Crystallographic features of ammonium fluoro­elpasolites: dynamic orientational disorder in crystals of (NH₄)₃HfF₇ and (NH₄)₃Ti(O₂)F₅

A classical elpasolite-type structure is considered with respect to dynamically disordered ammonium fluoro-(oxo­fluoro-)metallates. Single-crystal X-ray diffraction data from high quality (NH₄)₃HfF₇ and (NH₄)₃Ti(O₂)F₅ samples enabled the refinement of the ligand and cationic positions in the cubic (Z = 4) structure. Electron-density atomic profiles show that the ligand atoms are distributed in a mixed (split) position instead of 24e. One of the ammonium groups is disordered near 8c so that its central atom (N1) forms a tetrahedron with vertexes in 32f. However, a center of another group (N2) remains in the 4b site, whereas its H atoms (H2) occupy the 96k positions instead of 24e and, together with the H3 atom in the 32f position, they form eight spatial orientations of the ammonium group. It is a common feature of all ammonium fluoroelpasolites with orientational disorder of structural units of a dynamic nature.

1. Introduction

There is a large family of A₂BMX₆ compounds (A, B = alkali cations or ammonium, R_A > R_B; M = tri-, tetra-, penta- or hexavalent metal; X = O, F) with an elpasolite structure derived from a perovskite superstructure with doubled cell parameter (Massa & Babel, 1988; Flerov et al., 1998). Named after the mineral K₂NaAlF₆, elpasolite-type compounds are cubic face-centered with space group (Z = 4; Morss, 1974). In this structure of A₂BMF₆, B ions locate in the octahedral 4b sites surrounded by six F⁻ ligands, each of them belonging to a different MF₆³⁻ anion, and A ions are located in the tetrahedral 8c sites surrounded by 12 F⁻ ions, each three of them belonging to one of the four MF₆³⁻ ions around the A ion. Precision structural determination of the Rb analogue of the mineral elpasolite, synthetic Rb₂NaAlF₆, was recently performed (Yakubovich et al., 2013) in the classic style with 4a, 4b, 8c and 24e positions of the group for Al, Na, Rb and F atoms, respectively. Most of the structures of cubic elpasolites were solved in a similar way. Nevertheless, the use of a classical 24e ligand position is not able to explain some structural transformations at phase transitions (PTs) inherent to cubic elpasolites. Recently, a synchrotron powder diffraction study of a synthetic cryolite Na₃AlF₆ revealed that the high-temperature (HT) cubic phase was characterized by static displacive disorder of the F anions from the 24e sites to four nearby 96k sites 25% occupied (Zhou & Kennedy, 2004). However, a simple static displacement of the F atoms is not capable of explaining the structure of the high-temperature β phase (Smrčok et al., 2009). Relatively frequent reorientations of the AlF₆ octahedra of the β phase explain the thermal disorder in positions of the F⁻ ions observed in X-ray diffraction experiments (Bučko & Šimko, 2016). The dynamic nature of the β phase was confirmed by the entropy value (close to Rln4) during a first-order phase transition from monoclinic (α phase) symmetry (Yang et al., 1993). The 96k position was taken into consideration to refine a cubic structure of Rb₂KFeF₆ (Vasilovsky et al., 2006), while Massa et al. (1986) used the 96j position. The compound undergoes a PT at 170 K with the entropy change ΔS = Rln6. A PT in the related Rb₂KTiOF₅ at 215 K is accompanied by quite a large change in the entropy, ΔS = Rln8 (Fokina et al., 2008; Gorev et al., 2010), which is characteristic of order–disorder transformations as opposed to displacive ones associated with small octahedral tilts and followed by a rather small entropy change, which is of the order of 0.2R (Flerov et al., 1998, 2002, 2004).

The PT entropy changes should be taken into account to refine the structures of elpasolites. It especially concerns ammonium fluoroelpasolites, which are usually dynamically disordered. Suga and co-authors (Moriya et al., 1977, 1979; Kobayashi et al., 1985; Tressaud et al., 1986) measured the heat capacity of (NH₄)₃MF₆ (M = Fe, Al, V, Cr, Ga) and interpreted the observed large entropy changes of the phase transition in terms of a model in which the disordered orientations of the tetrahedral NH₄ ions at the 4b sites and of the octahedral MF₆³⁻ ions in the lattice freeze into an ordered state below the transition points. Fluorine octahedra were assumed to be disordered with eight possible orientations in the general 192l position, and one of the ammonium ions at the 4b site was disordered in two distinct orientations. The total entropy change connected with both octahedra and tetrahedra ordering could be given as ΔS = Rln8 + Rln2 = Rln16, which is in good agreement with the experimental values. However, the NH₄ group in the 8c position can also take part in the PT. PTs and ionic motions in hexafluoroaluminates (NH₄)_3 − xK_xAlF₆ (x = 1, 2) studied by ¹H, ¹⁹F and ²⁷Al magnetic resonance were interpreted in terms of overall reorientations of NH₄⁺ (8c position) and AlF₆³⁻ ions. Rapid reorientations of both ions freeze into an ordered state below the PT points (Hirokawa & Furukawa, 1988). A recent study of the (NH₄)₃GaF₆ structure by ¹⁹F and ^69,71Ga magic angle spinning NMR in comparison with X-ray Rietveld refinement supported the model of rigid GaF₆ octahedra. In spite of the very low deviation of the GaF₆ octahedra from exact cubic symmetry, it was concluded that the fluorine 192l position was much subjected to errors. Both NH₄⁺ ions and GaF₆³⁻ octahedra undergo rapid reorientation rotations (Krahl et al., 2008).

Our structural refinement of a series of ammonium fluoro­elpasolites (NH₄)₃AlF₆, (NH₄)₃TiOF₅, (NH₄)₃FeF₆ and (NH₄)₃WO₃F₃ by localizing anions (F⁻, O²⁻) in four acceptable positions of the system (24e, 96k, 24e + 96j, 192l) revealed that F (O) atoms should be preferably distributed in mixed (split) 24e + 96j positions (Udovenko et al., 2003). The same concerns (NH₄)₃MoO₃F₃ and seven-coordinated (NH₄)₃ZrF₇ and (NH₄)₃NbOF₆ (Udovenko & Laptash, 2008a, 2008b). Both ammonium groups are disordered: N1H₄ is tetrahedrally displaced from the 8c position into the 32f site, and the H atoms of N2H₄ are statistically distributed in the 96k and 32f positions, so that it takes eight equivalent spatial orientations instead of two accepted ones (Udovenko & Laptash, 2011). This disorder has a dynamic nature (both ammonium cations and anions are disordered) that was supported by solid-state NMR (Kavun et al., 2010; 2011) and calorimetric measurements (Flerov et al., 2011; Fokina et al., 2007, 2013). This concerns equally both six-coordinated and seven-coordinated complexes.

Seven ligand atoms around a central metal atom lead with the need to the splitting of the ligand positions as in the case of ammonium fluoroperoxoelpasolites (NH₄)₃Ti(O₂)F₅ and (NH₄)₃Zr(O₂)F₅ (Massa & Pausewang, 1978; Schmidt et al., 1986). In this paper, the crystallographic features of ammonium fluoroelpasolite structures are highlighted by examples of the dynamically disordered (NH₄)₃HfF₇ and (NH₄)₃Ti(O₂)F₅.

2. Experimental

2.1. Synthesis

All the starting materials were of analytical reagent grade and used without further purification; deionized water was used as a solvent. Either solid NH₄HF₂ or hydrofluoric acid (40% HF by weight) were used as fluorinating agents. Ammonium hafnium fluoroelpasolite (NH₄)₃HfF₇ (I) was synthesized according to the reactions

Excess NH₄HF₂ or (HF + NH₃) is needed to obtain the complex; we used a double excess. In the first case, HfO₂ or HfF₄ were fluorinated with NH₄HF₂ at 423–473 K followed by water leaching of the cake with the addition of a small amount of HF to pH = 2–3. The solution was filtered and slowly evaporated in air at ambient conditions with the formation of well faceted colorless octahedral single crystals of (NH₄)₃HfF₇. In the second case, HfO₂ was dissolved in the HF solution (40%) followed by the addition of NH₃ aq (25%) and slow evaporation of the resulting solution.

An attempt was made to obtain (NH₄)₃HfOF₅ by ammonia hydrolysis of the hot aqueous solution of (NH₄)₃HfF₇ with excess NH₄F, similar to (NH₄)₃TiOF₅ (Laptash et al., 1999). At pH = 8 a white precipitate was formed (not identified) but (NH₄)₃HfF₇ crystallized again from the mother liquor. EDX analysis was used to check the composition of the crystal, which corresponded to (NH₄)₃Hf(OH)_xF_7 − x (x = 0.2–0.4).

Ammonium titanium peroxofluoroelpasolite (NH₄)₃Ti(O₂)F₅ (II) was prepared by synthesis from fluoride solution according to the reaction

An excess (50–100% with respect to the stoichiometric proportion) of NH₄F (40% solution) and then a concentrated (30%) solution of H₂O₂ were added to aqueous (NH₄)₂TiF₆ (the solution pH was adjusted at 7–8 by the addition of ammonia, if necessary). As a result, an abundant yellow–lemon deposition of (NH₄)₃Ti(O₂)F₅ formed consisting of fine octahedral single crystals (∼ 10 µm in size). Further slow evaporation of the solution in air resulted in larger bright yellow single crystals suitable for X-ray determination.

2.2. Crystallographic determination

Single-crystal X-ray diffraction data were collected using Bruker KAPPA APEX II and Bruker SMART-1000 CCD diffractometers equipped with a graphite monochromator (Mo Kα radiation, λ = 0.71073 Å). Data collections were carried out at 296 K, 0.3° ω-scans were performed in a hemisphere of reciprocal space with an exposure time of 20 s per frame at a crystal–detector distance of 40 mm. Data collection, reduction and refinement of the lattice parameters were performed using the APEXII software package (Bruker, 1998, 2000). All the calculations were performed using the SHELXL/PC program (Sheldrick, 2015).

The structures were solved by direct methods with an analysis of the electron-density distribution and refined against F² by the full-matrix least-squares method with anisotropic approximation. At the first stage, the H atoms of ammonium groups were determined from difference electron-density maps. The H1 atoms around N1 form a tetrahedron with the N—H distances of 0.89 and 0.79 Å for (I) and (II), respectively, while the H2 atoms around N2 form an octahedron with the N—H distances of 0.92 and 0.83 Å for (I) and (II), respectively. Next, the coordinates of the H atoms were calculated geometrically in accordance with N1 disordering and the real geometry of N2H₄, and they were not refined. Information on the structure determinations is summarized in Table 1. Selected bond distances and angles are listed in Table 2. The hydrogen-bond parameters are presented in Table 3.

Table 1
Crystal and experimental data for (NH₄)₃HfF₇ (I) and (NH₄)₃Ti(O₂)F₅ (II)

For all structures: Cubic, , Z = 4. Experiments were carried out at 296 K with Mo Kα radiation using a Bruker APEXII CCD diffractometer. Absorption was corrected for by multi-scan methods, SADABS (Bruker, 2008). H atom parameters were not refined.

	(I)	(II)
Crystal data
Chemical formula	(NH4)3HfF7	(NH4)3Ti(O2)F5
Mr	365.62	229.03
a (Å)	9.3964 (1)	9.2327 (1)
V (Å^3)	829.63 (3)	787.02 (3)
Dx (Mg m^−3)	2.927	1.933
μ (mm^−1)	12.645	1.143
Crystal size (mm)	0.25 × 0.23 × 0.22	0.24 × 0.23 × 0.22
Data collection
Tmin, Tmax	0.593, 0.750	0.695, 0.749
No. of measured, independent and observed [I > 2σ(I)] reflections	8194, 293, 293	9680, 190, 190
Rint	0.019	0.020
(sin θ/λ)max (Å^−1)	1.116	0.961
Refinement
R[F^2 > 2σ(F^2)], wR(F^2), S	0.009, 0.019, 1.19	0.014, 0.0400, 1.032
No. of reflections	293	190
No. of parameters	22	24
Δρmax, Δρmin (e Å^−3)	1.14, −0.66	0.14, −0.33
Computer programs used: SMART (Bruker, 1998), SAINT (Bruker, 2000), SHELXTL (Sheldrick, 2015).

Table 2
Selected distances (Å) and angles (°) for (I) and (II)

(NH4)3HfF7
Hf—F1	1.963 (2) × 3	F1—F3	2.912 (4) × 4
Hf—F2	2.032 (5) × 2	F1B—F2	2.374 (6) × 2
Hf—F3	2.151 (5) × 2	F2—F3	2.484 (8) × 2
F1—F1B	2.776 (3) × 2	F3—F3A	2.425 (10)
F1—F2	2.826 (4) × 4
F1—Hf—F1A	180	F2—Hf—F3	72.8 (2) × 2
F1—Hf—Feq	90 × 10	F3—Hf—F3A	68.6 (3)
F2—Hf—F1B	72.9 (2) × 2
(NH4)3Ti(O2)F5
Ti—O1	1.974 (3) × 2	O1—O1A	1.491 (4)
Ti—F1	1.895 (1) × 3	O1—F2	2.362 (5) × 2
Ti—F2	1.928 (3) × 2	O1—F1B	2.707 (3) × 2
F1—F1A	2.673 (2) × 2	F1A—F1B	2.483 (3)
F1—F2	2.386 (3) × 2	F1A—F2A	2.816 (2) × 2
		F2—F2A	2.611 (4)
F1—Ti—F1A	89.73 (7) × 2	O1—Ti—F1B	88.78 (5) × 2
F1—Ti—F2	77.21 (9) × 2	F1A—Ti—F1B	81.90 (7)
O1—Ti—O1A	44.38 (8)	F1A—Ti—F2A	94.89 (5) × 2
O1—Ti—F2	74.5 (1) × 2	F2—Ti—F2A	85.24 (3)

Table 3
Hydrogen-bonding geometry (Å, °) in (I) and (II)

D—H⋯A	D—H	H⋯A	D⋯A	D—H⋯A
(NH4)3HfF7
N1—H11⋯F3	0.90	2.04	2.798 (6)	141
N1—H12⋯F2^i	0.88	2.25	2.967 (3)	138
N1—H12⋯F2^ii	0.88	2.11	2.856 (5)	142
N1—H12⋯F3^ii	0.88	1.85	2.584 (4)	140
N1—H12⋯F3^i	0.88	1.99	2.695 (3)	136
N1—H12⋯F3^iii	0.88	1.89	2.620 (3)	138
N1—H12⋯F2^iii	0.88	2.20	2.933 (4)	139
N1—H11⋯F2	0.90	2.32	3.085 (7)	143
N2—H2⋯F1^iv	0.91	1.88	2.735 (2)	157
N2—H2⋯F2^iv	0.91	1.94	2.820 (6)	164
N2—H2⋯F3^iv	0.91	2.30	3.163 (5)	158
N2—H2⋯F2^v	0.91	2.04	2.820 (6)	143
(NH4)3Ti(O2)F5
N1—H13⋯O1^vi	0.88	2.00	2.721 (2)	138
N1—H14⋯O1^vii	0.88	2.00	2.721 (2)	138
N1—H12⋯F2^viii	0.88	2.17	2.908 (2)	140
N1—H11⋯F1	0.87	2.49	3.243 (4)	145
N1—H11⋯O1^ix	0.87	2.08	2.838 (4)	145
N1—H12⋯O1^x	0.88	1.84	2.613 (3)	145
N1—H12⋯F2^xi	0.88	2.06	2.831 (3)	145
N1—H13⋯F1^xii	0.88	2.37	3.102 (2)	140
N2—H2⋯O1^xiii	0.89	2.27	3.130 (4)	161
N2—H2⋯F1^xiii	0.89	1.87	2.737 (1)	162
N2—H2⋯F1^xiv	0.89	1.90	2.737 (1)	156
N2—H2⋯F2^xv	0.89	1.96	2.825 (3)	164
Symmetry codes: (i) ; (ii) ; (iii) ; (iv) ; (v) ; (vi) ; (vii) ; (viii) ; (ix) -z, y, x; (x) ; (xi) ; (xii) ; (xiii) ; (xiv) ; (xv) .

2.3. Spectroscopic measurements and additional characterization

Mid-IR (400–4000 cm⁻¹) spectra were collected in Nujol mull using a Shimadzu FTIR Prestige-21 spectrometer operating at 2 cm⁻¹ resolution. The FT–Raman spectra of the compounds were recorded with an RFS 100/S spectrometer. The 1064 nm line of an Nd:YAG laser (130 mW maximum output) was used for excitation of the samples. The spectra were recorded at room temperature. In addition, the IR spectrum of (NH₄)₃HfF₇ was recorded directly from the pure single crystal using a FT–IR Bruker Vertex 70v spectrometer with the Platinum ATR attachment.

For a description of the vibrational spectra of (NH₄)₃HfF₇, quantum-chemical calculations of the HfF₇³⁻ anion were performed employing the GAMESS software package (Schmidt et al., 1993) within the density functional theory framework (DFT) with exchange–correlation potential B3LYP. The TZVP basis set was used for F atoms and SBKJC basis set for Hf.

The elemental composition of (NH₄)₃HfF₇ was checked using the X-ray microanalyser JXA-8100 Jeol, Japan (the operating voltage is 20 kV, operating current is 1 × 10⁻⁸ A) and energy-dispersive spectrometer INCAx–sight, Oxoford (resolution is 137 eV).

3. Results and discussion

3.1. Crystal structures

Both compounds (NH₄)₃HfF₇ (I) and (NH₄)₃Ti(O₂)F₅ (II) crystallize in the cubic space group . The crystal structure of (I) consists of isolated statistically disordered polyhedra HfF₇ in the form of a pentagonal bipyramid (PB) and two kinds of ammonium groups (Fig. 1). The PB configuration for the related (NH₄)₃ZrF₇ has been reliably established by Hurst & Taylor (1970) and confirmed by us (Udovenko & Laptash, 2008b). It is this polyhedron that was realised in most monomeric crystal structures of Zr and Hf fluoride complexes reviewed by Davidovich (1998) and Davidovich et al. (2013).

Figure 1 Disordered structure of (NH4)3HfF7 (a) and the isolated polyhedron HfF7^3− (b). Green, blue and white balls are the F, N and H atoms, respectively (the central Hf atoms are not seen). Displacement ellipsoid plots are shown at 50% probability.

The crystal structure of (II) is built from disordered polyhedra Ti(O₂)F₅³⁻ in the form of distorted octahedron with the peroxide group at one of the axial corners and two kinds of ammonium groups (Fig. 2). It should be noted that this structure was determined initially by Stomberg et al. (1977) with isolated Ti(O₂)F₅³⁻ in the PB form, and the peroxide group was placed in the equatorial plane of PB. Then Massa & Pausewang (1978) presented a polyhedron as an octahedron with a peroxide `dumbbell' in the axial position. It can also be represented as a distorted (bevelled) monocapped trigonal prism with an O—O edge.

Figure 2 Disordered structure of (NH4)3Ti(O2)F5 (a) and the isolated polyhedron Ti(O2)F5^3− (b). Red, blue and white balls are the F, N and H atoms, respectively (the central Ti atoms are not seen). Displacement ellipsoid plots are shown at 50% probability.

At the first phase of structural determination it was difficult to isolate the local polyhedral symmetry. Direct methods identified uniquely only the M, N1 and N2 atoms in the 4a, 8c and 4b positions in accordance with the elpasolite structure. Their atomic coordinates were refined by the least-squares method (LS) with anisotropic approximation to R₁ = 0.0626 and 0.1445 for (I) and (II), respectively. From electron-density syntheses calculated for these atoms, only the F atoms in the (x,0,0) position are localized, which corresponds to the MF₆ octahedron that contradicts the chemical composition of the compound. Therefore, electron-density sections in the range of the F1 atom have been constructed (Figs. 3a and c), which show that two independent additional F (O) atoms surround the Hf and Ti atoms in the 96j position (Figs. 3b and d). The structural refinement with these atoms reduced R₁ to 0.0104 and 0.0281 for (I) and (II), respectively. Three independent F atoms (F1, F2 and F3) in (I) form 12 spatial orientations of HfF₇ in the PB form (Fig. 1b). Two F atoms (F1 and F2) and one O1 in (II) form 24 orientations of Ti(O₂)F₅ in the form of a distorted octahedron (Fig. 2b) with the (O₂)²⁻ group in the axial vertex.

Figure 3 (a) Electron-density distribution of F1 in (NH4)3HfF7 on the (001) plane at z = 0.20. (b) Arrangement of F1, F2 and F3 atoms on the 24e and 96j positions. (c) Electron-density distribution of F2 in (NH4)3Ti(O2)F5 on the (001) plane at z = 0.20. (d) Arrangement of F1, F2 and O atoms on the 24e and 96j positions.

Determined at this stage, our structure of (NH₄)₃Ti(O₂)F₅ was similar to those of K₃Ti(O₂)F₅ (Schmidt & Pausewang, 1986) and (NH₄)₃Ti(O₂)F₅ (Schmidt et al., 1986) with a `split-atom' model. Interestingly, K1 and K2 in the K₃Ti(O₂)F₅ structure were located in the 24e and 32f positions, respectively. However, in all cases two significantly short distances O—F2 = 2.17–2.18 Å were present (Fig. 2b). In addition, electron-density synthesis for F1 indicates the 24e position, while Schmidt et al. (1986) give the 96k position. The results of structural determination in both cases were very similar, but during several cycles of structural refinement with F1 in the (x,x,z) position the value of x decreased and converged to zero. This is probably owing to the relatively low population of the F1 position and its close surroundings by F2 atoms (F1–F2: 4 × 0.41 Å, Fig. 3d). To find the true F1 position, its difference electron-density profiles were built for (I) and (II) for comparison (Fig. 4; F1 was not specified).

Figure 4 (a) Electron-density distribution of the F1 atom in the (001) plane at z = 0.20 of (NH4)3HfF7. (b) Electron-density distribution of the F1 atom in the (001) plane at z = 0.20 of (NH4)3Ti(O2)F5.

The sections show that in the (NH₄)₃HfF₇ structure F1 occupies the 24e position, while in the (NH₄)₃Ti(O₂)F₅ structure it is placed in the 96k one, but the problem of short O—F distances was not solved. The next step of the structural revision of (NH₄)₃Ti(O₂)F₅ was the change of F1 and F2 populations, wherein two F2 atoms (instead of four) and two F1 atoms were placed in the equatorial octahedral plane. In this case, the structure refinement was successful to R₁ = 0.0268 with equalized distances O—F2 = 2.362 and F2—F1 = 2.386 Å instead of 2.183 and 2.623 Å, respectively, and the F1 coordinates remained in the 96k position.

In accordance with our previous work (Udovenko & Laptash, 2011), where the tetrahedral displacement of N1 from the 8c position was found, electron-density sections of N1 for (I) and (II) were constructed. Only the sections for (I) are given (Fig. 5), which are very similar to those for (II). The sections show that N1 is displaced from the 8c position. The structure refinement confirmed the escape of N1 from the initial position on 0.14 and 0.15 Å for (I) and (II), respectively. R₁ changed insignificantly (0.0102 and 0.0256, respectively). The coordinates of H atoms in N1H₄ were calculated geometrically.

Figure 5 Electron-density distribution of N1 in (NH4)3HfF7 on the (001) plane at z = 0.20 (a) and z = 0.30 (b). Disorder of tetrahedrally displaced N1H4 from the 8c position (c).

Next, the real location of N2H₄ was found. Two possible models were considered.

Model A: Atom N2 is cubically shifted from the 4b position into the 32f site, and the H2 atoms occupy the 24e position. Taking into account the additional H3 atom in the 32f position, the N2H₄ group forms eight spatial orientations in the structure as was described for the case of (NH₄)₃MoO₃F₃ (Udovenko & Laptash, 2008a).

Model B: The N2 atom does not leave the 4b position and the H2 atoms are shifted from the 24e position into the 96k one. Taking into account the additional H3 atom in the 32f position, the N2H₄ group also forms eight spatial orientations.

These two models were not previously supported experimentally. The problem has been solved in the present work owing to the good quality of single crystals and a large set of experimental data. Electron-density sections of N2 for (I) and (II) in the (001) plane with z = 0.518 and z = 0.593 were constructed. The z coordinate of N2 and H2 was taken from the (NH₄)₃MoO₃F₃ structure (Udovenko & Laptash, 2008a) and from the (NH₄)₃AlF₆ structure (Udovenko & Laptash, 2011), the H atoms were not specified (Fig. 6). The sections for (I) and (II) are similar.

Figure 6 Electron-density distribution of the N2 atom in (NH4)3Ti(O2)F5 on the (001) plane at z = 0.518 (a) and z = 0.593 (b). Statistically disordered arrangement of H2 and H3 atoms in N2H4 (c).

It is seen from Fig. 6 that the outer electron cloud of the N2 atom is deformed by the octahedron, while its internal cloud is spherical which is inconsistent with the N2 escape on the cube from the 4b position. The structural refinement with the displaced atom returns it into the initial position and the N2 atom therefore occupies the 4b position.

It follows from Figs. 6(a) and (b) that the H2 atoms are statistically distributed in the 96k position, and every vertex of the N2Q₆ octahedron is surrounded by four H2 atoms with a side of the square equal to 0.35 Å. A superposition of electron densities from four H2 atoms in squares forms an octahedral surrounding of the N2 atom by the Q electron-density peaks (Fig. 6c). The final refinement of the structure in the space group including H atoms reduced the R₁ value to 0.0090 and 0.0140 for (I) and (II), respectively.

Finally, the structural refinements of (I) and (II) were performed in other possible space groups. The results of the refinement of (I) in , and F432 were identical, while in F23 they became worse [F_eq—F_eq = 2.58 and 2.27 instead of 2.38 and 2.47 (1) Å; U¹¹ = 0.26 instead of 0.11 (1) Ų]. The refinement of (II) in F432 and F23 resulted in strong distortion of the Ti(O₂)F₅ polyhedron. The refinement in gave the O—F distance 2.20 (1) instead of 2.36 (1) Å for at the same R₁ = 0.0140. Thus, the space group for (I) and (II) is .

(NH₄)₃HfF₇ is isostructural with (NH₄)₃ZrF₇ and (NH₄)₃NbOF₆, the crystal structures of which were described by us previously in the space group F23 (Udovenko &Laptash, 2008b), which allowed us to eliminate abnormally short F—F distances (2.16 Å) in the equatorial plane of PB determined by Hurst & Taylor (1970) for (NH₄)₃ZrF₇ in . Now we repeated the refinement of these structures in both F23 and space groups. The geometrical parameters of the polyhedron NbOF₆ in these two groups are the same within experimental error [F_eq—F_eq 2.36 (1) and 2.37 (1); 2.41 (1) and 2.41 (1); 2.31 (1) and 2.32 (1) Å for F23 and , in pairs, respectively], whereas the parameters of ZrF₇ are appreciably different [F_eq—F_eq = 2.47 (1), 2.50 (1) and 2.36 (1) Å in F23 and F_eq—F_eq = 2.61 (1), 2.67 (1) and 2.26 (1) Å in ]. The latter geometry is less preferable than the former one due to the shorter F—F contact (2.26 relative to 2.36 Å). Nevertheless, both cubic space groups ( and F23) are characteristic of the crystal structure of (NH₄)₃ZrF₇. The heat capacity (studied by differential scanning microcalorimetry and adiabatic calorimetry), thermal dilation and permittivity investigations revealed the existence of transitions between these two cubic phases (Fokina et al., 2013) near room temperature (290 K). Group theory analysis of PTs has shown that both cubic phases can be transformed into an ortho­rhombic one (Immm) found by polarizing optical studies at T₁ = 280 K (Misyul et al., 2008). The crystal structure determination of the latter was unsuccessful because of its complicated twinning structure. The same concerns (NH₄)₃HfF₇ as our preliminary calorimetric measurements show, different to those for (NH₄)₃NbOF₆ (Fokina et al., 2007). The refinement of (NH₄)₃HfF₇ in F23 increased the R₁ from 0.0090 to 0.0110, and the F—F equatorial distances were less acceptable [F—F 2.274 (8), 2.419 (6), 2.565 (1) Å instead of 2.374 (6), 2.425 (10), 2.484 (8) Å], and the Uⁱⁱ (U¹¹, U²², U³³) parameters of F atoms increased significantly (0.20–0.26 instead of 0.06–0.11 Ų). Therefore, the symmetry of (NH₄)₃HfF₇ is really , which is the parent phase for both (NH₄)₃ZrF₇ and (NH₄)₃HfF₇ compounds.

We also revised the crystal structures of ammonium fluoro­elpasolites (NH₄)₃ZrF₇, (NH₄)₃NbOF₆, (NH₄)₃MoO₃F₃, (NH₄)₃WO₃F₃ and (NH₄)₃AlF₆ with respect to the escape of N1 and N2 from the special 8c and 4b positions. It is shown that the N1 atom is displaced from the 8c position into the 32f site and tetrahedrally disordered, while the N2 atom remains in the 4b position. The H atoms of N2H₄ statistically occupy the 64k and 32f positions and form eight spatial orientations in the structure.

X-ray crystallographic files in CIF format for the structure determinations of (NH₄)₃ZrF₇, (NH₄)₃NbOF₆, (NH₄)₃MoO₃F₃, (NH₄)₃WO₃F₃ are in the supporting information and can also be obtained from Fachinformationszentrum Karlsruhe, 76344 Eggenstein-Leopoldshafen, Germany [fax: [phone]; e-mail: [e-mail]; https://www2.fiz-karlsruhe.de/icsd_home.html] on quoting the deposition numbers: CSD-431917; CSD-431918; CSD-431919 and CSD-431920, respectively.

3.2. On the (NH₄)₃HfOF₅ elpasolite

Recently the synthesis and crystal structure of ammonium hafnium oxofluoroelpasolite (NH₄)₃HfOF₅ was described (Underwood et al., 2013). The compound was prepared hydrothermally from HfF₄ and an aqueous solution of NH₄F at 673–848 K over 3–5 d. Interestingly, (NH₄)₃HfOF₅ has been observed regardless of the reaction conditions. The crystal structure of this compound was solved classically with ammonium ions being fully ordered at 4b and 8c sites. The F atom was present at the 24e site. When the substitutional model (5/6 F and 1/6 O at the 24e site) was used, the R₁ value was 0.0259. The authors attempted to disorder the F and O atoms between the 24e site and a 96j site in accordance with our mixed ligand position, but their refinements were unsuccessful. The authors also provide the IR spectrum of (NH₄)₃HfOF₅ (Fig. S3 in their paper), which is identical to that of our (NH₄)₃HfF₇ recorded from the sample pressed into pellets with KBr or in the Nujol mull. Fig. 7 shows the IR spectrum of a pure single crystal of (NH₄)₃HfF₇ together with its Raman spectrum. It should be noted that the vibrational spectra of (NH₄)₃HfF₇ and (NH₄)₃ZrF₇ (Krylov et al., 2012) are very similar. Spectral lines and their positions agree better with D_5h symmetry for an isolated Hf(Zr)F₇³⁻ ion, in spite of this symmetry group not being a subgroup of the O_h factor group of the crystal. The optimization of geometric parameters of ZrF₇³⁻ (Voit et al., 2015) resulted in a distorted PB configuration with the C₁ (C_s) symmetry, where the F atoms were displaced from the equatorial plane with one of them shifted most strongly. The axial F atoms are also shifted from the axial position that is consistent with a large amplitude vibration of the F1 atoms in our HfF₇³⁻ (Fig. 1b). This means the non-rigidity of the anion (the F1 atom tends to leave the equatorial plane). Thus, the Raman band at 563 cm⁻¹ (Fig. 7) is assigned to a fully symmetric stretch (ν_s) of the HfF₇ PB (D_5h symmetry). Two IR bands at 403 and 466 cm⁻¹ are assigned to the asymmetric stretch of Hf–axial fluorines (νHfF1_ax–νHfF2_ax) and to asymmetric doubly degenerate Hf–equatorial fluorines [ν_as(HfF_2eq–νHfF_eq)], respectively, in accordance with DFT calculations. Minor bands at 730 and 1080 cm⁻¹ are connected with the presence of the hydroxide ion (OH⁻). The first one is a transversal vibration of the proton in the triple system O—H⋯F with a strong hydrogen bond (HB), the second one is the bending vibration of nonbonding OH⁻ (δHfO–H). Above 1400 cm⁻¹, bending, combinational and stretching vibrations of NH₄ groups lie, typical to ammonium elpasolites (Epple et al., 1982). Energy-dispersive X-ray (EDX) analysis corroborates the presence of OH⁻ at the level of 2–4 at. % (Fig. 8), which corresponds to the composition (NH₄)₃Hf(OH)_xF_7 − x (x = 0.3). It is difficult to obtain fluorometallate without the partial substitution of OH⁻ for F⁻.

Figure 7 Vibrational spectra of (NH4)3HfF7 at room temperature: IR – top image, Raman – lower figure.

Figure 8 EDX spectrum of (NH4)3Hf(OH)0.3F6.7.

If the compound composition corresponds to the formula (NH₄)₃HfOF₅, its vibrational spectra should contain the intensive band (both IR and Raman active) in the range 900 cm⁻¹, in accordance with the triple character (one σ + two π) of the Hf—O bond and a short distance of this bond (Gong et al., 2012). Similarly, the Ti—O bond has a triple character (σ + 2π) that ensures a rather short Ti—O distance in accordance with our structural determinations, and the Ti—O stretches appear at 870 and 897 cm⁻¹ for (NH₄)₃TiOF₅ and Rb₂KTiOF₅, respectively (Udovenko & Laptash, 2011). Thus, the absence of a similar band in the IR spectrum of ammonium hafnium fluoroelpasolite presented by Underwood et al. (2013) means that the authors deal with the other compound. According to their elemental analysis (EDX) indicating the presence of oxygen at 6.5−9.1 at. % and fluorine at 51.0−53.6 at %, one can suppose that the real composition of the compound is close to (NH₄)₃Hf(OH)F₆. Our attempts to obtain (NH₄)₃HfOF₅ from solution (by ammonia hydrolysis) were unsuccessful. It seems that is almost impossible. Only zirconium oxofluoroelpasolite with alkali cations A₂BZrOF₅ are known but they were obtained by solid-state reaction: 2AF + BF + ZrOF₂ = A₂BZrOF₅ (A = Cs, Rb, Tl, K; B = Cs, Rb, Tl, K, Na and Li; Verdine et al., 1972). Some of the structures were solved in the classical way.

However, if the compound composition is (NH₄)₃HfOF₅, it would be reasonable to displace a central atom (Hf) from the center of an octahedron towards the O atom to determine the true geometry of the polyhedron. It is possible when the existing disorder has a dynamic nature (Laptash & Udovenko, 2016).

4. Conclusions

Single crystals of (NH₄)₃HfF₇ and (NH₄)₃Ti(O₂)F₅ of high quality were obtained that enabled a large set of experimental data to be collected and the ligand refined with cationic positions in the cubic (Z = 4) structure with respect to the classic version of the elpasolite structure. All our previously investigated crystal structures of ammonium fluoro- or oxofluoroelpasolites characterized by dynamic orientational disorder were revised in accordance with new features of the fluoroelpasolite structure. The electron-density profiles of all the constituent atoms in the compounds investigated show that the ligand atoms are distributed in a mixed (split) position instead of 24e. One of the ammonium groups is disordered near 8c so that its central atom (N1) forms a tetrahedron with vertexes in 32f, but a center of another group (N2) remains in 4b, whereas its H atoms (H2) occupy the 96k position instead of 24e, and together with the H3 atom in the 32f position they form eight spatial orientations of the ammonium group. On cooling these compounds undergo PTs of an order–disorder type with a rather large value of entropy changes. These values are rather different [from Rln3 for (NH₄)₃Ti(O₂)F₅ to Rln136 for (NH₄)₃NbOF₆], but they should be taken into account during the structure refinement to clarify the mechanism of PTs. Easy transformation between two cubic phases ( and F23) near the room temperature in the case of (NH₄)₃ZrF₇ and (NH₄)₃HfF₇ is very interesting and deserves further special consideration.

Supporting information

Computing details

For both compounds, data collection: Bruker APEX2; cell refinement: Bruker SAINT; data reduction: Bruker SAINT; program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL2014/7 (Sheldrick, 2014); molecular graphics: Bruker SHELXTL; software used to prepare material for publication: Bruker SHELXTL.

(I) ammonium heptafluorohafnate

Crystal data

(H12N3HfF7)	Mo Kα radiation, λ = 0.71073 Å
Mr = 365.62	Cell parameters from 6673 reflections
Cubic, Fm3m	θ = 3.8–46.1°
a = 9.3964 (1) Å	µ = 12.65 mm^−1
V = 829.63 (3) Å^3	T = 296 K
Z = 4	Octahedron, colourless
F(000) = 672	0.25 × 0.23 × 0.22 mm
Dx = 2.927 Mg m^−3

Data collection

Bruker APEX-II CCD diffractometer	293 reflections with I > 2σ(I)
Detector resolution: 8.33 pixels mm^-1	Rint = 0.019
ω scans	θmax = 52.5°, θmin = 3.8°
Absorption correction: multi-scan Bruker SADABS	h = −20→19
Tmin = 0.593, Tmax = 0.750	k = −20→19
8194 measured reflections	l = −20→20
293 independent reflections

Refinement

Refinement on F^2	Secondary atom site location: difference Fourier map
Least-squares matrix: full	Hydrogen site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.009	H-atom parameters not refined
wR(F^2) = 0.019	w = 1/[σ^2(Fo^2) + (0.0032P)^2 + 0.6486P] where P = (Fo^2 + 2Fc^2)/3
S = 1.19	(Δ/σ)max = 0.005
293 reflections	Δρmax = 1.14 e Å^−3
22 parameters	Δρmin = −0.67 e Å^−3
0 restraints	Extinction correction: SHELXL-2014/7 (Sheldrick 2014, Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
Primary atom site location: structure-invariant direct methods	Extinction coefficient: 0.01226 (12)

Special details

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
Hf	0.0000	0.0000	0.0000	0.02423 (2)
N1	0.2588 (4)	0.2588 (4)	0.2588 (4)	0.0436 (7)	0.25
N2	0.5000	0.5000	0.5000	0.0558 (9)
F1	0.0000	0.0000	0.2089 (2)	0.0765 (9)	0.5
F2	0.0000	0.0637 (6)	0.2067 (6)	0.0520 (15)	0.0833
F3	0.0000	0.1290 (6)	0.1891 (6)	0.0484 (12)	0.0833
H11	0.2038	0.2038	0.2038	0.086*	0.25
H12	0.2038	0.3128	0.3128	0.086*	0.0833
H13	0.3128	0.3128	0.2038	0.086*	0.0833
H14	0.3128	0.2038	0.3128	0.086*	0.0833
H2	0.5930	0.4814	0.4814	0.065*	0.125
H3	0.4445	0.4445	0.4445	0.065*	0.125

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Hf	0.02423 (2)	0.02423 (2)	0.02423 (2)	0.000	0.000	0.000
N1	0.0436 (7)	0.0436 (7)	0.0436 (7)	0.0005 (12)	0.0005 (12)	0.0005 (12)
N2	0.0558 (9)	0.0558 (9)	0.0558 (9)	0.000	0.000	0.000
F1	0.1063 (14)	0.1063 (14)	0.0170 (6)	0.000	0.000	0.000
F2	0.062 (3)	0.065 (3)	0.0293 (18)	0.000	0.000	−0.0139 (19)
F3	0.041 (2)	0.059 (3)	0.044 (2)	0.000	0.000	−0.0276 (17)

Geometric parameters (Å, º)

Hf—F1	1.963 (2)	F1—F2^ii	2.826 (4)
Hf—F1^i	1.963 (2)	F1—F3^xi	2.912 (4)
Hf—F1^ii	1.963 (2)	F1—F3^ix	2.912 (4)
Hf—F2	2.032 (5)	F1—F3^x	2.912 (4)
Hf—F2^iii	2.032 (5)	F1—F3^ii	2.912 (4)
Hf—F3	2.151 (5)	N1—N1^xii	0.234 (10)
Hf—F3^iii	2.151 (5)	N1—F3^xiii	2.584 (4)
F1—F2^iv	2.374 (6)	N1—F3^xiv	2.620 (3)
F1—F2^v	2.374 (6)	N1—H11	0.8952
F2—F3^vi	2.484 (8)	N1—H12	0.8843
F3—F3^vii	2.425 (10)	N1—H13	0.8843
F1—F1^i	2.776 (3)	N1—H14	0.8843
F1—F1^viii	2.776 (3)	N2—F1^xv	2.735 (2)
F1—F2^ix	2.826 (4)	N2—F2^xvi	2.820 (6)
F1—F2^x	2.826 (4)	N2—H2	0.9081
F1—F2^xi	2.826 (4)	N2—H3	0.9033
F1—Hf—F1^i	90.0	F1^ii—Hf—F1^v	90.0
F1—Hf—F1^ii	90.0	F1^i—Hf—F1^xvii	90.0
F1^i—Hf—F1^ii	180.0	F1^ii—Hf—F1^xvii	90.0
F1—Hf—F1^viii	90.0	F1^ii—Hf—F2	72.88 (17)
F1^i—Hf—F1^viii	90.0	F1^i—Hf—F2^iii	72.88 (17)
F1^ii—Hf—F1^viii	90.0	F2^xviii—Hf—F3^xix	72.8 (2)
F1—Hf—F1^v	90.0	F2^vii—Hf—F3^iv	72.8 (2)
F1^i—Hf—F1^v	90.0	F3^iv—Hf—F3^xx	68.6 (3)

Symmetry codes: (i) −y, −z, −x; (ii) y, z, x; (iii) −z, −y, x; (iv) −x, z, y; (v) z, x, y; (vi) −x, −z, y; (vii) −x, −y, z; (viii) −z, −x, −y; (ix) z, −y, x; (x) z, y, −x; (xi) −y, z, −x; (xii) x, −y+1/2, −z+1/2; (xiii) z, −y+1/2, x+1/2; (xiv) y, x+1/2, −z+1/2; (xv) −y+1/2, −z+1, −x+1/2; (xvi) −z+1, y+1/2, −x+1/2; (xvii) −x, −y, −z; (xviii) x, y, −z; (xix) x, −z, −y; (xx) x, z, −y.

(II) pentafluorooxotitanium

Crystal data

(H12N3TiO2F5)	Mo Kα radiation, λ = 0.71073 Å
Mr = 229.03	Cell parameters from 7086 reflections
Cubic, Fm3m	θ = 3.8–37.6°
a = 9.2327 (1) Å	µ = 1.14 mm^−1
V = 787.02 (3) Å^3	T = 296 K
Z = 4	Octahedron, colourless
F(000) = 464	0.24 × 0.23 × 0.22 mm
Dx = 1.933 Mg m^−3

Data collection

Bruker APEX-II CCD diffractometer	190 reflections with I > 2σ(I)
Detector resolution: 8.33 pixels mm^-1	Rint = 0.020
w scans	θmax = 43.1°, θmin = 3.8°
Absorption correction: multi-scan Bruker SADABS	h = −17→17
Tmin = 0.695, Tmax = 0.749	k = −17→17
9680 measured reflections	l = −15→17
190 independent reflections

Refinement

Refinement on F^2	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.014	Hydrogen site location: difference Fourier map
wR(F^2) = 0.040	H-atom parameters not refined
S = 1.03	w = 1/[σ^2(Fo^2) + (0.0333P)^2 + 0.0481P] where P = (Fo^2 + 2Fc^2)/3
190 reflections	(Δ/σ)max = 0.050
24 parameters	Δρmax = 0.14 e Å^−3
0 restraints	Δρmin = −0.33 e Å^−3

Special details

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
Ti1	0.0000	0.0000	0.0000	0.02239 (3)
N1	0.2593 (2)	0.2593 (2)	0.2593 (2)	0.0439 (4)	0.25
N2	0.5000	0.5000	0.5000	0.0592 (6)
O1	0.1808 (4)	0.1142 (3)	0.0000	0.0660 (9)	0.0833
F1	0.20425 (11)	0.01404 (17)	0.01404 (17)	0.0462 (4)	0.125
F2	0.2000 (3)	0.0602 (3)	0.0000	0.0498 (8)	0.0833
H11	0.2049	0.2049	0.2049	0.098*	0.25
H12	0.2049	0.3149	0.3149	0.098*	0.0833
H13	0.3149	0.2049	0.3149	0.098*	0.0833
H14	0.3149	0.3149	0.2049	0.098*	0.0833
H2	0.5930	0.4814	0.4814	0.044*	0.125
H3	0.4445	0.4445	0.4445	0.098*	0.125

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ti1	0.02239 (3)	0.02239 (3)	0.02239 (3)	0.000	0.000	0.000
N1	0.0439 (4)	0.0439 (4)	0.0439 (4)	0.0058 (6)	0.0058 (6)	0.0058 (6)
N2	0.0592 (6)	0.0592 (6)	0.0592 (6)	0.000	0.000	0.000
O1	0.0615 (15)	0.096 (2)	0.0406 (14)	−0.0518 (12)	0.000	0.000
F1	0.0186 (3)	0.0600 (5)	0.0600 (5)	−0.0024 (4)	−0.0024 (4)	−0.007 (2)
F2	0.0268 (8)	0.0619 (17)	0.0608 (17)	−0.0129 (9)	0.000	0.000

Geometric parameters (Å, º)

Ti1—F1	1.8946 (10)	N2—F1^xiii	2.7367 (10)
Ti1—F1^i	1.8947 (10)	N2—F1^xiv	2.7367 (10)
N1—N1^ii	0.243 (6)	N2—F1^ii	2.7367 (10)
N1—N1^iii	0.243 (6)	N2—H2	0.8923
N1—N1^iv	0.243 (6)	N2—H3	0.8875
N1—O1^v	2.613 (3)	O1—O1^xv	1.491 (4)
N1—O1^vi	2.613 (3)	F2—O1^xvi	2.362 (5)
N1—O1^vii	2.613 (3)	F1—F2^xvi	2.386 (3)
N1—O1^viii	2.613 (3)	F1—F2^xvii	2.386 (3)
N1—O1^ix	2.613 (3)	F1—O1^xviii	2.707 (3)
N1—O1^x	2.613 (3)	F1—O1^xix	2.707 (3)
N1—O1^xi	2.6530 (19)	F1—F1^xx	2.6732 (15)
N1—H11	0.8701	F1—F1^xxi	2.6731 (15)
N1—H12	0.8828	F1—F1^xxii	2.484 (3)
N1—H13	0.8827	F1—F2^xxiii	2.816 (2)
N1—H14	0.8827	F1—F2^xxiv	2.816 (2)
N2—F1^xii	2.7367 (10)	F2—F2^xxv	2.611 (4)
F1—Ti1—F1^xxvi	81.90 (10)	F1—Ti1—F1^xx	89.732 (7)

Symmetry codes: (i) −y, −z, −x; (ii) x, −y+1/2, −z+1/2; (iii) −x+1/2, y, −z+1/2; (iv) −x+1/2, −y+1/2, z; (v) −z+1/2, −y+1/2, x; (vi) x, z+1/2, −y+1/2; (vii) −y+1/2, z+1/2, x; (viii) z+1/2, x, −y+1/2; (ix) x, −y+1/2, z+1/2; (x) −y+1/2, x, −z+1/2; (xi) z+1/2, y, −x+1/2; (xii) y+1/2, z+1/2, −x+1; (xiii) −y+1/2, −z+1/2, x; (xiv) −x+1, y+1/2, z+1/2; (xv) x, z, −y; (xvi) y, −x, z; (xvii) y, −z, −x; (xviii) −z, −y, x; (xix) z, x, −y; (xx) −y, z, x; (xxi) −z, x, y; (xxii) z, x, y; (xxiii) z, −y, −x; (xxiv) −z, −x, −y; (xxv) z, y, −x; (xxvi) y, z, x.