Symmetry reduction due to gallium substitution in the garnet Li6.43(2)Ga0.52(3)La2.67(4)Zr2O12

Robben, L.; Merzlyakova, E.; Heitjans, P.; Gesing, T.M.

doi:10.1107/S2056989016001924

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ISSN: 2056-9890

Volume 72| Part 3| March 2016| Pages 287-289

doi:10.1107/S2056989016001924

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Symmetry reduction due to gallium substitution in the garnet Li_6.43(2)Ga_0.52(3)La_2.67(4)Zr₂O₁₂

Lars Robben,^a ^* Elena Merzlyakova,^b Paul Heitjans ^b and Thorsten M. Gesing ^a

^aChemische Kristallographie fester Stoffe, Institut für Anorganische Chemie und Kristallographie, FB02, Leobener Strasse/NW2, and MAPEX Center for Materials and Processes, Universität Bremen, Bibliotheksstrasse 1, 28359 Bremen, Germany, and ^bInstitut für Physikalische Chemie und Elektrochemie, Leibniz Universität Hannover, Callinstrasse 3-3a, D-30167 Hannover, Germany
^*Correspondence e-mail: lrobben@uni-bremen.de

Edited by M. Weil, Vienna University of Technology, Austria (Received 4 January 2016; accepted 1 February 2016; online 6 February 2016)

Single-crystal structure refinements on lithium lanthanum zirconate (LLZO; Li₇La₃Zr₂O₁₂) substituted with gallium were successfully carried out in the cubic symmetry space group I $[\overline{4}]$ 3d. Gallium was found on two lithium sites as well as on the lanthanum position. Due to the structural distortion of the resulting Li_6.43(2)Ga_0.52(3)La_2.67(4)Zr₂O₁₂ (Ga–LLZO) single crystals, a reduction of the LLZO cubic garnet symmetry from Ia $[\overline{3}]$ d to I $[\overline{4}]$ 3d was necessary, which could hardly be analysed from X-ray powder diffraction data.

Keywords: crystal structure; garnet; lithium lanthanum zirconate (LLZO); symmetry reduction.

CCDC reference: 1451178

1. Chemical context

Garnets can be described with the ideal formula A₃B₂(XO₄)₃ in space group Ia $[\overline{3}]$ d, with different coordination polyhedra of the respective elements with oxygen, resulting in a distorted cube for A (e.g. Ca), an octahedron for B (e.g. Al) and a tetrahedron for X (e.g. Si). The variability of the elements on the crystallographic sites (thereby keeping the high symmetry) gives rise to interesting material properties like ferrimagnetism (Geller, 1967 ). In recent years, garnet-type compounds containing Li have gained considerable interest as promising electrolyte materials for all-solid-state Li-ion batteries. The so-called `Li-stuffed' garnets, which contain more Li than available on tetrahedral sites (X), meaning that excess Li occupies other sites as well, show an increase in Li-ion mobility. An exhaustive overview of these compounds was recently given by Thangadurai et al. (2014 ). The garnet-type fast lithium ion conductor Li₇La₃Zr₂O₁₂, abbreviated as LLZO, is such an `Li-stuffed' garnet. Awaka et al. (2009 ) described the crystal structure of pure LLZO at ambient conditions in space group I4₁/acd. Even a small amount of Al in the structure (Al-LLZO) stabilizes the cubic garnet symmetry described in space group Ia $[\overline{3}]$ d by Geiger et al. (2011 ). These authors reported that Al could be found on two different tetrahedral sites using ²⁷Al MAS NMR spectroscopy but a final analysis was not possible due to the minor Al content. Rettenwander et al. (2014 ) reported on ⁷¹Ga MAS NMR spectroscopy measurements on gallium substituted Li_7-3xGa_xLa₃Zr₂O₁₂ (Ga–LLZO) indicating a fourfold coordination of the gallium atoms. The authors excluded the presence of Ga at the 24d position (Ia $[\overline{3}]$ d) and assumed that the local symmetry could be lower than indicated by diffraction methods. In principle, the following exchanges are possible: (i) 3 Li⁺ ↔ Ga³⁺ + 2 voids, which is the most probable one and yields a good explanation for the higher conductivity due to the higher lithium atom jump probability to empty positions as discussed (Rettenwander et al., 2014); (ii) La³⁺ ↔ Ga³⁺, a valence-neutral exchange which should lead to a dynamical disorder of the gallium atoms in order to lower the coordination number and shorten the Ga—O bond lengths for bond-valence balance, taking the different radii into account. The valence-neutral exchange should finally lead to higher displacement parameters of the atoms on the lanthanum position compared to that of the lighter zirconium atoms. (iii) Zr⁴⁺ ↔ Ga³⁺ + Li⁺, which needs slightly more lithium for charge balance and could therefore be of minor probability.

2. Structural commentary

The unit cell of the obtained single crystals could be well indexed using a body-centered cubic lattice with lattice parameter a = 12.9681 (15) Å. The space group determination with XPREP (Bruker, 2014 ) leads at once to the highest possible space group Ia $[\overline{3}]$ d. However, a satisfactory structure solution or refinement with published structural data (Geiger et al., 2011) in this space group type was not possible. Consequently, structure solutions by charge flipping (Bruker, 2009 ) were tried in all possible subgroups of Ia $[\overline{3}]$ d and the lowest R-values were obtained for the charge-flipping run in space group I $[\overline{4}]$ 3d. Subsequent refinements lead to the present structure model and clearly indicate the substitution of Ga³⁺ on the former 24c La³⁺ site as well as 24d Li⁺ site in the aristotype in space group Ia $[\overline{3}]$ d. The latter site splits into two sites due to the symmetry reduction as indicated by the Bärnighausen tree (Bärnighausen, 1980 ) given in Fig. 1. The deviation from six symmetry-equivalent Zr—O distances in LLZO (Ia $[\overline{3}]$ d) results in a distortion of the ZrO₆ octahedron with Zr—O distances of 3 × 2.095 (2) and 3 × 2.113 (2) Å in Ga–LLZO. Another significant reduction of the highest possible symmetry for LLZO is the distortion of the eightfold coordinate La position (Fig. 2), for which distances between 2.496 (2) and 2.595 (2) Å are found in Ga–LLZO. This distortion results from the splitting of the 96h position of the oxygen atom in Ia $[\overline{3}]$ d into two 48e positions in I $[\overline{4}]$ 3d (Fig. 1). Because the two lithium positions (Li22 and Li32) occupied by gallium are in principle identical to those positions of the higher symmetry structure (but with slightly shorter bond length due to the gallium substitution, viz. 4 × 1.916 (1) Å in LLZO and 4 × 1.908 (2) Å in Ga–LLZO), and the Li1 and Li2 positions are not occupied by gallium, the symmetry reduction is a confirmation of gallium atoms to be found also on the lanthanum position. This is also supported by the higher displacement parameter of the La site compared to the Zr site, as explained previously.

Figure 1
Bärnighausen tree (Bärnighausen, 1980

) of the group–subgroup relation between cubic LLZO and the symmetry-reduced cubic Ga–LLZO.

Figure 2
Crystal structure of Li_6.43(2)Ga_0.52(3)La_2.67(4)Zr₂O₁₂ (Ga–LLZO) with all possible atom positions between the ZrO₆ octahedra (bottom) and the atom position specific coordination polyhedra (top). Displacement ellipsoids (top) are given at the 50% probability level.

3. Synthesis and crystallization

The synthesis was configured to yield a compound with nominal composition Li_6.25Ga_0.25La₃Zr₂O₁₂. 2 g of a stoichiometric mixture of the pre-dried (30 h at 373 K in vacuum) educts Li₂O (with an excess of 10%_wt to compensate the lithium loss due to thermal treatment), La₂O₃, ZrO₂ and Ga₂O₃ was weighted into a WC milling beaker (45 ml, 100 WC milling balls of 5 mm diameter, Fritsch, Germany) under inert conditions (glovebox) and high-energy ball-milled in a planetary ball mill (Pulverisette 7 premium line, Fritsch, Germany) under argon atmosphere for 8 h at a rotational speed of 10 s⁻¹ as reported previously (Düvel et al., 2012 ) for Al-substituted LLZO. The obtained powder was pressed to a pellet using a uniaxial pressure of 0.8 GPa. A stack of three pellets was placed on a platinum ring seated on a corundum plate, covered with a corundum crucible and heated for 12 h at 1323 K in a muffle furnace before cooling to room-temperature. The middle pellet from the stack had smooth green color and showed visible grains. The surface of the pellet was grey and brittle and consisted mainly of lanthanum zirconates due to Li loss. From this pellet single crystals were extracted using a polarization microscope. Rietveld refinement of X-ray powder diffraction data of the green product shows a mixture of 96.8 (9)%_wt cubic garnet-type Ga–LLZO and 3.2 (9)%_wt Li₂ZrO₃ with a lattice parameter of a = 12.9738 (19) Å for its garnet-type structure. Energy dispersive X-ray analysis of the single crystal gave a tentative formula of Li_6.5 (1)Ga_0.5 (1)La_2.8 (1)Zr_2.0 (1)O₁₂, in good agreement with the refined formula Li_6.43 (2)Ga_0.52 (3)La_2.67 (4)Zr₂O₁₂ determined from single crystal X-ray diffraction data.

4. Refinement

Crystal data, data collection and structure refinement details are summarized in Table 1. Structure refinement was carried out as a two-component (merohedral) twin. Sites showing a statistical occupancy were constrained with respect to positions and anisotropic displacement parameters. An independent refinement of the anisotropic displacement parameters of Ga and Li on the Ga2/Li22 and Ga3/Li33 sites was not possible, although the reflection-to-parameter ratio is rather high. To ensure charge neutrality during the refinement of the Ga and Li occupancies on the Ga2/Li22 and Ga3/Li33 sites, the occupancies were restrained to exchange three Li atoms against one Ga atom.

Table 1
Experimental details

Crystal data
Chemical formula	Li_6.43Ga_0.52La_2.67Zr₂O₁₂
M_r	826.20
Crystal system, space group	Cubic, I $[\overline{4}]$ 3d
Temperature (K)	301
a (Å)	12.9681 (15)
V (Å³)	2180.9 (8)
Z	8
Radiation type	Mo Kα
μ (mm⁻¹)	13.41
Crystal size (mm)	0.25 × 0.15 × 0.13

Data collection
Diffractometer	Bruker APEXII CCD
Absorption correction	Multi-scan (SADABS; Bruker, 2014)
T_min, T_max	0.495, 0.754
No. of measured, independent and observed [I > 2σ(I)] reflections	472450, 3678, 3508
R_int	0.046
(sin θ/λ)_max (Å⁻¹)	1.340

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.026, 0.056, 1.46
No. of reflections	3678
No. of parameters	50
No. of restraints	3
Δρ_max, Δρ_min (e Å⁻³)	2.08, −1.91
Absolute structure	Flack x determined using 1493 quotients [(I⁺)−(I⁻)]/[(I⁺)+(I⁻)] (Parsons et al., 2013 )
Absolute structure parameter	0.045 (9)
Computer programs: APEX2 and SAINT (Bruker, 2014), TOPAS (Bruker, 2009), SHELXL2014 (Sheldrick, 2015 ), DIAMOND (Brandenburg, 1999 ) and publCIF (Westrip, 2010 ).

Supporting information

CCDC reference: 1451178

Crystal structure: contains datablock I. DOI: 10.1107/S2056989016001924/wm5261sup1.cif

Structure factors: contains datablock I. DOI: 10.1107/S2056989016001924/wm5261Isup2.hkl

checkCIF report

Chemical context top

Garnets can be described with the ideal formula A₃B₂(XO₄)₃ in space group Ia3d, with different coordination polyhedra of the respective elements with oxygen, resulting in a distorted cube for A (e.g. Ca), an octahedron for B (e.g. Al) and a tetrahedron for X (e.g. Si). The variability of the elements on the crystallographic sites (thereby keeping the high symmetry) gives rise to interesting material properties like ferrimagnetism (Geller, 1967). In recent years, garnet-type compounds containing Li have gained considerable interest as promising electrolyte materials for all-solid-state Li-ion batteries. The so-called `Li-stuffed' garnets, which contain more Li than available on tetrahedral sites (X), meaning that excess Li occupies other sites as well, show an increase in Li-ion mobility. An exhaustive overview of these compounds was given by Thangadurai et al. (2014). The garnet-type fast lithium ion conductor Li₇La₃Zr₂O₁₂, abbreviated as LLZO, is such an `Li-stuffed' garnet. Awaka et al. (2009) described the crystal structure of pure LLZO at ambient conditions in space group I4₁/acd. Even a small amount of Al in the structure (Al-LLZO) stabilizes the cubic garnet symmetry described in space group Ia3d by Geiger et al. (2011). These authors reported that Al could be found on two different tetrahedral sites using ²⁷Al MAS NMR spectroscopy but a final analysis was not possible due to the minor Al content. Rettenwander et al. (2014) reported on ⁷¹Ga MAS NMR spectroscopy measurements on gallium substituted Li_7–3xGa_xLa₃Zr₂O₁₂ (Ga–LLZO) indicating a fourfold coordination of the gallium atoms. The authors excluded the presence of Ga at the 24d position (Ia3d) and assumed that the local symmetry could be lower than indicated by diffraction methods. In principle, the following exchanges are possible: (i) 3 Li⁺ ↔ Ga³⁺ + 2 voids, which is the most probable one and yields a good explanation for the higher conductivity due to the higher lithium atom jump probability to empty positions as discussed (Rettenwander et al., 2014); (ii) La³⁺ ↔ Ga³⁺, a valence-neutral exchange which should lead to a dynamical disorder of the gallium atoms in order to lower the coordination number and shorten the Ga—O bond lengths for bond-valence balance, taking the different radii into account. The valence-neutral exchange should finally lead to a higher displacement parameters of the atoms on the lanthanum position compared to that of the lighter zirconium atoms. (iii) Zr⁴⁺ ↔ Ga³⁺ + Li⁺, which need slightly more lithium for charge balance and could therefore be of minor probability.

Structural commentary top

The unit cell of the obtained single crystals could be well indexed using a body-centered cubic lattice with lattice parameter a = 12.9681 (15) Å. The space group determination with XPREP (Bruker, 2014) lead at once to the highest possible space group Ia3d. However, a satisfactory structure solution or refinement with published structural data (Geiger et al., 2011) in this space group type was not possible. Consequently, structure solutions by charge flipping (Bruker, 2009) were tried in all possible subgroups of Ia3d and the lowest R-values were obtained for the charge-flipping run in space group I43d. Subsequent refinements lead to the present structure model and clearly indicate the substitution of Ga³⁺ on the former 24c La³⁺ site and 24d Li⁺ site in the aristotype in space group Ia3d.. The latter site splits into two sites due to the symmetry reduction as indicated by the Bärnighausen tree (Bärnighausen, 1980) given in Fig. 1. The deviation from six symmetry-equivalent Zr—O distances in LLZO (Ia3d) results in a distortion of the ZrO₆ octahedron with Zr—O distances of 3 × 2.095 (2) Å and 3 × 2.113 (2) Å in Ga–LLZO. Another significant reduction of the highest possible symmetry for LLZO is the distortion of the eightfold coordinate La position (Fig. 2), for which distances between 2.496 (2) and 2.595 (2) Å are found in Ga–LLZO. This distortion results from the splitting of the 96h position of the oxygen atoms in Ia3d into two 48e positions in I43d (Fig. 1). Because the two lithium positions (Li22 and Li32) occupied by gallium are in principle identical to those positions of the higher symmetry structure (but with slightly shorter bond length due to the gallium substitution, viz. 4 × 1.916 (1) Å in LLZO and 4 × 1.908 (2) Å in Ga–LLZO), and the Li1 and Li2 positions are not occupied by gallium, the symmetry reduction is a confirmation of gallium atoms to be found also on the lanthanum position. This is also supported by the higher displacement parameter of the La site compared to the Zr site, as explained previously.

Synthesis and crystallization top

The synthesis was configured to yield a compound with nominal composition Li_6.25La₃Ga_0.25Zr₂O₁₂. 2 g of a stoichiometric mixture of the pre-dried (30 h at 373 K in vacuum) educts Li₂O (with an excess of 10%_wt to compensate the lithium loss due to thermal treatment), La₂O₃, ZrO₂ and Ga₂O₃ was weighted into a WC milling beaker (45 ml, 100 WC milling balls of 5 mm diameter, Fritsch, Germany) under inert conditions (glovebox) and high-energy ball-milled in a planetary ball mill (Pulverisette 7 premium line, Fritsch, Germany) under argon atmosphere for 8 h at a rotational speed of 10 s⁻¹ as reported previously (Düvel et al., 2012) for Al-substituted LLZO. The obtained powder was pressed to a pellet using a uniaxial pressure of 0.8 GPa. A stack of three pellets was placed on a platinum ring seated on a corundum plate, covered with a corundum crucible and heated for 12 h at 1323 K in a muffle furnace before cooling to room-temperature. The middle pellet from the stack had smooth green color and showed visible grains. The surface of the pellet was grey and brittle and consisted mainly of lanthanum zirconates due to Li loss. From this pellet single crystals were extracted using a polarization microscope. Rietveld refinement of X-ray powder diffraction data of the green product shows a mixture of 96.8 (9)%_wt cubic garnet-type Ga–LLZO and 3.2 (9)%_wt Li₂ZrO₃ with a lattice parameter of a = 12.9738 (19) Å for its garnet-type structure. Energy dispersive X-ray analysis of the single-crystal gave a tentative formula of Li_6.5 (1)Ga_0.5 (1)La_2.8 (1)Zr_2.0 (1)O₁₂, in good agreement with the refined formula Li_6.43 (2)Ga_0.52 (3)La_2.67 (4)Zr₂O₁₂ determined from single-crystal X-ray diffraction data.

Refinement top

Structure description top

The unit cell of the obtained single crystals could be well indexed using a body-centered cubic lattice with lattice parameter a = 12.9681 (15) Å. The space group determination with XPREP (Bruker, 2014) lead at once to the highest possible space group Ia3d. However, a satisfactory structure solution or refinement with published structural data (Geiger et al., 2011) in this space group type was not possible. Consequently, structure solutions by charge flipping (Bruker, 2009) were tried in all possible subgroups of Ia3d and the lowest R-values were obtained for the charge-flipping run in space group I43d. Subsequent refinements lead to the present structure model and clearly indicate the substitution of Ga³⁺ on the former 24c La³⁺ site and 24d Li⁺ site in the aristotype in space group Ia3d.. The latter site splits into two sites due to the symmetry reduction as indicated by the Bärnighausen tree (Bärnighausen, 1980) given in Fig. 1. The deviation from six symmetry-equivalent Zr—O distances in LLZO (Ia3d) results in a distortion of the ZrO₆ octahedron with Zr—O distances of 3 × 2.095 (2) Å and 3 × 2.113 (2) Å in Ga–LLZO. Another significant reduction of the highest possible symmetry for LLZO is the distortion of the eightfold coordinate La position (Fig. 2), for which distances between 2.496 (2) and 2.595 (2) Å are found in Ga–LLZO. This distortion results from the splitting of the 96h position of the oxygen atoms in Ia3d into two 48e positions in I43d (Fig. 1). Because the two lithium positions (Li22 and Li32) occupied by gallium are in principle identical to those positions of the higher symmetry structure (but with slightly shorter bond length due to the gallium substitution, viz. 4 × 1.916 (1) Å in LLZO and 4 × 1.908 (2) Å in Ga–LLZO), and the Li1 and Li2 positions are not occupied by gallium, the symmetry reduction is a confirmation of gallium atoms to be found also on the lanthanum position. This is also supported by the higher displacement parameter of the La site compared to the Zr site, as explained previously.

Synthesis and crystallization top

Refinement details top

Computing details top

Data collection: APEX2 (Bruker, 2014); cell refinement: SAINT (Bruker, 2014); data reduction: SAINT (Bruker, 2014); program(s) used to solve structure: TOPAS (Bruker, 2009); program(s) used to refine structure: SHELXL2014 (Sheldrick, 2015); molecular graphics: DIAMOND (Brandenburg, 1999); software used to prepare material for publication: publCIF (Westrip, 2010).

Figures top

	Fig. 1. Bärnighausen tree (Bärnighausen, 1980) of the group–subgroup relation between cubic LLZO and the symmetry-reduced cubic Ga–LLZO.
	Fig. 2. Crystal structure of Li_6.43 (2)Ga_0.52 (3)La_2.67 (4)Zr₂O₁₂ (Ga–LLZO) with all possible atom positions between the ZrO₆ octahedra (bottom) and the atom position specific coordination polyhedra (top). Displacement ellipsoids (top) are given at the 50% probability level.

Lithium gallium lanthanum zirconate top

Crystal data top

Li_6.43Ga_0.52La_2.67Zr₂O₁₂	Mo Kα radiation, λ = 0.71073 Å
M_r = 826.20	Cell parameters from 9913 reflections
Cubic, I43d	θ = 3.1–72.3°
a = 12.9681 (15) Å	µ = 13.41 mm⁻¹
V = 2180.9 (8) Å³	T = 301 K
Z = 8	Irregular, green
F(000) = 340	0.25 × 0.15 × 0.13 mm
D_x = 5.033 Mg m⁻³

Data collection top

Bruker APEXII CCD diffractometer	3508 reflections with I > 2σ(I)
φ and ω scans	R_int = 0.046
Absorption correction: multi-scan (SADABS; Bruker, 2014)	θ_max = 72.3°, θ_min = 2.2°
T_min = 0.495, T_max = 0.754	h = −34→34
472450 measured reflections	k = −34→34
3678 independent reflections	l = −34→34

Refinement top

Refinement on F²	w = 1/[σ²(F_o²) + (0.011P)² + 8.6617P] where P = (F_o² + 2F_c²)/3
Least-squares matrix: full	(Δ/σ)_max = 0.049
R[F² > 2σ(F²)] = 0.026	Δρ_max = 2.08 e Å⁻³
wR(F²) = 0.056	Δρ_min = −1.91 e Å⁻³
S = 1.46	Extinction correction: SHELXL2014 (Sheldrick, 2015), Fc^*=kFc[1+0.001xFc²λ³/sin(2θ)]^-1/4
3678 reflections	Absolute structure: Flack x determined using 1493 quotients [(I⁺)-(I^-)]/[(I⁺)+(I^-)] (Parsons et al., 2013)
50 parameters	Absolute structure parameter: 0.045 (9)
3 restraints

Crystal data top

Li_6.43Ga_0.52La_2.67Zr₂O₁₂	Z = 8
M_r = 826.20	Mo Kα radiation
Cubic, I43d	µ = 13.41 mm⁻¹
a = 12.9681 (15) Å	T = 301 K
V = 2180.9 (8) Å³	0.25 × 0.15 × 0.13 mm

Data collection top

Bruker APEXII CCD diffractometer	3678 independent reflections
Absorption correction: multi-scan (SADABS; Bruker, 2014)	3508 reflections with I > 2σ(I)
T_min = 0.495, T_max = 0.754	R_int = 0.046
472450 measured reflections

Refinement top

R[F² > 2σ(F²)] = 0.026	3 restraints
wR(F²) = 0.056	Δρ_max = 2.08 e Å⁻³
S = 1.46	Δρ_min = −1.91 e Å⁻³
3678 reflections	Absolute structure: Flack x determined using 1493 quotients [(I⁺)-(I^-)]/[(I⁺)+(I^-)] (Parsons et al., 2013)
50 parameters	Absolute structure parameter: 0.045 (9)

Special details top

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. Refined as a 2-component twin.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq	Occ. (<1)
La1	0.62292 (2)	0.0000	0.2500	0.00746 (2)	0.889 (4)
Ga1	0.62292 (2)	0.0000	0.2500	0.00746 (2)	0.111 (4)
Zr1	0.25005 (2)	0.25005 (2)	0.25005 (2)	0.00552 (4)
O1	0.19586 (18)	0.28163 (18)	0.10116 (16)	0.0118 (3)
O2	0.46910 (17)	0.55410 (17)	0.65064 (16)	0.0114 (2)
Li1	0.428 (3)	0.593 (2)	0.813 (2)	0.029 (5)	0.33333 (14)
Li2	0.642 (3)	0.178 (2)	0.065 (2)	0.029 (5)	0.33333 (14)
Ga2	0.3750	0.5000	0.7500	0.0061 (4)	0.0857 (12)
Li22	0.3750	0.5000	0.7500	0.0061 (4)	0.743 (4)
Ga3	0.2500	0.3750	0.0000	0.0110 (9)	0.0403 (12)
Li32	0.2500	0.3750	0.0000	0.0110 (9)	0.879 (4)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
La1	0.00912 (4)	0.00656 (5)	0.00668 (5)	0.000	0.000	−0.00141 (3)
Ga1	0.00912 (4)	0.00656 (5)	0.00668 (5)	0.000	0.000	−0.00141 (3)
Zr1	0.00552 (4)	0.00552 (4)	0.00552 (4)	0.00021 (3)	0.00021 (3)	0.00021 (3)
O1	0.0129 (6)	0.0138 (6)	0.0087 (5)	0.0014 (5)	−0.0007 (5)	0.0006 (5)
O2	0.0131 (6)	0.0116 (6)	0.0096 (5)	0.0010 (5)	0.0000 (5)	−0.0013 (4)
Li1	0.051 (15)	0.015 (6)	0.022 (6)	−0.013 (9)	−0.013 (8)	0.006 (6)
Li2	0.051 (15)	0.015 (6)	0.022 (6)	−0.013 (9)	−0.013 (8)	0.006 (6)
Ga2	0.0078 (10)	0.0052 (6)	0.0052 (6)	0.000	0.000	0.000
Li22	0.0078 (10)	0.0052 (6)	0.0052 (6)	0.000	0.000	0.000
Ga3	0.0100 (14)	0.013 (2)	0.0100 (14)	0.000	0.000	0.000
Li32	0.0100 (14)	0.013 (2)	0.0100 (14)	0.000	0.000	0.000

Geometric parameters (Å, º) top

La1—O1ⁱ	2.496 (2)	O2—Li2^xxiii	2.09 (3)
La1—O1ⁱⁱ	2.496 (2)	O2—Zr1^xxiv	2.113 (2)
La1—O2ⁱⁱⁱ	2.520 (2)	O2—Li1	2.23 (4)
La1—O2^iv	2.520 (2)	O2—La1^xxv	2.520 (2)
La1—O2^v	2.590 (2)	O2—Li2^xxvi	2.54 (3)
La1—O2^vi	2.590 (2)	O2—La1^xxiii	2.590 (2)
La1—O1^vii	2.595 (2)	O2—Li2^xxvii	2.61 (4)
La1—O1^viii	2.595 (2)	Li1—O2^xxviii	1.91 (4)
Zr1—O1^ix	2.095 (2)	Li1—O2^xxii	2.04 (3)
Zr1—O1^x	2.095 (2)	Li1—O1^xxix	2.16 (3)
Zr1—O1	2.095 (2)	Li1—O1^xxx	2.65 (3)
Zr1—O2^xi	2.113 (2)	Li2—O1^viii	1.90 (3)
Zr1—O2^xii	2.113 (2)	Li2—O2^vi	2.09 (3)
Zr1—O2^xiii	2.113 (2)	Li2—O1^xvi	2.22 (4)
O1—Li2^xiv	1.90 (3)	Li2—O1^xxxi	2.32 (3)
O1—Ga3	1.918 (2)	Li2—O2^xxxii	2.54 (3)
O1—Li1^xv	2.16 (3)	Li2—O2^xxxiii	2.61 (4)
O1—Li2^xvi	2.22 (4)	Li2—Li2^xxxiv	2.68 (6)
O1—Li2^xvii	2.32 (3)	Ga2—O2^xxi	1.908 (2)
O1—La1^xviii	2.496 (2)	Ga2—O2^xxii	1.908 (2)
O1—La1^xix	2.595 (2)	Ga2—O2^xxviii	1.908 (2)
O1—Li1^xx	2.65 (3)	Ga3—O1^xxxv	1.918 (2)
O2—Ga2	1.908 (2)	Ga3—O1^xxxvi	1.918 (2)
O2—Li1^xxi	1.91 (4)	Ga3—O1^xxxvii	1.918 (2)
O2—Li1^xxii	2.04 (3)

O1ⁱ—La1—O1ⁱⁱ	73.18 (10)	La1^xviii—O1—Li1^xx	79.5 (6)
O1ⁱ—La1—O2ⁱⁱⁱ	160.55 (5)	La1^xix—O1—Li1^xx	68.9 (8)
O1ⁱⁱ—La1—O2ⁱⁱⁱ	111.27 (5)	Ga2—O2—Li1^xxi	49.8 (10)
O1ⁱ—La1—O2^iv	111.27 (5)	Ga2—O2—Li1^xxii	48.0 (8)
O1ⁱⁱ—La1—O2^iv	160.55 (5)	Li1^xxi—O2—Li1^xxii	77.4 (11)
O2ⁱⁱⁱ—La1—O2^iv	71.21 (10)	Ga2—O2—Li2^xxiii	66.9 (11)
O1ⁱ—La1—O2^v	73.18 (7)	Li1^xxi—O2—Li2^xxiii	18.2 (10)
O1ⁱⁱ—La1—O2^v	95.73 (8)	Li1^xxii—O2—Li2^xxiii	85.1 (16)
O2ⁱⁱⁱ—La1—O2^v	123.67 (5)	Ga2—O2—Zr1^xxiv	128.57 (12)
O2^iv—La1—O2^v	68.75 (9)	Li1^xxi—O2—Zr1^xxiv	104.4 (9)
O1ⁱ—La1—O2^vi	95.73 (8)	Li1^xxii—O2—Zr1^xxiv	87.4 (8)
O1ⁱⁱ—La1—O2^vi	73.18 (7)	Li2^xxiii—O2—Zr1^xxiv	88.5 (10)
O2ⁱⁱⁱ—La1—O2^vi	68.75 (9)	Ga2—O2—Li1	44.9 (8)
O2^iv—La1—O2^vi	123.67 (5)	Li1^xxi—O2—Li1	72.9 (12)
O2^v—La1—O2^vi	166.44 (9)	Li1^xxii—O2—Li1	85.9 (12)
O1ⁱ—La1—O1^vii	125.03 (5)	Li2^xxiii—O2—Li1	89.7 (13)
O1ⁱⁱ—La1—O1^vii	68.53 (9)	Zr1^xxiv—O2—Li1	173.2 (7)
O2ⁱⁱⁱ—La1—O1^vii	72.72 (6)	Ga2—O2—La1^xxv	94.15 (8)
O2^iv—La1—O1^vii	94.96 (7)	Li1^xxi—O2—La1^xxv	143.6 (9)
O2^v—La1—O1^vii	73.07 (5)	Li1^xxii—O2—La1^xxv	80.5 (11)
O2^vi—La1—O1^vii	108.77 (5)	Li2^xxiii—O2—La1^xxv	161.0 (11)
O1ⁱ—La1—O1^viii	68.53 (9)	Zr1^xxiv—O2—La1^xxv	103.05 (9)
O1ⁱⁱ—La1—O1^viii	125.03 (5)	Li1—O2—La1^xxv	77.0 (9)
O2ⁱⁱⁱ—La1—O1^viii	94.96 (7)	Ga2—O2—Li2^xxvi	57.6 (8)
O2^iv—La1—O1^viii	72.72 (6)	Li1^xxi—O2—Li2^xxvi	76.3 (11)
O2^v—La1—O1^viii	108.77 (5)	Li1^xxii—O2—Li2^xxvi	99.9 (14)
O2^vi—La1—O1^viii	73.07 (5)	Li2^xxiii—O2—Li2^xxvi	91.0 (11)
O1^vii—La1—O1^viii	165.12 (9)	Zr1^xxiv—O2—Li2^xxvi	172.6 (9)
O1^ix—Zr1—O1^x	86.37 (10)	Li1—O2—Li2^xxvi	14.0 (8)
O1^ix—Zr1—O1	86.37 (10)	La1^xxv—O2—Li2^xxvi	79.4 (7)
O1^x—Zr1—O1	86.37 (10)	Ga2—O2—La1^xxiii	122.63 (10)
O1^ix—Zr1—O2^xi	93.51 (9)	Li1^xxi—O2—La1^xxiii	95.8 (10)
O1^x—Zr1—O2^xi	179.59 (11)	Li1^xxii—O2—La1^xxiii	170.6 (8)
O1—Zr1—O2^xi	94.02 (9)	Li2^xxiii—O2—La1^xxiii	90.4 (8)
O1^ix—Zr1—O2^xii	94.02 (9)	Zr1^xxiv—O2—La1^xxiii	100.77 (8)
O1^x—Zr1—O2^xii	93.51 (9)	Li1—O2—La1^xxiii	85.8 (7)
O1—Zr1—O2^xii	179.59 (11)	La1^xxv—O2—La1^xxiii	101.98 (8)
O2^xi—Zr1—O2^xii	86.10 (9)	Li2^xxvi—O2—La1^xxiii	71.8 (9)
O1^ix—Zr1—O2^xiii	179.59 (11)	Ga2—O2—Li2^xxvii	56.1 (7)
O1^x—Zr1—O2^xiii	94.02 (9)	Li1^xxi—O2—Li2^xxvii	83.4 (14)
O1—Zr1—O2^xiii	93.51 (9)	Li1^xxii—O2—Li2^xxvii	8.2 (9)
O2^xi—Zr1—O2^xiii	86.10 (9)	Li2^xxiii—O2—Li2^xxvii	89.2 (9)
O2^xii—Zr1—O2^xiii	86.10 (9)	Zr1^xxiv—O2—Li2^xxvii	80.4 (7)
Li2^xiv—O1—Ga3	55.1 (12)	Li1—O2—Li2^xxvii	93.0 (11)
Li2^xiv—O1—Zr1	100.2 (12)	La1^xxv—O2—Li2^xxvii	78.2 (6)
Ga3—O1—Zr1	129.12 (12)	Li2^xxvi—O2—Li2^xxvii	107.0 (12)
Li2^xiv—O1—Li1^xv	17.3 (11)	La1^xxiii—O2—Li2^xxvii	178.8 (7)
Ga3—O1—Li1^xv	71.3 (8)	O2^xxviii—Li1—O2^xxii	108.5 (14)
Zr1—O1—Li1^xv	84.8 (8)	O2^xxviii—Li1—O1^xxix	98.6 (18)
Li2^xiv—O1—Li2^xvi	80.8 (13)	O2^xxii—Li1—O1^xxix	93.9 (12)
Ga3—O1—Li2^xvi	50.0 (9)	O2^xxviii—Li1—O2	101.2 (12)
Zr1—O1—Li2^xvi	85.8 (9)	O2^xxii—Li1—O2	86.8 (14)
Li1^xv—O1—Li2^xvi	87.3 (14)	O1^xxix—Li1—O2	158.9 (18)
Li2^xiv—O1—Li2^xvii	78.1 (15)	O2^xxviii—Li1—O1^xxx	144.7 (15)
Ga3—O1—Li2^xvii	48.2 (10)	O2^xxii—Li1—O1^xxx	106.5 (15)
Zr1—O1—Li2^xvii	177.3 (10)	O1^xxix—Li1—O1^xxx	83.1 (9)
Li1^xv—O1—Li2^xvii	93.8 (10)	O2—Li1—O1^xxx	76.4 (12)
Li2^xvi—O1—Li2^xvii	91.8 (16)	O1^viii—Li2—O2^vi	101.0 (12)
Li2^xiv—O1—La1^xviii	147.5 (13)	O1^viii—Li2—O1^xvi	102.1 (17)
Ga3—O1—La1^xviii	92.55 (8)	O2^vi—Li2—O1^xvi	91.1 (12)
Zr1—O1—La1^xviii	103.48 (9)	O1^viii—Li2—O1^xxxi	98.5 (14)
Li1^xv—O1—La1^xviii	163.4 (9)	O2^vi—Li2—O1^xxxi	160.3 (14)
Li2^xvi—O1—La1^xviii	79.1 (7)	O1^xvi—Li2—O1^xxxi	82.0 (13)
Li2^xvii—O1—La1^xviii	77.3 (7)	O1^viii—Li2—O2^xxxii	151.8 (19)
Li2^xiv—O1—La1^xix	94.7 (9)	O2^vi—Li2—O2^xxxii	86.9 (13)
Ga3—O1—La1^xix	123.13 (10)	O1^xvi—Li2—O2^xxxii	104.8 (10)
Zr1—O1—La1^xix	100.26 (9)	O1^viii—Li2—O2^xxxiii	84.1 (12)
Li1^xv—O1—La1^xix	89.9 (10)	O2^vi—Li2—O2^xxxiii	85.2 (14)
Li2^xvi—O1—La1^xix	173.1 (9)	O1^xvi—Li2—O2^xxxiii	173.3 (16)
Li2^xvii—O1—La1^xix	82.1 (10)	O1^xxxi—Li2—O2^xxxiii	99.7 (11)
La1^xviii—O1—La1^xix	102.50 (8)	O2^xxxii—Li2—O2^xxxiii	69.5 (10)
Li2^xiv—O1—Li1^xx	81.4 (12)	O2^xxi—Ga2—O2^xxii	114.14 (7)
Ga3—O1—Li1^xx	60.5 (8)	O2^xxi—Ga2—O2^xxviii	100.49 (13)
Zr1—O1—Li1^xx	169.2 (8)	O2^xxii—Ga2—O2^xxviii	114.14 (7)
Li1^xv—O1—Li1^xx	95.1 (9)	O1—Ga3—O1^xxxv	113.48 (7)
Li2^xvi—O1—Li1^xx	105.0 (14)	O1—Ga3—O1^xxxvi	101.73 (14)
Li2^xvii—O1—Li1^xx	13.3 (11)	O1^xxxv—Ga3—O1^xxxvi	113.48 (7)

Symmetry codes: (i) −y+3/4, x−1/4, −z+1/4; (ii) −y+3/4, −x+1/4, z+1/4; (iii) −x+5/4, −z+3/4, y−1/4; (iv) −x+5/4, z−3/4, −y+3/4; (v) −z+5/4, y−3/4, −x+3/4; (vi) −z+5/4, −y+3/4, x−1/4; (vii) −z+3/4, −y+1/4, x+1/4; (viii) −z+3/4, y−1/4, −x+1/4; (ix) y, z, x; (x) z, x, y; (xi) z−1/4, y−1/4, x−1/4; (xii) y−1/4, x−1/4, z−1/4; (xiii) x−1/4, z−1/4, y−1/4; (xiv) −z+1/4, y+1/4, −x+3/4; (xv) x−1/4, −z+5/4, −y+3/4; (xvi) −x+1, −y+1/2, z; (xvii) x−1/2, −y+1/2, −z; (xviii) −y+1/4, −x+3/4, z−1/4; (xix) z−1/4, −y+1/4, −x+3/4; (xx) y−1/2, z−1/2, x−1/2; (xxi) −x+3/4, z−1/4, −y+5/4; (xxii) x, −y+1, −z+3/2; (xxiii) z+1/4, −y+3/4, −x+5/4; (xxiv) y+1/4, x+1/4, z+1/4; (xxv) −x+5/4, z+1/4, −y+3/4; (xxvi) −z+1/2, x, −y+1; (xxvii) −z+1/2, −x+1, y+1/2; (xxviii) −x+3/4, −z+5/4, y+1/4; (xxix) x+1/4, −z+3/4, −y+5/4; (xxx) z+1/2, x+1/2, y+1/2; (xxxi) x+1/2, −y+1/2, −z; (xxxii) y, −z+1, −x+1/2; (xxxiii) −y+1, z−1/2, −x+1/2; (xxxiv) z+3/4, −y+1/4, −x+3/4; (xxxv) z+1/4, −y+3/4, −x+1/4; (xxxvi) −x+1/2, y, −z; (xxxvii) −z+1/4, −y+3/4, x−1/4.

Experimental details

Crystal data
Chemical formula	Li_6.43Ga_0.52La_2.67Zr₂O₁₂
M_r	826.20
Crystal system, space group	Cubic, I43d
Temperature (K)	301
a (Å)	12.9681 (15)
V (Å³)	2180.9 (8)
Z	8
Radiation type	Mo Kα
µ (mm⁻¹)	13.41
Crystal size (mm)	0.25 × 0.15 × 0.13

Data collection
Diffractometer	Bruker APEXII CCD
Absorption correction	Multi-scan (SADABS; Bruker, 2014)
T_min, T_max	0.495, 0.754
No. of measured, independent and observed [I > 2σ(I)] reflections	472450, 3678, 3508
R_int	0.046
(sin θ/λ)_max (Å⁻¹)	1.340

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.026, 0.056, 1.46
No. of reflections	3678
No. of parameters	50
No. of restraints	3
Δρ_max, Δρ_min (e Å⁻³)	2.08, −1.91
Absolute structure	Flack x determined using 1493 quotients [(I⁺)-(I^-)]/[(I⁺)+(I^-)] (Parsons et al., 2013)
Absolute structure parameter	0.045 (9)

Computer programs: APEX2 (Bruker, 2014), SAINT (Bruker, 2014), TOPAS (Bruker, 2009), SHELXL2014 (Sheldrick, 2015), DIAMOND (Brandenburg, 1999), publCIF (Westrip, 2010).

Acknowledgements

Financial support of the Deutsche Forschungsgemeinschaft (DFG) in the Heisenbergprogram (TMG: GE1981/31, GE1981/32) and the Niedersächsisches Ministerium für Wissenschaft und Kultur (MWK) (PH: 74ZN994) is gratefully acknowledged.

References

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Volume 72| Part 3| March 2016| Pages 287-289

doi:10.1107/S2056989016001924

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