,
Michal Korenko, Zuzana Netriova,́ Ilja B. Polovov, and Catherine Bessada
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ABSTRACT: A crystallographic approach incorporating multinuclear high field solid state NMR (SSNMR), X-ray structure
determinations, TEM observation, and density functional theory (DFT) was used to characterize two polymorphs of rubidium
cryolite, Rb3AlF6. The room temperature phase was found to be ordered and crystallizes in the Fddd (no. 70) space group with a =
37.26491(1) Å, b = 12.45405(4) Å, and c = 17.68341(6) Å. Comparison of NMR measurements and computational results revealed
the dynamic rotations of the AlF6 octahedra. Using in situ variable temperature MAS NMR measurements, the chemical exchange
between rubidium sites was observed. The β-phase, i.e., high temperature polymorph, adopts the ideal cubic double-perovskite
structure, space group Fm3m, with a = 8.9930(2) Å at 600 °C. Additionally, a series of polymorphs of K3AlF6 has been further
characterized by high field high temperature SSNMR and DFT computation.

■ INTRODUCTION
The binary system RbF−AlF3 belongs to a bigger family of
and Cs3AlF6 by DTA and XRD methods.9 Cooling curves of
pure Rb3AlF6 contained two exothermic peaks: liquid−solid
cryolitic systems MF−AlF3 (M = Li, Na, K, Rb, Cs, Fr). While phase transition at 920 °C and the other modification
one member of this family, molten sodium cryolite (NaF− transition at 357 °C. XRD investigations showed that the
AlF3), is the main constituent of the electrolyte for the room temperature form of Rb3AlF6 has tetragonal symmetry,
industrial production of aluminum worldwide, the other while its high temperature modification is assumed to be face-
members of that cryolitic family (Li, K, Rb) could have also centered cubic. Chen and Zhang10 studied the quenched
been considered because of their role as the constituents for samples of the system RbF−AlF3 by DTA, DSC, and XRD
the new “low-melting” electrolytes in electrometallurgy.1 methods. Three compounds were identified: Rb3AlF6, RbAlF4,
The structure of rubidium cryolite and the solubility of the
alumina, with consequent formation of the electroactive
species, is the principal task for the potential utilization of Received: February 10, 2020
rubidium cryolite in the aluminum electrowinning. Little
information is however available about Rb3AlF6 in the open
literature compared to, for example its analogueslithium,
sodium, and potassium cryolite (Li3AlF6,2,3 Na3AlF6,4−6 and
K3AlF6,7,8). Holm analyzed the three cryolites K3AlF6, Rb3AlF6,

© XXXX American Chemical Society https://dx.doi.org/10.1021/acs.inorgchem.0c00415

A Inorg. Chem. XXXX, XXX, XXX−XXX
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and RbAl3F7. Rb3AlF6 melts congruently at 878 °C, and its α temperature. XRD patterns is shown in Supporting Information
↔ β forms transformed reversibly at 340 °C. The crystal (Figure S1).
structures of both Rb3AlF6 modifications have not yet been Thermal Analysis Measurements. The classical thermal analysis
was performed as described by Š imko et al.19 in a Pt crucible with a
completely described.
lid. The cooling rate was 1.4 °C/min. By using such a slower cooling
The cryolite systems of alkali metals could also have other rate in a larger quantity of sample (10 g), it was possible to detect the
industrial applications. Recently, Mn4+-activated K3AlF6 was real temperature of primary crystallization of Rb3AlF6. The slow
studied as a potential red phosphor for warm white light- cooling rate is essential for the thermal analysis of materials like
emitting diodes.11 It shows an efficient luminous efficacy Rb3AlF6, which often show extended thermal dissociation.20
beyond 190 lm/W, along with an excellent color rendering SSNMR Measurements. Room temperature solid-state NMR
index (Ra = 84) and a lower correlated color temperature experiments were carried out on a Bruker Avance III NMR
(CCT = 3665 K). These types of materials with improved spectrometers operating at 9.4 and 20.0 T, using a 2.5 mm resonance
performance that can be industrially produced at competitive probe at MAS frequency varying between 30 and 34 kHz. In addition,
to enhance resolution in some of the 19F solid state NMR
cost are needed in different fields of industry and particle experiments, we used a 1.3 mm probe to be able to rotate samples
physics research.12,13 up to 67 kHz. 27Al NMR spectra were acquired using a double
The specific crystal structural features, phase transitions, and frequency sweep (DFS) pulse due to a possibility of signal
related physical properties of the cryolite materials can be enhancement. The parameters of the dipolar 87Rb−19F HMQC21,22
linked to structural similarity with a larger group of materials experiments were identical to our previous study.19
known as elpasolite halides (after the name of the mineral
87
Rb MQMAS spectra were acquired with Z-filtering23 and
elpasolite, K2NaAlF6). These materials have a “mixed-cation” hypercomplex (States)24 phase detection. A sweep width of 60 kHz
fluoride perovskite-type structure, in which the corner-sharing and 120 kHz (4νr) was used in the direct and indirect dimension,
respectively. The optimized excitation and conversion pulse width was
octahedral network is made up of alternating (AlF6) and 4 μs (νrf = 62.5 kHz) and 1.3 μs (νrf = 192 kHz), respectively. A
(Na(K)F6) octahedra. Elpasolite (A2BB′X6) and cryolite repetition delay was 0.66 s.
(A3B′X6) structure types derive from the perovskite by cationic The in situ high temperature NMR experiments were carried out on
ordering. Unlike simple ABX3 perovskites, where all octahedra a Bruker Avance III HD NMR spectrometer operating at 17.6 T with
are equivalent, in elpasolites (also known as ordered resonance frequencies of 245.4 and 705.8 MHz for 87Rb and 19F,
perovskites), there are two kinds of nonequivalent ionic respectively, employing a 7 mm Bruker laser MAS probe. The
groups BX6 and B′X6 alternating along the three 4-fold cubic bottom-less MAS rotor is equipped with an inner container made
axes. Numerous elpasolite-like crystals are known to undergo from aluminum nitride (AlN) which carries the sample. Heating of
the sample is achieved using a 200 W DILAS diode laser operating at
structural phase transitions or to exist in distorted phases up to 980 nm. The laser beam is fed through an optical fiber into the probe,
the melting temperature. the fiber ending ca. 1 cm underneath the stator, and then directed to
The structures of K3AlF6,7,8 Sr3WO6,14 Rb2K(Cr or Ga)F6,15 the AlN container. The 27Al background signal is very large hence no
and (K or Rb)3MoO3F316 are a small part of the elpasolite or 27
Al NMR measurements were recorded. In all in situ HT
double perovskite type which show noncooperative octahedral experiments, the MAS frequency was 5000 Hz. Because of the
tilting (NCOT). In these phases, one of the octahedra is broad NMR patterns of 19F and 87Rb resulting from large chemical
rotated by ∼45° while the other remains untilted. Some of the shift anisotropy and low MAS rate, two-dimensional (2D) NMR
elpasolite-type materials are suitable for scintilators, showing techniques, MATPASS25 and QMATPASS,26 for 19F and 87Rb
desirable isotropic optical and mechanical properties.17 respectively that able to separate the isotropic and the anisotropic
chemical shifts in two different dimensions were employed, as ideal
In this paper, we will present a new example of the structure approach to study our samples at very high temperature. They yield
of Rb3AlF6 with noncooperative octahedral tilting and the first high-resolution NMR isotropic peaks free of CSA-related broadening
complex NMR investigation of such compounds like K3AlF6 in one dimension and the corresponding anisotropic powder sideband
and Rb3AlF6. We will present a characterization of the pattern for each isotropic peak, in the second dimension. The
structure of rubidium cryolites using X-ray diffraction (XRD) separation of the side bands has been carried out with 5-π MATPASS
and transmission electron microscopy (TEM). Both potassium experiment for 19F and 9-π QMATPASS pulse sequence for 87Rb.
and rubidium cryolites were characterized using various 1D Duration of the π pulse was 15.5 μs for 19F and 10 μs for 87Rb. To
and 2D solid state NMR techniques including in situ HT MAS avoid the time conflict caused by the finite length of the pulse, even π
pulses were placed at 2/3 and 4/3 of the rotor period in case of
NMR. The interpretation of all experimental NMR results is MATPASS and 2/5, 4/5, 6/5, and 8/5 of the rotor period in case of
significantly enhanced by the contribution of the first principle QMAT, such that the whole pulse sequences spanned almost 3τr at
DFT calculations. We think that this computing approach has first t1 increment and 2τr at the last one. Here, 12-step and 20-step
been applied, for the first time, to such a complex structure. cogwheel phase cycling27 was used to select the alternating coherence

■
transfer pathway in MATPASS and QMATPASS experiments,
EXPERIMENTAL SECTION respectively. Each t1 increment was acquired at 48 transients for 19F
and at 1000 scans for 87Rb.
Preparation of Pure Compounds. K3AlF6. Potassium cryolite 19
F, 27Al, and 87Rb chemical shifts are referenced to CFCl3, 1 M
was prepared in a glovebox following the preparation detailed by Al(NO3)3, and 0.01 M RbNO3, respectively. The NMR parameters
Abakumov et al.7 and Š imko et al.18 (chemical shifts, chemical shift anisotropies, asymmetry parameters,
Rb3AlF6 and RbAlF4. The synthesis protocol of rubidium cryolite line widths, and quadrupolar parameters) were fitted for several
was identical to that described in our previous work.19 Rubidium different rotor frequencies and for two magnetic fields to the
tetrafluoroaluminate was prepared by heating a stoichiometric mixture experimental spectra by means of the DMfit program.28
of RbF and AlF3. Two grams of mixture were mechanically Temperature Calibration. Temperature measurement in the
homogenized in a glovebox under inert atmosphere (Ar, Messer, case of laser heating cannot be performed directly; hence, an indirect
99.999% purity), placed in a Pt crucible and heated in a tightly closed calibration of the temperature was used. It is obvious that heating the
vertical resistance furnace with water-cooling from room temperature container from only one side leads to a considerable temperature
to 600 °C, at a rate of 5 °C/min. The mixture was held for 1 h at 20 gradient in the sample. To reduce the value of the temperature
bar to avoid the dissociation reaction, and then cooled to room gradient, a small amount of the powder was used (about 20 mg). The

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temperature calibration was performed using several reference diffraction data.10 Chen and Zhang suggested that the low
compounds K3AlF6 (19F spectra),8 this paper Rb3AlF6 (19F and temperature α form is orthorhombic with a = 7.748(5) Å, b =
87
Rb),9 this paper Na2SiF6 (23Na),29 and CuI, CuBr (63Cu),30 whose 5.365(3) Å, and c = 4.388(2) Å, while the high temperature β
phase transition temperature is well-defined. The laser power exhibits one is cubic with a = 7.612(4) Å.
a temperature dependence given by Shakhovoy et al.31 P = aT4 + bT
Diffraction Data. Using high-resolution synchrotron
− c, where a, b, and c are constants, and P is a percentage of the
maximum laser power controlled by the experimenter. In addition, the powder diffraction data, we first performed an autoindexing
calibration was double checked by employing the temperature analysis of the room temperature phase. The orthorhombic cell
dependence of the 79Br MAS NMR signal of KBr:32 T = −40 × δiso dimensions a = 37.2649 Å, b = 12.4541 Å and c = 17.6834 Å
+ RT. In the temperature range 200−500 °C, the agreement between were determined with good reliability factors by indexing using
the two methods of calibration is highly satisfying (Figure S2). Dicvol39 and Treor40 programs and by analyzing the peak
First-Principles Calculations. Calculations of NMR parameters positions in the powder synchrotron patterns. These cell
were identical to our previous study18 and the computational details parameters strongly differ from the proposed indexation of α-
are presented in the Supporting Information. Linear regressions led to Rb3AlF6.10 A subsequent ICDD database search using similar
the following relationships for 19F: δiso(ppm) = −0.795 × σiso +
89.444.33 cell parameters, volume tolerance fixed at 10%, and chemistry
Electron Diffraction. Electron diffraction patterns were collected restrictions (only alkali metals, transition metals, and fluorine)
on a Philips CM20 microscope fitted with an Oxford energy resulted in one compound with similar indexation: γ-K3AlF6
dispersive spectrometry (EDS) analyzer. In order to avoid rapid (ICSD 262077). This compound crystallizes in the Fddd space
deterioration of the samples under the electron beam, a nitrogen- group. The proposed orthorhombic indexation was then tested
cooled sample holder was used. via a LeBail fit of the SPD pattern, and the obtained good
Synchrotron Powder Diffraction. Synchrotron powder diffrac- reliability factors (Rwp = 5.48%, Rp = 3.31%, and GOF = 0.7)
tion measurements were performed at the ESRF beamline ID22 confirmed that α-Rb3AlF6 appears to be isostructural to γ-
(Grenoble, France) operating at the wavelength 0.32623 Å. The
measurements were performed at several temperatures using a hot-air
K3AlF6. Moreover, the cell parameters and the space group
blower sensor while heating the Rb3AlF6 sample from room Fddd of the rubidium cryolite compound was confirmed by an
temperature up to 600 °C. A 12 min waiting time was used at each electron diffraction study (Figure 1).
temperature step in order to ensure thermal equilibration, then
powder synchrotron data was collected over the 0.5−48° 2θ with a
0.002° step size. Polycrystalline powder samples were sealed in 0.5
mm diameter borosilicate capillaries, which were rotated in order to
reduce potential texture effects.

■ RESULTS
M3AlF6 (M = Li, Na, K) compositions generally belong to
congruently melting compounds with one simple endothermic
signature. During cooling, Li3AlF6 shows an endothermic peak
corresponding to crystallization at 782−785 °C,34 Na3AlF6 at
1011 °C,1 and K3AlF6 at 974 °C.9 The thermal endothermic
effect of Rb3AlF6 was, in this work, obtained from the melt by
thermal analysis at 920 °C (Figure S3). The whole thermal
cooling curve also contains another endothermic delay located
at 346 °C. This delay corresponds to the polymorphic solid
transition of the high temperature β-modification of Rb3AlF6
to the low temperature of α-Rb3AlF6 (Figure S3, right). This is Figure 1. [010] selected area electron diffraction pattern of α-
in good agreement with values previously reported by Holm,9 Rb3AlF6. Indexed in the a = 37.27 Å, b = 12.45 Å, and c = 17.68 Å cell
Chen, and Zhang.10 The similar behavior of solid state crystal with an Fddd space group.
transformation is not unusual, even in between others M3AlF6
compounds. This behavior relates to the phase transition from
high-temperature, high-symmetry modifications to a low- In order to precisely determine the structure of α-Rb3AlF6, a
temperature, low symmetry forms. Li3AlF6, for example, Rietveld refinement of the SPD pattern was performed. The
forms four modifications: δ-, γ-, β-, and α-forms. High- starting model was based on the γ-K3AlF6 structure using the
temperature δ-form transforms to γ-form at 597 °C and γ ↔ β orthorhombic cell parameters previously determined by
transformation occurs at 510 °C.2 The last β ↔ α equilibrium autoindexing methods and replacing potassium by rubidium
occurs at 210 °C.3 On the other hand, Na3AlF6 forms only one atom. Both cationic and fluorine positions, as well as atomic
solid−solid transformation. The cubic high-temperature β- displacement parameters, were refined (Table 1). Good
Na3AlF6 is at 563 °C in equilibrium with the low-temperature reliability factors were obtained (Rwp = 6.23%, Rp = 4.12%,
monoclinic α-Na3AlF6.5 Three phase transitions of K3AlF6 are and GOF = 0.8). The Rietveld refinement also allowed the
identified at 306, 153, and 132 °C. The high-temperature δ- identification of a secondary phase of RbSiO4, which
phase is at 306 °C in equilibrium with orthorhombic γ-phase. quantification was determined as 2.45(5) wt %. This phase is
The γ-phase forms at 153 °C an intermediate β-phase, which probably a result of a contamination caused by a reaction of
exists only in very narrow temperature intervals, and it is then RbF and the ceramic materials (alumino-silicate tube) in the
being transformed at 132 °C to a stable monoclinic α-phase.8 furnace when the synthesis was performed.
α-Rb3AlF6. Although the crystal structure of Rb3AlF6 has The fit of the SPD Rietveld refinement is shown in Figure 2.
not been described up to now, unit cell parameters and Atomic coordinates, atomic displacement parameters and Rb−
symmetry were previously proposed based on X-ray powder F and Al−F interatomic distances are summarized in Tables 2
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Table 1. Crystallographic Data for the Polymorphs of The 87Rb MAS NMR spectrum shows three different kinds
Rb3AlF6 from XRD Rietveld Refinementa of Rb atoms environments and the presence of overlapping
quadrupolar resonances (Figure 5a). To improve the
chemical formula α-Rb3AlF6 β-Rb3AlF6
resolution, we have used the two-dimensional 87Rb MQMAS
source synchrotron synchrotron
technique at two magnetic fields, 9.4 and 20 T (Figure S5 and
formula weight (g mol−1) 397.4 397.4
5b), which reveals the presence of five resonances. The whole
temperature (°C) RT (20) 600
wavelength (Å) 0.32623 0.32623
set of 1D and 2D 87Rb NMR spectra recorded at different
crystal system orthorhombic cubic
fields were modeled using a single consistent set of parameters
space group Fddd (no. 70) Fm3m (no. 225)
given in Table 3.
unit cell dimensions (Å) a = 37.26491(1), a = 8.9930(2)
A description of the potassium environment in γ-K3AlF6 was
b = 12.45405(4), reported by King et al.8 In α-Rb3AlF6, half of the Rb1 atoms is
c = 17.68341(6) 7-coordinated while the other half of atoms shows a 6-
cell volume (Å3) 8206.85 727.30 coordinated octahedral environment. Rb2 atoms are 7-
Z 48 4 coordinated. Rb3, Rb4, and Rb5 atoms are each surrounded
d-space range 0.4−37 0.4−37 by 10, 11, or 12 fluorine atoms, due to partial occupancy of F3,
χ2 0.8 0.89 F4, and F5 sites. Consequently, six 87Rb resonances with
Rp (%) 4.12 4.7 relative intensities of 1 for 1/2 Rb1F6, 1 for the second 1/2
Rwp (%) 6.23 7.92 Rb1F7, 1 for Rb2, and 2/2/2 for Rb3/Rb4/Rb5 were expected
a
For definition of R-factors see references 39 and 40. on the 87Rb MAS NMR spectrum. However, only three broad
peaks were observed (Figure 5a).
The MQMAS NMR spectrum provides a better resolution.
In fact, five resonances, which are overlapped on the 1D NMR
spectrum, are now clearly distinguish (Figure 5b). The
resonances are in the range −20 to 40 ppm. The only
reported 87Rb NMR spectra in literature are that of RbF and a
RbLaF4. Rubidium fluoride adopts a cubic structure with RbF8
coordination (resonance is located at 19.1 ppm).35 The
structure of RbLaF4 contains a RbF7 edge-tricapped trigonal
prism. The rubidium resonance at 51.1 ppm has a quadrupolar
broadening with CQ value of 10.97 MHz and ηQ value of 1.36 It
means that there is no established relationship between the
coordination number of the rubidium cation and their
chemical shift. In the case of RbAlF4, the rubidium atoms,
like in RbF, have 8-fold cubic coordination environments. The
87
Rb NMR RbAlF4 spectrum shows a single resonance at 1.8
ppm (see Figure S6). In an attempt to better understand and
assign the 87Rb NMR spectrum of α-Rb3AlF6, we also recorded
Figure 2. Experimental (red), calculated (black), and difference a 87Rb−19F D-HMQC HETCOR MAS NMR spectrum (see
(blue) SPD Rietveld refinement of α-Rb3AlF6 (green marks); the Figure S7). The strong overlap of the 87Rb resonances,
Bragg peak positions of the secondary phase RbSiO4 as an impurity however, did not allow any further assignment of the
were visible in purple. An enlargement of the 18−30° range is resonances.
embedded. First-Principles Calculations. In order to confirm the
structure of α-Rb3AlF6 and to gain a better understanding of
and S1. Projections of the unit cell structure of α-Rb3AlF6 are the discrepancy regarding the 19F NMR spectra, a GIPAW
seen in Figure 3. calculation of the NMR parameters was performed. Since
Solid-State NMR Data. Both room temperature 27Al MAS CASTEP cannot handle partial occupancies of fluorine F3, F4,
NMR spectra (Figure S4) recorded at two magnetic fields of and F5, a set of structures (compatible with the experimental
9.4 and 20 T show a single narrow peak (full width at half- site occupancy factors) were at the beginning generated by a
maximum, fwhm = 135 Hz) in the octahedral region at combinatorial approach.37 The whole set of combinations of a
δiso(27Al) = 0.0 ppm. All four aluminum sites give rise to supercell are used, which is in this case is 213744. This is too
overlapping resonances, indicating that their environments in big to be able be processed it in one single step. Figure 6a
the structure are similar and symmetrical. The 19F MAS (34 depicts a chart of the electrostatic energies, which are lined up
kHz) NMR spectrum of α-Rb3AlF6 recorded at 20 T revealed by rising order of all structures. The minimum calculated
four signals located at −142.0, −143.5, −145.1, and −148.0 Coulomb energy (Ecmin = −1188.6 eV) was taken as a base to
ppm with relative intensities of 1:2:1:2, respectively (Figure which the energy values are relative to ca. 59 eV (a whole
4a). We know from the powder diffraction that the crystal extent of the distribution of the calculated energies).38 Figure
structure is described based on 11 inequivalent fluorine atoms: 6b is aiming to the 250 lowest-Ec structures, where we hope,
F2 occupies a site 16g, F1, F6−F10 fully occupy a position 32h the best correlation with the real system, can be found. The
while F3, F4, and F5 partially occupy their 32h position. It initial 10 lowest-Ec structures and every 20 up to 200
means that at least 12 19F resonances with relative intensity 1 structures were selected for further optimization. The
for F2, 2 for F6−F10, 1 for F3, 0.7 for F4, and 1.3 for F5 can optimization of the geometry of the last three structures
be expected in the 19F MAS NMR spectrum. (ranked 160th, 180th, and 200th), was not however reached,
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Table 2. Atomic Coordinates and Atomic Displacement Parameters of α-Rb3AlF6 Determined from Rietveld Refinement of
Synchrotron Powder Diffraction Data Collected at Room Temperature
atom Wyckoff site occupancy x/a y/b z/c Uiso/Å2
Rb1 32h 1 0.19678(3) 0.40398(1) 0.12410(9) 0.0295(6)
Rb2 16g 1 0.125 0.125 0.41691(9) 0.0281(8)
Rb3 32h 1 0.12419(6) 0.34203(9) 0.2649147) 0.0283(6)
Rb4 32h 1 0.20933(4) 0.1216(2) 0.24863(9) 0.0279(6)
Rb5 32h 1 0.21713(4) 0.1287(2) 0.76400(8) 0.0298(6)
Al1 8a 1 0.25 0.125 0.125 0.019(4)
Al2 8b 1 0.125 0.625 0.125 0.010(3)
Al3 16e 1 0.28964(2) 0.125 0.125 0.024(3)
Al4 16e 1 0.45799(2) 0.125 0.125 0.008(2)
F1 32h 1 0.15945(2) 0.0253(5) 0.1247(7) 0.060(3)
F2 16g 1 0.125 0.125 0.2280(4) 0.028(3)
F3 32h 0.527(1) 0.1664(4) 0.6193(2) 0.1705(6) 0.033(3)
F4 32h 0.348(1) 0.1023(8) 0.557(2) 0.1958(1) 0.033(3)
F5 32h 0.632(1) 0.1194(4) 0.7414(9) 0.1866(8) 0.033(3)
F6 32h 1 0.28934(2) 0.1185(1) 0.0246(3) 0.030(2)
F7 32h 1 0.25429(2) 0.2272(5) 0.1210(8) 0.028(2)
F8 32h 1 0.32447(2) 0.0210(5) 0.1181(7) 0.028(2)
F9 32h 1 0.45774(2) 0.1357(1) 0.0232(3) 0.036(2)
F10 32h 1 0.49293(2) 0.2279(5) 0.1301(8) 0.034(2)
F11 32h 1 0.42444(2) 0.0231(5) 0.1318(7) 0.035(2)

Figure 4. (a) Experimental (black) and simulated (color lines) 19F

MAS NMR spectra of α-Rb3AlF6 at 20 T. (b) Sum of 17 19F spectra
reconstructed with a set of the calculated chemical shift parameters
(all full width at half-maximum, fwhm = 0.5 ppm). (c) 19F spectrum
reconstructed (only isotropic resonances) using average fluorine
positions for each of the calculated structures. (d) Structural
arrangements around aluminum atoms. (e) Schematic representation
of the dynamics of F atoms in AlF6 octahedra.

Figure 3. Projections of the unit cell structure of α-Rb3AlF6 in the in room temperature, a reorientation (dynamic rotations of the
(010) and (001) planes.
AlF6 octahedra).9
By analyzing the Al environments, one can notice that the
even after 1 week of iterations. It was due to a strong four Al atomic positions have two or three distinct fluorine
movement of fluorine atoms from the initial positions. atoms in their coordination spheres: Al1F1 4 F2 2 ,
The final outcome is based on 17 structures. All calculated Al2F32F41.5F52.5, Al3F62F72F82, and Al4F92F102F112. Consid-
19
F δiso are shown in Figure 4b, where the comparison to the ering fast hopping of the fluorine on each position around one
experimental MAS NMR spectrum can also be seen. The AlF6 octahedron, the 19F δiso is then the barycenter of the
disapproval between the experimental and calculated data is individual δiso. We suppose that the fluorine atoms change their
larger than what is generally considered as a normal for positions between the crystallographic sites by flipping. Since
inorganic fluorides. This discrepancy may has arisen either motion is not introduced in CASTEP, we can simply average
from bad position of atoms in the unit cell, or from dynamic the fluorine positions on each of the calculated structures. The
effects that had not been taken in to the GIPAW calculations. multiplicities of the Al1:Al2:Al3:Al4 sites are 1:1:2:2, and
Because SPD refinements had not given a clear proof for expected integral intensities agree well with the experimental
residual electron density, we inquired the dynamic-reorienta- values. The overall good agreement between the reconstructed
tion hypothesis. This hypothesis is based on the fact that and experimental 19F spectrum enables to perform accurate
isolated AlF6 polyhedra in inorganic fluorides can display, even spectral assignment of the NMR resonances with the
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Figure 5. (a) Experimental (black) and simulated (color lines) 87Rb MAS NMR spectra and (b) 87Rb MQ MAS experimental (color lines) NMR
spectrum of Rb3AlF6 at 20 T and spinning rate of 30 kHz and its simulation (black line) with the parameters presented in Table 3 (ssb stands for
spinning side bands).

Table 3. 87Rb Isotropic Chemical Shift (δiso), Mean calculations could not be done since each Rb atom has in its
Quadrupolar Constants (CQ), and Relative Intensities coordination sphere several fluoride ions coming from different
Obtained from the Simulation of the 87Rb MAS and AlF6 polyhedra, each one having independent dynamics.
MQMAS at 9.4 and 20 T These dynamic rotations of the AlF6 octahedra were
Rb δiso, ppm CQ, MHz integral intensity, % observed in δ-K3AlF6 phase, and it was supposed that such
line (±0.2 ppm) (±0.1 MHz) ηQ (±0.1) (±2%) rotations could be occurring in some of the lower temperature
5 44.7 5.3 0.6 18 phases as well.8 Our data confirm this supposition.
4 42.2 6.2 0.65 17 β-Rb3AlF6. High-Temperature Synchrotron Powder Dif-
3 18.6 5.3 0.5 30 fraction Data. In order to track the α-Rb3AlF6 to β-Rb3AlF6
2 14.1 3.8 0.5 12 phase transition, observed by thermal analysis around 350 °C,
1 −22.4 2.7 0.8 23 high-resolution synchrotron powder diffraction diagrams were
collected (Figure 7) from room temperature up to 600 °C
crystallographic sites. This last result enables validation of (i) (using 100 °C steps). The phase transformation between 300
the structural model and (ii) the fast hopping hypothesis and 400 °C was also observed.
occurring at room temperature. To reconstruct the 19F The same procedure, as used for the room temperature
spectrum, the line widths (fwhm) were used corresponding polymorph, was applied to solve and refine the crystal structure
to the experimental values. Note that the obtained average of the high temperature polymorph (data recorded in situ at
isotropic magnetic shielding values σiso for fluorine atoms have 600 °C). A cubic unit cell with a = 8.9930(2) Å was
very close values (±0.7 ppm), which allows us to assert that
determined from auto indexing routines, whereas the most
increasing the number of structures used for prediction will not
significantly change the final result. Seventeen structures are symmetric Fm3m space group was found suitable for the high-
enough to image the real structure. temperature β-Rb3AlF6 polymorph. An isostructural model
The fast motion of fluorine atoms is also responsible for the could be identified, namely δ-K3AlF6 (ICSD 262078). The
small CQ value observed for the 27Al resonances, when the structure refinement was therefore performed using this
calculated values range 1−8.2 MHz. This motion is also structural model as starting point using a Rb substitution for
responsible for the uniqueness of all four Al resonances. K atomic positions and isotropic thermal factors for Rb, Al,
Regarding rubidium atoms, the analysis of the DFT and F. The refinement converged to low RB-factor values of

Figure 6. (a) Chart of the electrostatic energies (EC) of the 213744 distinct structural models lined up by rising order of all structures. (b)
Extended view of the 250 structures of lowest EC. The first 10 lowest-EC and every 20−200 structures, shown as red circles, were chosen for further
calculations.

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β-Rb3AlF6 has an ideal cubic structure of a double perovskite

with space group Fm3m. The AlF6 octahedra are centered at
the origin and the face centers of the cubic cell. Rubidium
atoms adopt an RbF6 and RbF12 coordination (Figure 9).

Figure 9. Structural arrangements around aluminum, fluorine, and

rubidium atoms.

Figure 7. Synchrotron powder diffraction patterns of Rb3AlF6 The fluorine atomic displacement parameter (ADP) is very
recording as a function of temperature upon heating. The diagrams
large (Uiso = 0.111 Å2), which might reflect static or dynamic
corresponding to low temperature form (orthorhombic Fddd with a =
37.26491(1) Å, b = 12.45405(4) Å, and c = 17.68341(6) Å) and high disorder. This large value was previously observed in case of δ-
temperature form (cubic Fm3m with a = 8.9930(2) Å) are indicated phase of K3AlF6.8 Based on reverse Monte Carlo simulations,
by α and β symbols, respectively. the authors8 explained the large anisotropy of the fluorine
ADPs by significant rotations of AlF6 octahedra. It can be
(Figure 8) (Rwp = 7.92%, Rp = 4.70%, and GOF = 0.89). The noted that disorder on F atomic positions was also previously
main results of the Rietveld refinement are reported in Table 4. reported in the β-sodium cryolite.5
High-Temperature MAS NMR Data. β-Rb3AlF6. As was
shown previously, the room temperature 19F MAS NMR
spectrum of Rb3AlF6 (α-phase) has shown four isotropic
resonances. At the low MAS frequency (5 kHz, required for
the HT measurements) and high field (17.6 T), numerous
spinning sidebands are presented due to the chemical shift
anisotropy (Figure S8). Therefore, the MATPASS pulse
sequence was used. As it was expected, the resolution of the
room temperature 19F MATPASS NMR spectrum recorded at
5 kHz MAS frequency is much lower than at 30 kHz, but still
the four 19F resonances can still be distinguished (Figure 10).
For 87Rb, the 30 kHz MAS and 5 kHz QMATPASS NMR
spectra are identical. 19F MATPASS and 87Rb QMATPASS
NMR spectra were recorded in the temperature range RT < t

Figure 8. Rietveld refinement of the SPD pattern of β-Rb3AlF6

collected at 600 °C. Experimental (red), calculated (black), difference
(blue), and Bragg reflections (cubic Fm3m a = 8.9930(2) Å) (green
marks) are represented.

Table 4. Atomic Coordinates and Atomic Displacement

Parameters of β-Rb3AlF6 Determined from in Situ Rietveld
Refinement of Synchrotron Powder Diffraction Data
Collected at 600 °C

Wyckoff
atom site occupancy x/a y/b z/c Uiso/Å2
Rb1 8c 1 0.25 0.25 0.25 0.0676(3)
Rb2 4b 1 0.5 0.5 0.5 0.0685(4)
Al1 4a 1 0 0 0 0.0531(1) Figure 10. 19F NMR spectra of Rb3AlF6 acquired at 17.6 T and MAS
5 kHz as a function of temperature: Isotropic slices of MATPASS for t
F1 24e 1 0.2002(2) 0 0 0.1110(1)
≤ 358 °C and one pulse for t > 358 °C.

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≤ 352 °C (Figures 10 and 11). For higher temperature, the phase is clearly revealed in the 19F and 87Rb NMR spectra at
transverse relaxation time significantly decreased, so that the 352 °C. This temperature range also matches the transition
temperature measured by DSC.
The 19F and 87Rb spectra recorded at 397 °C exhibit an
extremely narrow (fwhm ∼750 Hz for 87Rb and ∼550 Hz for
19
F) singlet resonance without any spinning sidebands. The
rubidium and fluorine signals were simulated by one Gaussian
line with a chemical shift at 0.7 ppm and −143.7 ppm at T =
397 °C, respectively. From this observation and the fact that
there are two rubidium sites in the structure, we conclude that
the rubidium sites in β-Rb3AlF6 are involved in chemical
exchange process. The calculated 19F chemical shift value is
−153.5 ppm, and it is in reasonably good agreement with our
experimental result.
K3AlF6: Using the heating of the sample in the MAS NMR
rotor by a laser beam, the 19F MAS NMR spectra of all four
polymorphs (α → β 132 °C; β → γ 153 °C; γ → δ 310 °C) of
K3AlF6 could be recorded (Figure 12). The room temperature

Figure 11. 87Rb NMR spectra of Rb3AlF6 at 17.6 T and MAS 5 kHz
as a function of temperature: Isotropic slices of QMATPASS for t ≤
352 °C and one pulse for t > 352 °C.

intensity of the echo signal after three rotor periods was too
small to carry out the sideband separation. Therefore, in the
range 363 °C < t < 600 °C, the MAS NMR spectra were
recorded using a single pulse excitation. A complete
reversibility, without hysteresis of the spectral changes, was
observed.
It is worth noting that room temperature MAS NMR
measurements were performed without temperature regula-
tion. Due to frictional heating, the real temperatures of the
sample were 32 °C at 5 kHz MAS and 56 °C at 30 kHz.
The 19F lines were, upon slight heating (90 °C), significantly Figure 12. (a) Isotropic slices of 19F NMR MATPASS spectra of
sharpened, which confirmed the facile motion of the fluoride K3AlF6 acquired at 17.6 T and MAS 5 kHz as a function of
anions in the structure. A further sharpening of the 19F temperature. (b) Reconstructed 19F NMR spectra of polymorphs of
resonances (and also small shift) is visible while heating up to K3AlF6 (only isotropic resonances).
the phase transition temperature (Figure 10, left). At the phase
transition temperature (352 °C), an additional peak at −143.7 polymorph α-K3AlF6 adopts the elpasolite structure (ICSD
ppm appears, which is corresponding to the initial formation of 260574).7 It contains 5 Al sites in slightly distorted octahedral
the β-phase. This phase contains a single crystallographic F environments, 18 potassium crystallographic sites and 30
site. The coexistence of both α- and β-polymorphs can be seen crystallographically nonequivalent fluorine sites, and consists of
in the 352−363 °C range (Figure 10). The presence of both symmetrically equivalent layers of the AlF6 units. Every layer
phases was possible due to a temperature gradient in the body contains the octahedra rotated by π/4 around the c and a or b
of the sample. One can notice that the 19F resonance of the β- axes (noncooperative octahedral tilting, NCOT). As previously
phase has spinning sidebands, indicating limited fluorine reported, the 19F MAS NMR spectrum at 60 kHz and 20 T
motion up to 375 °C (Figure 10, blue spectrum in the consists of a broad envelope of signals in the −156 to −160
right). A fast fluorine motion, above this temperature, can be ppm range and four small signals at −162, −164.1, −167.3,
seen with an absence of spinning sidebands. and −168.5 ppm.18 It was not possible to make an assignment
A dynamic exchange between rubidium units could be of lines to F sites. The α phase is stable up to 132 °C and
clearly identified from the temperature dependent line shape further transforms into the tetragonal β-phase (ICSD 262076),
evolution in the 87Rb MAS NMR spectra (Figure 11). Above which is stable up to 153 °C. The structure of β-K3AlF6
175 °C, the 2−5 rubidium resonances broaden and then contains seven F and two Al crystallographic sites with
disappear, indicating the occurrence of dynamic exchange. It multiplicities of 8:4:8:8:8:8:16 for F and 2:8 for Al atoms. Its
19
should be noted that one line does not change and, therefore, F MAS NMR spectrum contains an asymmetrically
one of the rubidium site does not participate in this exchange. broadened peak with non-Lorenzian line shape at −160.1
Quantitative analysis of the exchange is hampered by the ppm. As in case of α polymorph, the assignment of 19F signals
strong overlap of the 2−5 resonances. Above the phase cannot be provided. In the range 153−306 °C, the
transition temperature, a new 87Rb resonance appears at 0.7 orthorhombic γ phase (ICSD 262077) exists. The crystalline
ppm, corresponding to the β-phase. Up to 363 °C, the structure of γ-K3AlF6 contains 11 fluorine sites. The 19F MAS
coexistence of both phases is confirmed. The phase transition NMR spectrum, recorded at 160 °C, contains four signals at
from the room-temperature α-phase to the high temperature β- −158.2, −159.2, −160.3, and −161.9 ppm with relative
H https://dx.doi.org/10.1021/acs.inorgchem.0c00415
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Inorganic Chemistry

■
pubs.acs.org/IC Article

intensities of 15/36/17/32, fewer resonances than expected. CONCLUSIONS

This again very likely arises from fast dynamics of fluoride ions. Synchrotron powder diffraction, solid-state NMR spectrosco-
The last phase transition occurs above 306 °C. The high py, electron diffraction, and first-principles calculations have
temperature cubic δ phase (ICSD 262078) has double- been used as a coupled approach to perform a complete
perovskite structure and it is stable up to the melting structural characterization of the two polymorphs of rubidium
temperature of 974 °C.9 δ-K3AlF6 exhibits one kind of fluorine cryolite Rb3AlF6. The structure of α-Rb3AlF6 is part of a small
atom, one kind of aluminum atom, and two kinds of potassium family of compounds with noncooperative octahedral tilting.
atoms. Two potassium atoms are in a 1/2 ratio. The 19F MAS Variable temperature MAS NMR studies enable the observa-
NMR spectrum measured at 335 °C exhibits, as expected, a tion of chemical exchange between rubidium sites in α-
narrow (fwhm ∼550 Hz) singlet resonance at 159.4 ppm. Rb3AlF6. High temperature NMR measurements show that α-
The both high temperature solid-state 19F NMR spectra of Rb3AlF6 is isostructural to γ-K3AlF6 and β-Rb3AlF6 is
γ-K3AlF6 and α-Rb3AlF6 contain four lines with the integral isostructural to δ-K3AlF6. Diffraction-based methods coupled
intensity ratio of 1:2:1:2. Only one resonance was observed in with NMR spectroscopy and DFT calculations was proved as a
the flour spectra of γ-K3AlF6 and β-Rb3AlF6. Thus, NMR data promising approach to obtain the information about the local
obtained for potassium and rubidium cryolites confirms that α- dynamics of AlF6 octahedra with the noncooperative
Rb3AlF6 is isostructural to γ-K3AlF6 and β-Rb3AlF6 is octahedral tilting.
isostructural to δ-phase of K3AlF6. We suppose the existence
of low temperature phases of Rb3AlF6 at temperatures below
room temperature, which are isostructural to α- and β-K3AlF6.
■
*
ASSOCIATED CONTENT
sı Supporting Information
Figure 12b shows the reconstructed 19F spectrum of The Supporting Information is available free of charge on the
polymorphs of K3AlF6. The calculation methods are presented ACS Publications Web site. The Supporting Information is
in the Supporting Information. Our calculated data show good available free of charge at https://pubs.acs.org/doi/10.1021/
agreement with 19F NMR results. acs.inorgchem.0c00415.
The cryolite mineral, Na3AlF6, adopts at room temperature
Temperature calibration, X-ray powder diffraction
(α-form)4 a monoclinic structure, which consists of an isolated
patterns of the RbAlF4, thermal analysis diagrams, 27Al
AlF6 octahedra interconnected by Na atoms. The AlF6 MAS NMR, 87Rb MQMAS, 87Rb MAS NMR, 2D D-
octahedron is in this structure very regular. Each bond HMQC MAS NMR, 19F MAS NMR, tables of bond
distance and angle does not differ very much from the distances (PDF)
respective mean value. When we substitute the Na+ ions by
other alkali cations (K+, Rb+ in particular), the cryolite
structure will changing, as much as the radius of the alkali
metal cation. In these systems, the substitution leads to a
■ AUTHOR INFORMATION
Corresponding Authors
lattice distortion due to a rotation of the fraction of the AlF6 Aydar Rakhmatullin − Conditions Extrêmes ét Matériaux:
octahedral units, which are rotated over a large angle of ∼45°. Haute Température et Irradiation, CEMHTI, UPR
NCOT leads to an increase of the coordination number of the 3079−CNRS Université Orléans, 45071 Orléans, France;
alkali atoms (from 6 up to 12) as it can be seen in our case. orcid.org/0000-0002-7328-5081; Phone: 0033-
Moreover, the substitution also causes the decrease of the 238255512; Email: rakhmat@cnrs-orleans.fr
phase transition temperature, so the highly symmetrical α- František Šimko − Institute of Inorganic Chemistry and Centre
Rb3AlF6 tends to be a stable even at low temperature. The size of Excellence for advanced Materials Application - CEMEA,
of the alkali anions is a key factor in the structural relations as Slovak Academy of Sciences, 845 36 Bratislava, Slovakia;
well as the physicochemical behavior of these elpasolite-related orcid.org/0000-0003-2390-1349; Phone: 00421-2-
fluoride phases. 59410495; Email: uachsim@savba.sk; Fax: 00421-2-
The following structures exhibiting NCOT have been so far 59410444
reported: K3AlF6,7,8 Sr3WO6,14 Rb2K(Cr or Ga)F6,15 and (K or Authors
Rb)3MoO3F3.16 These species contain several NMR active Emmanuel Véron − Conditions Extrêmes ét Matériaux: Haute
isotopes (17O, 19F, 27Al, 69/71Ga, 87Sr, 85/87Rb) that typically Température et Irradiation, CEMHTI, UPR 3079−CNRS
allow probing their environment by solid-state NMR spec- Université Orléans, 45071 Orléans, France
troscopy. To our knowledge, however, such an experiment has Mathieu Allix − Conditions Extrêmes ét Matériaux: Haute
not yet been reported. Also DFT calculations of NMR Température et Irradiation, CEMHTI, UPR 3079−CNRS
parameters of these compounds are missing in open literature. Université Orléans, 45071 Orléans, France
We think that the major reasons, why this information is still Charlotte Martineau-Corcos − Conditions Extrêmes ét
not available, relates to the difficulties to correctly interpret the Matériaux: Haute Température et Irradiation, CEMHTI, UPR
NMR data. The local dynamics taking places in these 3079−CNRS Université Orléans, 45071 Orléans, France;
structures via NCOT effect, is probably the main reason why Université de Versailles Saint-Quentin en Yvelines, 78035
it is so difficult to interpret the NMR. The DFT calculations Versailles Cedex, France; orcid.org/0000-0003-1887-1042
can usually help to explain confusing experimental data. Andy Fitch − ID22, ESRF, Grenoble, France
However, the atomic positions with partial occupation can also Franck Fayon − Conditions Extrêmes ét Matériaux: Haute
lead to other problems. This study was the first attempt with a Température et Irradiation, CEMHTI, UPR 3079−CNRS
demonstration how solid state NMR methods coupled with Université Orléans, 45071 Orléans, France
computations provide the useful insights into the nature of Roman A. Shakhovoy − Conditions Extrêmes ét Matériaux:
local dynamics that accompanying the structures with the Haute Température et Irradiation, CEMHTI, UPR
noncooperative octahedral tilting effect. 3079−CNRS Université Orléans, 45071 Orléans, France
I https://dx.doi.org/10.1021/acs.inorgchem.0c00415
Inorg. Chem. XXXX, XXX, XXX−XXX
Inorganic Chemistry pubs.acs.org/IC Article

Kirill Okhotnikov − Conditions Extrêmes ét Matériaux: Haute (5) Smrčok, L’.; Kucharík, M.; Tovar, M.; Ž ižak, I. High temperature
Température et Irradiation, CEMHTI, UPR 3079−CNRS powder diffraction and solid state DFT study of β-cryolite (Na3AlF6).
Université Orléans, 45071 Orléans, France Cryst. Res. Technol. 2009, 44, 834−840.
Vincent Sarou-Kanian − Conditions Extrêmes ét Matériaux: (6) Bučko, T.; Š imko, F. On the structure of crystalline and molten
cryolite: Insights from the ab initio molecular dynamics in NpT
Haute Température et Irradiation, CEMHTI, UPR
ensemble. J. Chem. Phys. 2016, 144, 064502−13.
3079−CNRS Université Orléans, 45071 Orléans, France (7) Abakumov, A. M.; King, G.; Laurinavichute, V. K.; Rozova, M.
Michal Korenko − Institute of Inorganic Chemistry and Centre G.; Woodward, P. M.; Antipov, E. V. The Crystal Structure of α-
of Excellence for advanced Materials Application - CEMEA, K3AlF6: Elpasolites and Double Perovskites with Broken Corner-
Slovak Academy of Sciences, 845 36 Bratislava, Slovakia Sharing Connectivity of the Octahedral Framework. Inorg. Chem.
Zuzana Netriová − Institute of Inorganic Chemistry, Slovak 2009, 48, 9336−9344.
Academy of Sciences, 845 36 Bratislava, Slovakia (8) King, G.; Abakumov, A. M.; Woodward, P. M.; Llobet, A.;
Ilja B. Polovov − Department of Rare Metals and Tsirlin, A. A.; Batuk, D.; Antipov, E. V. The High-Temperature
Nanomaterials, Institute of Physics and Technology Ural Polymorphs of K3AlF6. Inorg. Chem. 2011, 50, 7792−7801.
Federal University, Ekaterinburg, Russia (9) Holm, J.; et al. Phase Transitions and Structure of the High-
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Chem. Scand. 1965, 19, 261−263.
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The authors declare no competing financial interest. form of Rb2KCrF6 and Rb2KGaF6: The first example of an elpasolite-

■
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ACKNOWLEDGMENTS (16) Fry, A. M.; Woodward, P. M. Structures of α-K3MoO3F3 and α-
This study was financially supported by CAMPUS FRANCE Rb3MoO3F3: Ferroelectricity from Anion Ordering and Noncoop-
(PHC STEFANIK project No. 31799NM), the Slovak bilateral erative Octahedral Tilting. Cryst. Growth Des. 2013, 13, 5404−5410.
(17) Zhou, X. W.; Doty, F. P.; Yang, P. Atomistic models for
project (No. SK-FR-2013-0039), and Slovak Grant Agencies scintillator discovery. Proc. SPIE 2010, 7806, 78060E.
(VEGA-2/0060/18, APVV-15-0738), and ITMS project (with (18) Š imko, F.; Rakhmatullin, A.; Florian, P.; Kontrík, M.; Korenko,
code 313021T081) supported by Research & Innovation M.; Netriová, Z.; Danielik, V.; Bessada, C. (Oxo)(Fluoro)−
Operational Programme funded by the ERDF. For DFT Aluminates in KF−Al2O3 System: Thermal Stability and Structural
calculations, we thank the “Centre de Calcul Scientifique en Correlation. Inorg. Chem. 2017, 56, 13349−13359.
region Centre” (Orléans, France). We acknowledge the ICMN (19) Š imko, F.; Rakhmatullin, A.; Véron, E.; Allix, M.; Florian, P.;
(Orléans, France) for access to their Transmission Electron Kontrík, M.; Netriová, Z.; Korenko, M.; Kavečanský, V.; Bessada, C.
Oxo- and Oxofluoroaluminates in the RbF−Al2O3 System: Synthesis
Microscope. Financial support from the IR-RMN-THC
and Structural Characterization. Inorg. Chem. 2018, 57, 13702−
Fr3050 CNRS for conducting the research is gratefully 13712.
acknowledged. We thank also Dr. M. Suchomel and Dr. P. (20) Daněk, V.; Č ekovský, R. Phase Transitions and Structure of the
Florian for useful discussions. High-Temperature phases of some Compounds of the Cryolite

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