LiBaAlF₆ and the crystal chemistry of LiA^IIB^IIIF₆ phases

Lithium barium hexa­fluoro­aluminate (LBAF), LiBaAlF₆, is a new member of the large family of compounds of formula LiA^IIB^IIIF₆. These materials display a variety of structures depending on the sizes of the A and B cations. LiBaAlF₆, which is isomorphous with LiBaCoF₆, belongs to the monoclinic P2₁/c subset and has a three-dimensional network structure consisting of distorted LiF₄^3- tetra­hedra corner-sharing with AlF₆^3- octa­hedra and BaF₁₂ polyhedra. All of the atoms reside on general positions. An analysis of the ionic radii of the A cations versus formula volumes for the known members of the family yields a structure map that reasonably segregates the compounds by space group. The data obtained are thus suitable for predicting new isomorphic crystal structures.

S1. Comment

It is often possible to predict a new structure by analogy. The LiA^IIB^IIIF₆ family is one of the well studied sets of fluoride structures. The fluorides with cation pairs (A^IIB^III) PdAl (Bachmann & Mueller, 1993), YbAl (Koehler, 1999), CaAl (Bolotina et al., 1993), CaCr (Rupp et al., 1993), CdCo, CaNi, CaCo and SrNi (Fleischer & Hoppe, 1982) and SrAl (Schaffers & Keszler, 1991) crystallize in space group P3c. These crystals have layered structures in which face-sharing octahedra B^IIIF₆^3- and LiF₆^5- alternate with layers of divalent cations. Both the first and second coordination environments of A^II are octahedral. Distorted anionic 3⁶ grids are located in perpendicular planes (001) and (110). LiSmAlF₆ is characterized by the hexagonal space group P6₃22 (Koehler & Mueller, 1991). In contrast with those crystals with a P3c structure, the SmF₆^4- polyhedron is prismatic rather than octahedral.

A decrease in the radius of the divalent cation results in a change of symmetry to tetragonal P4₂/mnn in the case of LiMgCoF₆, LiNiCoF₆ and LiZnCoF₆ (Fleischer & Hoppe, 1982). All cations in these crystals have octahedral coordination environments, and the Li and Mg atoms are located in common sites. Increasing the radii of the di- and trivalent cations also causes changes in the space group. Fluorides with cation pairs A^IIB^III such as SrCo, SrFe and BaCo (Fleischer & Hoppe, 1982) and BaCr (Babel, 1974) are characterized by the monoclinic space group P2₁/c. Despite their identical space group and the closely similar atom positions in their unit cells, the structure of the strontium-containing fluorides differs from that of the barium fluorides. The coordination environment of Sr is a distorted square antiprism, while the Li atoms have an octahedral environment. In contrast, the Ba atoms are characterized by a coordination number of 12 and Li atoms have a coordination number of 4 in the barium fluorides. The tetrahedral Li-centred polyhedron is distorted due to the presence of one additional longer bond (ca. 2.65 Å) with an F atom of the second coordination sphere.

The previously unreported title compound, LiBaAlF₆, (I), belongs to the monoclinic P2₁/c subset of this family. The three-dimensional network structure, consisting of Li-centred distorted tetrahedra corner-sharing with Al-centred octahedra and Ba-centred polyhedra, is analogous to that of LiBaCoF₆ (Fig. 1). The large Ba polyhedron (distorted bicapped pentagonal prism) compresses the lithium coordination environment and transforms it from octahedral to tetrahedral. It might seem that the small volume of the Al polyhedra could provoke an increase of the Li coordination environment up to octahedral, but this is not the case.

The dependence of the formula volumes on the Shannon (1976) radii of divalent cations with coordination number 6 for the known LiA^IIB^IIIF₆ phases (Fig. 2a) shows a fairly good segregation of the different structures by space group. One can see a real possibility of structure prediction for some new crystals by analogy with known isomorphic structures. Nevertheless, there are some areas of overlap, making it difficult to predict the LiBaAlF₆ structure based on these data alone. Moreover, the structures of LiSrNiF₆ and LiSrCoF₆ differ despite the small differences in the Ni and Co radii.

It is possible to calculate the radii in these structures by a different method. All F—F distances in the coordination polyhedra were averaged and halved in order to estimate the anionic fluoride radius. Subtracting the anionic radius obtained in this manner from the mean cation–anion distance allows one to determine the cationic radius. There is good agreement between the Shannon ionic radii and the calculated values in the case of trivalent cation octahedra (Table 1). In the case of polyhedra with divalent cations, the situation is different. The anionic radii of fluoride found via the F—F distances are larger than the tabulated values, making the cationic radii smaller than the tabulated ones. This indicates that the divalent cations pull the fluoride anions together more weakly than do the trivalent cations. According to the Shannon data, the Ni^III ionic radius is larger than those of Co^III and Fe^III, which does not correlate with their relative positions in the periodic table. The increase of di- and trivalent cation radii in LiA^IIB^IIIF₆ crystals is accompanied by a gradual increase in the crystal [unit-cell?] volume and causes a symmetry change. Trigonal symmetry is the most prevalent for the fluorides considered here. In compounds with a small B^III radius and a rather large A^II radius, a reorganization from a trigonal structure into a hexagonal one (LiSmAlF₆) may take place. A small increase in the trivalent cation radius when passing from LiSrNiF₆ to LiSrCoF₆ causes a significant lowering of symmetry down to monoclinic. This may mean that the gradual increase in the size of the trivalent cation octahedron leads to compression of the strained divalent cation polyhedron. When the difference between the tabulated radius of Sr^II and the calculated radius reaches a maximum (0.48 Å), as in the case of LiSrNiF₆, the structure becomes reorganized back to trigonal. The increase of the A^II radius in the monoclinic structures (LiSrCoF₆ → LiBaCoF₆) causes a reorganization of the structures of the Li, Sr and Ba coordination polyhedra without a change of space group. The analogous structure map with our calculated A^II radii plotted against formula volume is shown in Fig. 2(b). For a small cationic radius the volume increases sharply with increasing radius. Once the cationic radius becomes similar to the anionic one, realignment of the unit cell occurs without a significant volume change. This map also provides good segregation of space groups.

In conclusion, the structure determination of LiBaAlF₆ completes a data set for the construction of correlations between ionic radii, unit-cell parameters and space groups for crystals in the LiA^IIB^IIIF₆ family, making it possible to predict reliably in many cases the structure type of new isomorphic crystals of similar compounds.

S2. Experimental

Lithium barium hexafluoroaluminate, LiBaAlF₆ (LBAF), was grown from the melt by the Bridgman method in quartz crucibles. Double fluorides of 99.99% purity were used as starting reagents. LiBaAlF₆ melts congruently at 1113–1133 K. The partial AlF₃ pressure was determined to be ~1 bar at this temperature (1 bar = 100 000 Pa). Because of the high volatility of this component, an excess ~2 wt.% of AlF₃ was added to the original composition. Crystal growth was carried out in a graphite container placed inside the silica ampoule. All operations were carried out in a dry box to avoid oxygen-containing impurities. To suppress decomposition, CF₄ was added to the reactor. The experiments were carried at a surplus pressure [Please state]. The axial temperature gradient was 10–20 K cm^-1 and the ampoule pulling rate varied from 0.5 to 5 mm d^-1. The crystal composition was analyzed using an EDS microprobe to 0.5% coincidence in composition.

S3. Refinement

Analysis of the X-ray data using the XPREP program (Bruker, 2004) indicated three possible space groups, P2₁/c, Pc and P2₁. The structure was refined in P2₁/c to a final wR₂ = 0.0352, R₁ = 0.0141 for 1607 reflections (1638 unique; R_int = 0.0173), 83 parameters. The corresponding data for the Pc group are: 2319 unique reflections, R_int = 0.0156, wR₂ = 0.0335, R₁ = 0.0128 for 2260 reflections, 164 parameters; the Flack (1983) parameter was 0.22 (3). There is a problem in the latter case with the anisotropic refinement of atom Li1. The TWIN, BASF and ISOR instructions (SHELXTL; Sheldrick, 2008) for Li1 resulted in wR₂ = 0.0319, R₁ = 0.0124, 165 parameters, twinning 0.52:0.48. The R₁ value for the P2₁ space group is larger than either of the other cases. Therefore, the crystal structure corresponds to either the centrosymmetric P2₁/c group or noncentrosymmetric Pc group. By analogy with the case of LiBaCoF₆, we chose the P2₁/c space group.

Computing details

Data collection: APEX2 (Bruker, 2004); cell refinement: SAINT (Bruker, 2004); data reduction: SAINT (Bruker, 2004); program(s) used to solve structure: SHELXTL (Version 6.12; Sheldrick, 2008); program(s) used to refine structure: SHELXTL (Version 6.12; Sheldrick, 2008); molecular graphics: BS (Ozawa & Kang, 2004); software used to prepare material for publication: SHELXTL (Version 6.12; Sheldrick, 2008).

Figures

Fig. 1. A polyhedral cell representation of the title compound along c. AlF6 polyhedra are light-coloured, LiF4 polyhedra are dark-coloured and Ba cations are shown as circles. The fifth Li—F contacts are shown as thick lines.

Fig. 2. (a) A structure map showing the dependence of the formula volumes V/Z on the Shannon (1976) radii of A^II cations of coordination number 6, and the distribution of the space groups of known LiA^IIB^IIIF6 structures. (b) A structure map showing the dependence of the formula volumes V/Z on the calculated radii of A^II cations of varied coordination number (as shown in Table 1), and the distribution of the space groups.

Lithium barium hexafluoridoaluminate

Crystal data

LiBaAlF6	F(000) = 504
Mr = 285.26	Dx = 4.098 Mg m^−3
Monoclinic, P21/c	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2ybc	Cell parameters from 4185 reflections
a = 5.3372 (10) Å	θ = 2.4–32.6°
b = 10.150 (2) Å	µ = 8.82 mm^−1
c = 8.535 (2) Å	T = 296 K
β = 90.34 (3)°	Prism, colourless
V = 462.35 (17) Å^3	0.22 × 0.18 × 0.18 mm
Z = 4

Data collection

Bruker Nonius X8-APEX CCD area-detector diffractometer	1638 independent reflections
Radiation source: fine-focus sealed tube	1607 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.017
Detector resolution: 25 pixels mm^-1	θmax = 32.6°, θmin = 3.1°
ϕ scans	h = −7→4
Absorption correction: multi-scan (SADABS; Bruker, 2004)	k = −15→15
Tmin = 0.159, Tmax = 0.210	l = −12→12
4624 measured 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	w = 1/[σ^2(Fo^2) + (0.0163P)^2 + 0.1651P] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.035	(Δ/σ)max = 0.001
S = 1.17	Δρmax = 1.48 e Å^−3
1638 reflections	Δρmin = −0.90 e Å^−3
83 parameters	Extinction correction: SHELXTL (Sheldrick, 2008), Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
0 restraints	Extinction coefficient: 0.0271 (8)

Special details

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

Refinement. Refinement of F² against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F², conventional R-factors R are based on F, with F set to zero for negative F². The threshold expression of F² > σ(F²) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F² are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

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

	x	y	z	Uiso*/Ueq
Al1	0.76102 (9)	0.08866 (4)	0.23055 (5)	0.00874 (9)
F1	0.61125 (19)	0.24917 (9)	0.25861 (11)	0.01352 (18)
F2	0.6713 (2)	0.10245 (11)	0.03123 (12)	0.0192 (2)
F3	0.89025 (19)	−0.07589 (10)	0.20663 (13)	0.0180 (2)
F4	0.8278 (2)	0.08905 (11)	0.43998 (12)	0.01721 (19)
F5	1.0623 (2)	0.15799 (12)	0.19808 (14)	0.0207 (2)
F6	0.47012 (17)	0.00991 (10)	0.28925 (12)	0.01348 (18)
Li1	0.7606 (6)	0.4150 (3)	0.3261 (4)	0.0161 (6)
Ba1	0.297669 (16)	0.312656 (9)	0.004198 (10)	0.01139 (5)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Al1	0.00820 (19)	0.00833 (19)	0.00971 (19)	0.00031 (15)	0.00053 (15)	0.00109 (15)
F1	0.0162 (4)	0.0093 (4)	0.0151 (4)	0.0019 (3)	0.0000 (3)	−0.0005 (3)
F2	0.0258 (5)	0.0219 (5)	0.0098 (4)	0.0025 (4)	−0.0009 (4)	−0.0007 (4)
F3	0.0149 (4)	0.0135 (5)	0.0256 (5)	0.0042 (4)	0.0050 (4)	0.0016 (4)
F4	0.0176 (5)	0.0211 (5)	0.0129 (4)	−0.0021 (4)	−0.0041 (3)	0.0026 (4)
F5	0.0123 (5)	0.0241 (5)	0.0258 (5)	−0.0052 (4)	0.0022 (4)	0.0074 (4)
F6	0.0103 (4)	0.0125 (4)	0.0176 (4)	−0.0031 (3)	0.0023 (3)	−0.0026 (3)
Li1	0.0144 (13)	0.0195 (15)	0.0143 (13)	0.0021 (11)	−0.0002 (10)	0.0036 (10)
Ba1	0.01137 (7)	0.01273 (6)	0.01006 (6)	0.00040 (3)	0.00115 (4)	0.00215 (3)

Geometric parameters (Å, º)

Al1—F1	1.8311 (11)	F2—Li1^vii	1.826 (3)
Al1—F2	1.7702 (12)	Li1—F1	1.948 (3)
Al1—F3	1.8189 (11)	Li1—F2^ii	1.826 (3)
Al1—F4	1.8206 (12)	Li1—F3^viii	1.888 (3)
Al1—F5	1.7787 (12)	Li1—F6^ix	1.843 (3)
Al1—F6	1.8192 (11)	Li1—F5^viii	2.649 (3)
Al1—Li1^i	3.142 (3)	Li1—Al1^viii	3.142 (3)
Al1—Ba1^ii	3.5556 (11)	Li1—Ba1^ii	3.715 (3)
Al1—Ba1^iii	3.6166 (7)	Li1—Ba1^x	3.959 (3)
Al1—Ba1^iv	3.8187 (12)	Li1—Ba1^iv	3.977 (3)
Al1—Ba1	3.8679 (9)	Li1—Ba1^v	4.115 (3)
F5—Ba1^v	2.6086 (12)	Ba1—F1^vii	2.7623 (13)
F5—Li1^i	2.649 (3)	Ba1—F1	2.8086 (13)
F5—Ba1^iv	2.9075 (15)	Ba1—F2	2.9285 (12)
F4—Ba1^iv	2.7512 (12)	Ba1—F3^ix	2.8994 (13)
F4—Ba1^iii	2.9239 (12)	Ba1—F3^vi	3.1619 (12)
F4—Ba1^ii	3.0527 (12)	Ba1—F4^xi	2.7512 (12)
F1—Ba1^ii	2.7623 (13)	Ba1—F4^ix	2.9239 (12)
F3—Li1^i	1.888 (3)	Ba1—F4^vii	3.0527 (12)
F3—Ba1^iii	2.8994 (13)	Ba1—F5^xii	2.6086 (12)
F3—Ba1^vi	3.1619 (12)	Ba1—F5^xi	2.9075 (15)
F6—Li1^iii	1.843 (3)	Ba1—F6^vii	2.7342 (11)
F6—Ba1^ii	2.7342 (11)	Ba1—F6^ix	2.9371 (12)
F6—Ba1^iii	2.9371 (12)
F2—Al1—F5	93.36 (6)	F4^xi—Ba1—F5^xi	52.80 (4)
F2—Al1—F3	93.75 (6)	F1^vii—Ba1—F5^xi	66.54 (3)
F5—Al1—F3	90.11 (6)	F1—Ba1—F5^xi	166.05 (3)
F2—Al1—F6	94.18 (6)	F3^ix—Ba1—F5^xi	125.11 (3)
F5—Al1—F6	172.16 (6)	F5^xii—Ba1—F4^ix	111.25 (4)
F3—Al1—F6	87.27 (5)	F6^vii—Ba1—F4^ix	63.62 (3)
F2—Al1—F4	173.55 (6)	F4^xi—Ba1—F4^ix	58.34 (4)
F5—Al1—F4	88.87 (6)	F1^vii—Ba1—F4^ix	118.81 (3)
F3—Al1—F4	92.30 (5)	F1—Ba1—F4^ix	103.31 (3)
F6—Al1—F4	83.85 (6)	F3^ix—Ba1—F4^ix	53.58 (3)
F2—Al1—F1	86.53 (5)	F5^xi—Ba1—F4^ix	87.13 (3)
F5—Al1—F1	93.68 (6)	F5^xii—Ba1—F2	80.90 (4)
F3—Al1—F1	176.18 (6)	F6^vii—Ba1—F2	107.51 (3)
F6—Al1—F1	88.91 (5)	F4^xi—Ba1—F2	154.07 (3)
F4—Al1—F1	87.29 (5)	F1^vii—Ba1—F2	58.60 (3)
F2—Al1—Li1^i	96.43 (7)	F1—Ba1—F2	50.92 (3)
F5—Al1—Li1^i	57.43 (7)	F3^ix—Ba1—F2	117.13 (3)
F3—Al1—Li1^i	32.73 (7)	F5^xi—Ba1—F2	115.83 (3)
F6—Al1—Li1^i	119.44 (7)	F4^ix—Ba1—F2	147.42 (3)
F4—Al1—Li1^i	89.87 (7)	F5^xii—Ba1—F6^ix	103.45 (4)
F1—Al1—Li1^i	151.03 (7)	F6^vii—Ba1—F6^ix	79.12 (4)
F2—Al1—Ba1^ii	115.07 (5)	F4^xi—Ba1—F6^ix	104.67 (3)
F5—Al1—Ba1^ii	128.60 (5)	F1^vii—Ba1—F6^ix	110.79 (3)
F3—Al1—Ba1^ii	126.73 (4)	F1—Ba1—F6^ix	56.29 (3)
F6—Al1—Ba1^ii	49.07 (4)	F3^ix—Ba1—F6^ix	50.95 (3)
F4—Al1—Ba1^ii	59.15 (4)	F5^xi—Ba1—F6^ix	130.39 (3)
F1—Al1—Ba1^ii	50.03 (3)	F4^ix—Ba1—F6^ix	49.03 (3)
Li1^i—Al1—Ba1^ii	145.89 (6)	F2—Ba1—F6^ix	99.48 (3)
F2—Al1—Ba1^iii	129.71 (4)	F5^xii—Ba1—F4^vii	139.54 (4)
F5—Al1—Ba1^iii	119.06 (5)	F6^vii—Ba1—F4^vii	49.33 (3)
F3—Al1—Ba1^iii	52.65 (4)	F4^xi—Ba1—F4^vii	133.67 (4)
F6—Al1—Ba1^iii	53.85 (4)	F1^vii—Ba1—F4^vii	51.07 (3)
F4—Al1—Ba1^iii	53.44 (4)	F1—Ba1—F4^vii	70.44 (3)
F1—Al1—Ba1^iii	124.60 (4)	F3^ix—Ba1—F4^vii	110.55 (4)
Li1^i—Al1—Ba1^iii	74.65 (6)	F5^xi—Ba1—F4^vii	101.60 (4)
Ba1^ii—Al1—Ba1^iii	75.160 (18)	F4^ix—Ba1—F4^vii	85.93 (3)
F2—Al1—Ba1^iv	139.88 (5)	F2—Ba1—F4^vii	67.72 (3)
F5—Al1—Ba1^iv	46.84 (4)	F6^ix—Ba1—F4^vii	59.78 (3)
F3—Al1—Ba1^iv	91.49 (4)	F5^xii—Ba1—F3^vi	75.60 (4)
F6—Al1—Ba1^iv	125.81 (4)	F6^vii—Ba1—F3^vi	103.04 (3)
F4—Al1—Ba1^iv	42.03 (4)	F4^xi—Ba1—F3^vi	82.91 (3)
F1—Al1—Ba1^iv	90.75 (4)	F1^vii—Ba1—F3^vi	65.61 (3)
Li1^i—Al1—Ba1^iv	68.53 (6)	F1—Ba1—F3^vi	116.82 (3)
Ba1^ii—Al1—Ba1^iv	92.661 (19)	F3^ix—Ba1—F3^vi	132.13 (3)
Ba1^iii—Al1—Ba1^iv	83.556 (18)	F5^xi—Ba1—F3^vi	55.43 (3)
F2—Al1—Ba1	45.97 (4)	F4^ix—Ba1—F3^vi	138.57 (3)
F5—Al1—Ba1	105.40 (4)	F2—Ba1—F3^vi	72.82 (3)
F3—Al1—Ba1	136.50 (4)	F6^ix—Ba1—F3^vi	172.30 (3)
F6—Al1—Ba1	81.47 (4)	F4^vii—Ba1—F3^vi	115.94 (3)
F4—Al1—Ba1	127.58 (4)	F2^ii—Li1—F6^ix	112.68 (16)
F1—Al1—Ba1	42.61 (3)	F2^ii—Li1—F3^viii	114.19 (16)
Li1^i—Al1—Ba1	140.41 (6)	F6^ix—Li1—F3^viii	123.53 (17)
Ba1^ii—Al1—Ba1	73.583 (17)	F2^ii—Li1—F1	95.21 (15)
Ba1^iii—Al1—Ba1	135.275 (17)	F6^ix—Li1—F1	91.32 (14)
Ba1^iv—Al1—Ba1	128.778 (19)	F3^viii—Li1—F1	113.63 (16)
Al1—F5—Ba1^v	140.91 (6)	F2^ii—Li1—F5^viii	105.08 (14)
Al1—F5—Li1^i	88.12 (8)	F6^ix—Li1—F5^viii	73.12 (11)
Ba1^v—F5—Li1^i	109.72 (8)	F3^viii—Li1—F5^viii	65.81 (10)
Al1—F5—Ba1^iv	106.66 (6)	F1—Li1—F5^viii	157.95 (15)
Ba1^v—F5—Ba1^iv	107.54 (4)	F2^ii—Li1—Al1^viii	114.76 (14)
Li1^i—F5—Ba1^iv	90.73 (7)	F6^ix—Li1—Al1^viii	99.54 (12)
Al1—F4—Ba1^iv	111.67 (6)	F3^viii—Li1—Al1^viii	31.38 (7)
Al1—F4—Ba1^iii	96.56 (4)	F1—Li1—Al1^viii	140.41 (14)
Ba1^iv—F4—Ba1^iii	121.66 (4)	F5^viii—Li1—Al1^viii	34.45 (5)
Al1—F4—Ba1^ii	90.05 (5)	F2^ii—Li1—Ba1^ii	50.89 (9)
Ba1^iv—F4—Ba1^ii	133.67 (4)	F6^ix—Li1—Ba1^ii	95.73 (12)
Ba1^iii—F4—Ba1^ii	94.07 (3)	F3^viii—Li1—Ba1^ii	138.60 (13)
Al1—F1—Li1	129.01 (11)	F1—Li1—Ba1^ii	46.49 (7)
Al1—F1—Ba1^ii	99.44 (4)	F5^viii—Li1—Ba1^ii	148.13 (11)
Li1—F1—Ba1^ii	102.75 (10)	Al1^viii—Li1—Ba1^ii	162.71 (10)
Al1—F1—Ba1	111.20 (5)	F2^ii—Li1—Ba1	119.40 (13)
Li1—F1—Ba1	105.72 (9)	F6^ix—Li1—Ba1	48.12 (8)
Ba1^ii—F1—Ba1	106.13 (4)	F3^viii—Li1—Ba1	122.73 (13)
Al1—F3—Li1^i	115.89 (11)	F1—Li1—Ba1	44.94 (7)
Al1—F3—Ba1^iii	97.43 (5)	F5^viii—Li1—Ba1	115.21 (10)
Li1^i—F3—Ba1^iii	116.96 (11)	Al1^viii—Li1—Ba1	124.30 (9)
Al1—F3—Ba1^vi	129.98 (5)	Ba1^ii—Li1—Ba1	72.35 (6)
Li1^i—F3—Ba1^vi	100.89 (10)	F2^ii—Li1—Ba1^x	136.95 (14)
Ba1^iii—F3—Ba1^vi	94.46 (3)	F6^ix—Li1—Ba1^x	37.41 (7)
Al1—F6—Li1^iii	130.61 (11)	F3^viii—Li1—Ba1^x	86.22 (11)
Al1—F6—Ba1^ii	100.76 (5)	F1—Li1—Ba1^x	111.27 (12)
Li1^iii—F6—Ba1^ii	118.42 (10)	F5^viii—Li1—Ba1^x	47.26 (6)
Al1—F6—Ba1^iii	96.14 (4)	Al1^viii—Li1—Ba1^x	63.86 (6)
Li1^iii—F6—Ba1^iii	104.03 (11)	Ba1^ii—Li1—Ba1^x	132.55 (8)
Ba1^ii—F6—Ba1^iii	100.88 (4)	Ba1—Li1—Ba1^x	68.34 (5)
Al1—F2—Li1^vii	147.48 (12)	F2^ii—Li1—Ba1^iv	76.62 (10)
Al1—F2—Ba1	108.27 (5)	F6^ix—Li1—Ba1^iv	170.18 (14)
Li1^vii—F2—Ba1	100.17 (11)	F3^viii—Li1—Ba1^iv	51.32 (8)
F5^xii—Ba1—F6^vii	170.84 (3)	F1—Li1—Ba1^iv	84.46 (10)
F5^xii—Ba1—F4^xi	84.42 (4)	F5^viii—Li1—Ba1^iv	108.29 (9)
F6^vii—Ba1—F4^xi	86.42 (4)	Al1^viii—Li1—Ba1^iv	78.47 (6)
F5^xii—Ba1—F1^vii	129.85 (4)	Ba1^ii—Li1—Ba1^iv	87.80 (6)
F6^vii—Ba1—F1^vii	55.43 (3)	Ba1—Li1—Ba1^iv	125.26 (8)
F4^xi—Ba1—F1^vii	119.14 (4)	Ba1^x—Li1—Ba1^iv	136.99 (8)
F5^xii—Ba1—F1	70.03 (4)	F2^ii—Li1—Ba1^v	143.35 (13)
F6^vii—Ba1—F1	117.93 (3)	F6^ix—Li1—Ba1^v	103.96 (12)
F4^xi—Ba1—F1	140.85 (3)	F3^viii—Li1—Ba1^v	38.90 (8)
F1^vii—Ba1—F1	100.00 (3)	F1—Li1—Ba1^v	82.52 (10)
F5^xii—Ba1—F3^ix	61.61 (4)	F5^viii—Li1—Ba1^v	86.15 (8)
F6^vii—Ba1—F3^ix	115.70 (3)	Al1^viii—Li1—Ba1^v	57.93 (5)
F4^xi—Ba1—F3^ix	73.06 (4)	Ba1^ii—Li1—Ba1^v	125.71 (8)
F1^vii—Ba1—F3^ix	161.59 (3)	Ba1—Li1—Ba1^v	84.35 (6)
F1—Ba1—F3^ix	68.84 (3)	Ba1^x—Li1—Ba1^v	75.70 (5)
F5^xii—Ba1—F5^xi	115.13 (4)	Ba1^iv—Li1—Ba1^v	66.74 (5)
F6^vii—Ba1—F5^xi	58.33 (3)

Symmetry codes: (i) −x+2, y−1/2, −z+1/2; (ii) x, −y+1/2, z+1/2; (iii) −x+1, y−1/2, −z+1/2; (iv) x+1, −y+1/2, z+1/2; (v) x+1, y, z; (vi) −x+1, −y, −z; (vii) x, −y+1/2, z−1/2; (viii) −x+2, y+1/2, −z+1/2; (ix) −x+1, y+1/2, −z+1/2; (x) −x+1, −y+1, −z; (xi) x−1, −y+1/2, z−1/2; (xii) x−1, y, z.