The polar phase of Li₂Ge₄O₉ at 298, 150 and 90 K

Dilithium tetra­germanate is ortho­rhom­bic, space group P2₁ca, at 298 K, and is thus in a polar and probably a ferroelectric state. The structure contains two independent Li, four Ge and nine O atoms, all on general positions with site symmetry 1. Three tetra­hedrally coordinated Ge positions form crumpled crankshaft-like chains, forming sheets within the ac plane, and these are inter­connected by the fourth, octa­hedrally coordinated, Ge sites along the b direction. The GeO₄ tetra­hedra and GeO₆ octa­hedra form a three-dimensional framework containing two different cavities, hosting the two 4+1-coordinated Li sites. Cooling to 90 K does not alter the space-group symmetry; the tetra­hedral chains behave as a rigid unit and changes occur mainly within the Li coordination spheres.

S1. Introduction

Li₂Ge₄O₉ is one of nine known phases in the Li₂O–GeO₂ system (Greenberg & Loiacono 1990; Garrault et al., 1973; Murthy & Ip, 1964). The title compound was first described by Wittmann & Modern (1965), who synthesized it by a ceramic sinter­ing route and noted that it cannot be obtained directly by cooling from the melt. Only lattice parameters and possible space-group symmetry (Pcca) were reported for Li₂Ge₄O₉ by Wittmann & Modern (1965); no complete atomic structure determination has been available up to now. Li₂Ge₄O₉ forms a complete solid solution with NaLiGe₄O₉. The structure of the latter compound was determined by Völlenkle et al. (1969) from two-dimensional Weissenberg images, giving only isotropic atomic displacement parameters. It has Pcca symmetry at room temperature (Völlenkle et al., 1969), with [GeO₃]_n chains connected to each other by [GeO₆] o­cta­hedra to form a three-dimensional framework. It is generally assumed that the title compound is isotypic with NaLiGe₄O₉. However, the pure Na₂Ge₄O₉ compound is trigonal, space group P3c1 (Fleet & Muthupari 1998). No information is available on the dependence of symmetry changes on the Na content of these tetra­germanates. This question will be addressed in future studies.

The members of the Li_2-xNa_xGe₄O₉ series with 0 < x < 1.0 are known to exhibit ferroelectric properties (Volnyanskii et al., 2006). LiNaGe₄O₉ has been studied several times and a ferroelectric phase-transition temperature of ~110 K is well established (Wada et al., 1993; Cach et al., 2004). In a neutron diffraction study at 30 and 298 K, Iwata et al. (1998) showed that the ferroelectric phase of LiNaGe₄O₉ has space group P2₁ca at 30 K, while at room temperature the Pcca symmetry was confirmed. With decreasing Na⁺ concentration, the Curie temperature T_c increases monotonically within the Li_2-xNa_xGe₄O₉ series up to 270 K at x ~0.3, while for Li_1.8Na_0.2Ge₄O₉ T_c = 335 K (Volnyanskii et al., 1992). However, for the pure Li₂Ge₄O₉ end member Volnyanskii & Kudzin (1991) report only a ferroelectric–paraelectric phase transition at ~190 K. The crystals used for these measurements were grown by the Czochralski method directly from the melt (Volnyanskii & Kudzin, 1991). It is astonishing that the reported T_c ~190 K in Li₂Ge₄O₉ deviates distinctly from the T_c value extrapolated from Vegard's rule, which would place it well above room temperature. Very recently, Takahashi et al. (2012) investigated Li₂Ge₄O₉ synthesized by a glass–ceramics route at 933 K using in situ observations of Raman scattering and emission spectra between room temperature and ~400 K. They found a heat capacity anomaly and a disappearance of the lowest frequency phonon at ~373 K, pointing to a structural phase transition.

From the above it may be questioned that Li₂Ge₄O₉ shows a ferroelectric phase transition at low temperatures of ~190 K but may still be in the ferroelectric phase at room temperature. The reported anomaly at ~373 K in the Raman scattering spectra (Takahashi et al. 2012) would thus correspond to the correct ferroelectric phase-transition temperature, fulfilling Vegard's rule much better. It may be assumed that the crystals analysed by Volnyanskii & Kudzin (1991) do not correspond to an Li₂Ge₄O₉ composition. Here, we present the first temperature-dependent X-ray diffraction study of Li₂Ge₄O₉ between 90 K and room temperature, which was addressed to give full structural data for the title compound and to clarify the nature of the proposed 190 K transition.

S2. Experimental

S2.1. Synthesis and crystallization

The title compound was obtained as a by-product during experiments to grow an LiAlGe₃O₈ feldspar-type material. Li₂CO₃, Al₂O₃ and GeO₂ in the above [Which?] stoichiometry served as starting materials. One part of the oxide/carbonate mixture and ten parts of a lithium molybdate/vanadate flux (80 wt% Li₂MoO₄, 20 wt% LiVO₃) were heated to 1473 K in a platinum crucible, held at this temperature for 12 h and cooled down to 873 K at a rate of 3 K h^-1. The resulting synthesis batch consisted of transparent idiomorphic re­cta­ngular needles up to 1 mm in length of the title compound, small amounts of glass and a dominant phase of hexagonal flaky habit, not yet identified. Single crystals from this experiment were used for structure determination and refinement.

In a second series of experiments, a polycrystalline sample of Li₂Ge₄O₉ was synthesized using a glass–ceramic sinter­ing route following Takahashi et al. (2012), i.e. melting a stoichiometric mixture of one part Li₂CO₃ plus four parts GeO₂ at 1473 K for 0.5 h, rapid quenching in iced water and crystallization of the glass at 923 K for 5 d. This procedure yields a phase-pure sample of the title compound. Simultaneous thermal analysis (differential thermal analysis/thermogravimetry, DTA/TG) of this polycrystalline material and qualitative high-temperature calorimetric investigation show a clear peak at ~353 K, probably corresponding to the ferro/paraelectric phase transition; at 1209 K a large DTA signal indicates the melting of the title compound (see supplementary material). However, slow cooling of a melt prepared from Li₂CO₃ and GeO₂, from 1373 to 1073 K at a rate of 5 K h^-1, did not yield the title compound, but instead produced a mixture of Li₄Ge₅O₁₂ and Li₂Ge₇O₁₅. The same outcome was obtained when melting pre-synthesized phase-pure Li₂Ge₄O₉ and cooling it under the same conditions as used for the Li₂CO₃—GeO₂ mixture. These findings are in agreement with Wittmann & Modern (1965). We conclude that it seems unrealistic that the single crystals obtained by Volnyanskii & Kudzin (1991) correspond to the composition of the title compound. A reinvestigation of the phase relations in the GeO₂-rich part of the Li₂O–GeO₂ series is highly desirable.

S2.2. Refinement

Crystal data, data collection and structure refinement details are summarized in Table 1. Structure solution and refinement of 298 K intensity data was also tested in space group Pcca, following the model given by Völlenkle et al. (1969), but the refinement only converged to agreement values of wR₂ (all data) = 0.126 and R₁ = 0.0573. Additionally, large and unrealistic anisotropic atomic displacement parameters were found for the O atoms. It might be noted here that, in using the model of Völlenkle et al. (1969), the Li atoms occupy the 8f positions, which are half filled, while the above authors put Na on a 4e position (1/4, 1/2, z). Structure solution and refinement were also tried in space group Pmca, but this failed to give reliable R values. As there is such a distinct difference between the P2₁ca and the Pcca model, with the first one giving excellent agreement factors and reliable anisotropic displacement parameters, it is concluded that the title compound is non-centrosymmetric. This also is in agreement with the proposal that pure Li₂Ge₄O₉ has a ferroelectric phase-transition temperature far above room temperature and that the material studied by Volnyanskii & Kudzin (1991) does not correspond to the composition of the title compound.

S3. Results and discussion

At room temperature, Li₂Ge₄O₉ is orthorhombic, space group P2₁ca, and thus has polar symmetry allowing ferroelectricity. The title compound contains two Li-, four Ge- and nine O-atom positions in the asymmetric unit, all of them on general position 4a, site symmetry 1 (Fig. 1). The structural model presented herein is related to the Pcca symmetry of paraelectric LiNaGe₄O₉ by a [0, 0, 1/4] shift of the unit-cell origin. Atoms Ge2, Ge3 and Ge4 are tetra­hedrally coordinated, with average <Ge—O> distances between 1.754 (2) and 1.758 (2) Å. These three GeO₄ tetra­hedra are connected to each other by common corners to form crumbled crankshaft-like chains running parallel to the a axis within the ac plane (Fig. 2). For these chains, the Ge—O—Ge bond angles range between 125.26 (9) and 128.14 (8)° and the Ge—Ge—Ge angles between 108.00 (9) and 115.45 (9)°. The Ge2O₄ tetra­hedron has a slightly larger polyhedral volume and is more regular in terms of tetra­hedral distortion compared with the other two (Ge3 and Ge4 sites; Table 2). This is in line with the observations of Iwata et al. (1998) and Völlenkle et al. (1969), who also found their Ge1 site (corresponding to Ge2 in this study) to exhibit larger polyhedral volumes and more regularity. The Ge3 and Ge4 sites are very similar in the title compound. These two GeO₄ tetra­hedra are the ones which become equivalent upon the ferroelectric–paraelectric phase transition (Völlenkle et al., 1969). They differ mainly in the connectivity orientation within the [GeO₃]_n chains, rather than in bond lengths and polyhedral distortion. A comparison of the bond lengths and volumes of the GeO₄ tetra­hedra in the title compound with those in NaLiGe₄O₉ shows only small differences, evidence of a minor effect of the substitution of Li⁺ by the larger Na⁺ on the bond topology of the rigid units of GeO₄. Only the polyhedral distortion is somewhat larger in the sodium-bearing compound.

Viewed along [100], a layer-like structure perpendicular to the b axis is evident, in which slabs containing the GeO₄ tetra­hedral chains alternate with slabs built up by the isolated Ge1O₆ o­cta­hedra, and a network of channels is formed parallel to the a and c directions and hosting the Li atoms (Fig. 3a). The Ge1 site is o­cta­hedrally coordinated, with an average <Ge—O> distance of 1.873 (2) Å. The corners of this isolated Ge1O₆ o­cta­hedron are shared with one Ge2, one Ge3 and one Ge4 tetra­hedron of each of the upper and lower slabs of tetra­hedral chains, thereby forming a three-dimensional framework. Thus, each O-atom corner of Ge1O₆ is also common to a tetra­hedral site, and they are additionally bonded to one Li2 and two Li1 sites. The Ge1 o­cta­hedron is remarkably regular, with an o­cta­hedral angle variance OAV of only 7.38°² (Table 2). In NaLiGe₄O₉, the average bond lengths and distortion parameters are very similar to those calculated for the title compound, again indicating that the substitution of Li⁺ by Na⁺ has only a small effect on the Ge sites and structural adjustments occur as rigid-body motions.

Within the Ge-site framework, two different cavities can be identified which host the Li atoms. The smaller one, which becomes evident in the projection along [001] shown in Fig. 3(a), hosts the Li1 atoms. These are 4+1-coordinated, with four Li—O bonds being between 1.867 (5) and 1.959 (5) Å, while the fifth one is 2.215 (4) Å. In a projection along [100], channels along the b axis are evident. These are built up by the larger cavities within the GeO₄–GeO₆ framework hosting the Li2 site. It also shows a 4+1 coordination but is much more distorted, with three Li2—O bond lengths ranging from 2.012 (6) to 2.232 (6) Å and a fourth one of 2.535 (6) Å, while the longest Li2—O bond length is 2.782 (6) Å. Due to the small size of the Li atom and the larger dimension of this cavity, atom Li2 shows a distinct anisotropic atomic displacement under ambient conditions. In NaLiGe₄O₉ this site is occupied by the larger Na⁺ atom. Iwata et al. (1998) observed a splitting of the Na⁺ site at room temperature (Pcca symmetry) along the a axis, with a split distance of 0.38 Å. They also noted a splitting of their Li site (corresponding to the Li1 site of the title compound here) which is even larger (0.48 Å). Völlenkle et al. (1969) also modelled their Li site with a split model, with a split distance of 0.6 (2) Å. At a low temperatures of 34 K, no splitting was observed by Iwata et al. (1998) in their neutron diffraction data, showing P2₁ca symmetry. Thus, they concluded that the ordering of the Na atom in one of the split positions must be the main mechanism for the ferroelectric–paraelectric phase transition and also leads to the generation of the polarization (Iwata et al., 1998). In the title compound, which is ferroelectric with the P2₁ca structure, no split position of the Li1 or Li2 site is observed. The large anisotropic atomic displacement parameters, especially of the Li2 site, decrease with decreasing temperature, which at least confirms the idea of an ordering of cations being responsible for the paraelectric–ferroelectric phase transition. [Fig. 3(b) is not iscussed anywhere - please supply suitable text]

Bond-valence sum calculations (BVS; Brese & O'Keeffe, 1991) show the Li1 site being distinctly overbonded, with S = 1.33 valence units (v.u.), while the Li2 site is underbonded with S = 0.62 v.u.. For the Ge atoms, the o­cta­hedrally coordinated Ge1 site shows overbonding, with S = 4.29 v.u., while the tetra­hedrally coordinated sites Ge2–Ge4 are somewhat underbonded, with S ~3.90, 3.95 and 3.93 v.u., respectively. The valence sums of the O atoms range between 1.89 and 2.11 v.u., with the O atom bonded to the Li2 site also showing slight underbonding.

Decreasing temperature does not alter the space-group symmetry of the title compound down to 90 K. The lattice parameters a and b decrease with T, while c expands; in total, the unit-cell volume decreases. The most prominent shifts in atomic positions are found for the Li1 and Li2 sites, with atomic movements observed predominantly along the y direction, i.e. the Li atoms are brought closer to the layers containing the GeO₄ chains. Generally, during cooling the atoms move almost exclusively in the y direction, the exception being atoms O7, O8 and O9, which show no changes in atomic positions between 298 and 90 K. These are the O atoms which bridge the GeO₄ tetra­hedra to form the crumbled chains. For the Ge1O₄ to Ge3O₄ tetra­hedra there are only very small changes in bond length, which are within one estimated standard deviation (e.s.d.). Also, the inter­connection of the tetra­hedra (Ge—O—Ge and O—O—O bridging angles) changes by only ~0.2° between 90 and 298 K, so the GeO₄ chains behave rigidly with varying temperature. The Ge1O₆ o­cta­hedron is less stiff. While <Ge1—O> is shortened only slightly (Table 2), there are some distinct alterations in individual bond lengths: Ge1—O1 decreases by 0.07 Å from 1.851 (2) to 1.844 (2) Å between 298 K and 90 K, while the Ge1—O4 bond increases by 0.05 Å from 1.867 (2) to 1.872 (2) Å. These two bonds go to the apex atoms of the o­cta­hedron and run approximately in the [110] direction. Thus, their average shortening on cooling is responsible for the decrease in the a and b lattice parameters with decreasing temperature. The bonds within the equatorial plane of the o­cta­hedra all decrease on cooling, thereby decreasing the polyhedral volume by 0.3%. The most distinct alterations in bond topology with decreasing T occur within the Li1 and Li2 oxygen coordination sphere. The Li1—O7 bond decreases by 3.5% from 2.215 (4) to 2.140 (5) Å, shifting atom Li1 closer to the bridging atom O7 between the Ge2 and Ge3 tetra­hedra, and at the same time the Li1—O5 (belonging to the Ge2 site) and Li1—O1 (belonging to the Ge3 site) bonds become somewhat longer towards low T.

For the Li2 site, the long Li2—O7 bond increases with decreasing T by 2.8%, from 2.782 (4) Å at 298 K to 2.862 (5) Å at 90 K, causing atom O7 to move progressively out of the coordination sphere of the Li atom. The Li2—O3 bond also increases, by 0.8% from 2.039 (4) to 2.054 (4) Å. These two bonds connect atom Li2 with a lower lying sheet of GeO₄ tetra­hedra, while the Li2—O2, Li2—O8 and Li2—O9 bonds inter­connect it with a higher lying sheet. The latter bonds all decrease with decreasing T, by 1.7, 1.8 and 3.0%, respectively, and reflect the movement of atom Li2 towards the sheet of GeO₄ tetra­hedra. At low temperature, atom Li2 has three short and one long bond to O atoms. The distinct alterations in bond topology, especially for atom Li2, support the assumption that the Li and Na atoms play an important role during the ferroelectric–paraelectric phase transition.

In conclusion, we have given a full structural description of the title compound, including anisotropic atomic displacement parameters. At room temperature, Li₂Ge₄O₉ crystallizes in the acentric space group P2₁ca, which would allow a ferroelectric state. It should be noted that ferroelectricity has not been evidenced so far, as the paper by Volnyanskii & Kudzin (1991) probably concerns another compound. No phase transition is observed between 298 K and 90 K as suggested by Volnyanskii & Kudzin (1991), supporting the idea that their crystals do not comply the composition of the title compound. The space group of Pcca, tentatively given to the title compound by Wittmann & Modern (1965) on the basis of their powder diffraction data, is not valid at room temperature but corresponds to the symmetry of the paraelectric phase. The latter is stable above ~353 K. In addition to the anomalies in the Raman scattering spectra above 373 K (Takahashi et al., 2012) and a clear observable peak in the heat capacity at 363 K (see supplementary materials), preliminary high-temperature powder X-ray diffraction experiments show changes in the lattice parameters with T around 360 K. This all suggests that the ferroelectric–paraelectric phase transition occurs within this temperature range, although the final proof remains to be given.

Related literature

For related literature, see: Brese & O'Keeffe (1991); Cach et al. (2004); Fleet & Muthupari (1998); Garrault et al. (1973); Greenberg & Loiacono (1990); Iwata et al. (1998); Murthy & Ip (1964); Takahashi et al. (2012); Völlenkle et al. (1969); Volnyanskii & Kudzin (1991); Volnyanskii et al. (1992, 2006); Wada et al. (1993); Wittmann & Modern (1965).

Computing details

For all compounds, data collection: APEX2 (Bruker, 2007); cell refinement: APEX2 (Bruker, 2007); data reduction: APEX2 (Bruker, 2007); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: DIAMOND (Brandenburg, 1999); software used to prepare material for publication: WinGX (Farrugia, 2012).

Figures

	Fig. 1. A view of the asymmetric unit and some symmetry-related atoms of the title compound at 298 K, showing 95% probability displacement ellipsoids and the atomic numbering scheme. [Symmetry codes: (i) 1/2 + x, y, 1/2 - z; (ii) 1/2 + x, 1 + y, 1/2 - z; (iii) 1/2 + x, 2 - y, 1 - z; (iv) x, 1 - y, 1/2 + z; (v) x, 2 - y, 1/2 + z.] [Li1 is green, as per key, but Li2 is orange. Should key be amended? Label Ge1 overlaps bond. Please send revised plot.]
	Fig. 2. A polyhedral representation of the Li2Ge4O9 structure at 298 K in a projection onto the ac plane, displaying the framework of GeO4 tetrahedal chains and GeO6 octahedral sites.
	Fig. 3. A polyhedral representation of the Li2Ge4O9 structure in projections (a) onto the bc plane and (b) onto the ab plane, depicting the channel-like structure hosting the Li1 and Li2 sites.

(laz1_298K_tr) Dilithium tetragermanate

Crystal data

Li2Ge4O9	F(000) = 824
Mr = 448.24	Dx = 4.368 Mg m^−3
Orthorhombic, P21ca	Mo Kα radiation, λ = 0.71073 Å
a = 9.31165 (9) Å	µ = 17.50 mm^−1
b = 4.62854 (5) Å	T = 298 K
c = 15.81663 (16) Å	Needle, colourless
V = 681.69 (2) Å^3	0.14 × 0.08 × 0.07 mm
Z = 4

Data collection

Bruker SMART APEX diffractometer	3036 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.026
rotation, ω scans at four different φ positions	θmax = 36.5°, θmin = 2.6°
Absorption correction: multi-scan (APEX2; Bruker, 2007)	h = −15→15
Tmin = 0.13, Tmax = 0.285	k = −7→7
19496 measured reflections	l = −25→25
3223 independent reflections

Refinement

Refinement on F^2	w = 1/[σ^2(Fo^2) + (0.0253P)^2 + 0.056P] where P = (Fo^2 + 2Fc^2)/3
Least-squares matrix: full	(Δ/σ)max = 0.001
R[F^2 > 2σ(F^2)] = 0.019	Δρmax = 0.71 e Å^−3
wR(F^2) = 0.047	Δρmin = −1.04 e Å^−3
S = 1.06	Extinction correction: SHELXL97 (Sheldrick, 2008)
3223 reflections	Extinction coefficient: 0.0056 (2)
138 parameters	Absolute structure: Flack (1983), with how many Friedel pairs?
1 restraint	Absolute structure parameter: 0.357 (11)

Special details

Geometry. All s.u.'s (except the s.u. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell s.u.'s are taken into account individually in the estimation of s.u.'s in distances, angles and torsion angles; correlations between s.u.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell s.u.'s is used for estimating s.u.'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 > 2σ(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
Li1	0.4691 (5)	0.4607 (8)	0.2632 (3)	0.0180 (9)
Li2	0.2705 (6)	0.5680 (12)	0.4751 (3)	0.0336 (11)
Ge1	0.23524 (5)	0.48943 (3)	0.155695 (10)	0.00565 (4)
Ge2	0.23430 (5)	0.99363 (4)	0.295703 (10)	0.00620 (4)
Ge3	0.52539 (3)	1.00411 (3)	0.402028 (16)	0.00629 (6)
Ge4	0.44481 (2)	1.01849 (4)	0.594728 (15)	0.00614 (6)
O1	0.0720 (2)	0.7169 (3)	0.16179 (9)	0.0079 (2)
O2	0.1521 (2)	0.2624 (3)	0.06926 (9)	0.0090 (3)
O3	0.32285 (19)	0.7072 (3)	0.07094 (9)	0.0084 (3)
O4	0.3963 (2)	0.2512 (3)	0.16448 (10)	0.0089 (3)
O5	0.31808 (19)	0.7155 (3)	0.24140 (10)	0.0086 (3)
O6	0.1451 (2)	0.2534 (3)	0.23714 (9)	0.0092 (3)
O7	0.36959 (18)	1.1686 (3)	0.35739 (9)	0.0100 (3)
O8	0.11424 (19)	0.8440 (3)	0.37173 (9)	0.0122 (3)
O9	0.46492 (18)	0.8406 (3)	0.49643 (9)	0.0118 (3)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Li1	0.009 (2)	0.0203 (16)	0.025 (3)	0.0022 (14)	−0.0057 (17)	−0.0064 (15)
Li2	0.033 (3)	0.038 (2)	0.030 (3)	0.000 (2)	0.0113 (19)	0.013 (2)
Ge1	0.00539 (8)	0.00598 (7)	0.00558 (8)	0.00004 (8)	−0.00023 (11)	0.00001 (6)
Ge2	0.00602 (7)	0.00644 (7)	0.00615 (8)	0.00071 (6)	−0.00026 (12)	0.00023 (5)
Ge3	0.00608 (13)	0.00665 (12)	0.00616 (12)	0.00006 (6)	0.00031 (9)	−0.00052 (5)
Ge4	0.00623 (13)	0.00660 (10)	0.00560 (11)	−0.00001 (12)	0.00019 (10)	0.00058 (5)
O1	0.0059 (7)	0.0090 (6)	0.0087 (6)	0.0017 (4)	0.0007 (5)	0.0028 (4)
O2	0.0096 (7)	0.0093 (6)	0.0080 (6)	−0.0032 (5)	−0.0006 (5)	−0.0007 (4)
O3	0.0104 (7)	0.0092 (6)	0.0057 (6)	−0.0029 (5)	−0.0005 (5)	0.0002 (4)
O4	0.0085 (7)	0.0100 (6)	0.0082 (6)	0.0021 (5)	−0.0001 (5)	−0.0011 (4)
O5	0.0077 (7)	0.0089 (5)	0.0093 (6)	0.0015 (5)	−0.0014 (5)	−0.0033 (4)
O6	0.0074 (7)	0.0098 (6)	0.0105 (7)	0.0008 (4)	0.0012 (5)	0.0034 (4)
O7	0.0078 (6)	0.0095 (6)	0.0127 (7)	0.0015 (4)	−0.0034 (5)	−0.0017 (5)
O8	0.0093 (6)	0.0134 (6)	0.0141 (7)	0.0033 (5)	0.0049 (5)	0.0046 (5)
O9	0.0184 (8)	0.0093 (5)	0.0077 (5)	−0.0017 (5)	0.0047 (6)	−0.0008 (4)

Geometric parameters (Å, º)

Li1—O5	1.867 (5)	Ge1—O2	1.8900 (14)
Li1—O6^i	1.899 (5)	Ge2—O6^iv	1.7303 (15)
Li1—O1^i	1.932 (5)	Ge2—O5	1.7332 (14)
Li1—O4	1.959 (5)	Ge2—O8	1.7820 (16)
Li1—O7^ii	2.215 (4)	Ge2—O7	1.7874 (16)
Li2—O2^iii	2.012 (6)	Ge3—O1^i	1.7248 (13)
Li2—O3^iii	2.039 (5)	Ge3—O2^v	1.7402 (16)
Li2—O9	2.232 (6)	Ge3—O9	1.7661 (15)
Li2—O8	2.535 (6)	Ge3—O7	1.7841 (17)
Ge1—O1	1.8512 (17)	Ge4—O4^iii	1.7259 (14)
Ge1—O3	1.8651 (14)	Ge4—O3^vi	1.7445 (15)
Ge1—O4	1.8671 (17)	Ge4—O9	1.7691 (14)
Ge1—O5	1.8780 (15)	Ge4—O8^vii	1.7820 (17)
Ge1—O6	1.8861 (15)
O5—Li1—O6^i	165.6 (3)	O5—Ge1—O2	179.87 (9)
O5—Li1—O1^i	95.71 (18)	O6—Ge1—O2	89.41 (7)
O6^i—Li1—O1^i	83.3 (2)	O6^iv—Ge2—O5	117.84 (6)
O5—Li1—O4	84.5 (2)	O6^iv—Ge2—O8	109.27 (9)
O6^i—Li1—O4	92.65 (18)	O5—Ge2—O8	109.15 (7)
O1^i—Li1—O4	164.8 (2)	O6^iv—Ge2—O7	108.40 (7)
O5—Li1—O7^ii	101.2 (2)	O5—Ge2—O7	106.85 (9)
O6^i—Li1—O7^ii	93.11 (18)	O8—Ge2—O7	104.48 (7)
O1^i—Li1—O7^ii	99.7 (2)	O1^i—Ge3—O2^v	120.76 (10)
O4—Li1—O7^ii	95.10 (17)	O1^i—Ge3—O9	104.17 (6)
O2^iii—Li2—O3^iii	79.91 (19)	O2^v—Ge3—O9	106.85 (6)
O2^iii—Li2—O9	96.4 (3)	O1^i—Ge3—O7	107.58 (7)
O3^iii—Li2—O9	92.7 (2)	O2^v—Ge3—O7	111.19 (7)
O2^iii—Li2—O8	88.1 (2)	O9—Ge3—O7	104.96 (8)
O3^iii—Li2—O8	158.7 (2)	O4^iii—Ge4—O3^vi	119.60 (9)
O9—Li2—O8	106.1 (2)	O4^iii—Ge4—O9	104.66 (7)
O1—Ge1—O3	95.12 (6)	O3^vi—Ge4—O9	102.59 (7)
O1—Ge1—O4	172.57 (5)	O4^iii—Ge4—O8^vii	107.42 (7)
O3—Ge1—O4	91.22 (8)	O3^vi—Ge4—O8^vii	112.37 (7)
O1—Ge1—O5	89.02 (6)	O9—Ge4—O8^vii	109.52 (8)
O3—Ge1—O5	92.18 (7)	Ge3^viii—O1—Ge1	127.92 (9)
O4—Ge1—O5	86.86 (7)	Ge3^ix—O2—Ge1	118.09 (8)
O1—Ge1—O6	85.89 (7)	Ge4^x—O3—Ge1	121.54 (8)
O3—Ge1—O6	176.94 (6)	Ge4^xi—O4—Ge1	126.13 (9)
O4—Ge1—O6	87.97 (7)	Ge2—O5—Ge1	125.92 (10)
O5—Ge1—O6	90.72 (5)	Ge2^ii—O6—Ge1	123.67 (11)
O1—Ge1—O2	91.01 (8)	Ge3—O7—Ge2	126.56 (8)
O3—Ge1—O2	87.69 (5)	Ge2—O8—Ge4^xii	128.14 (8)
O4—Ge1—O2	93.12 (7)	Ge3—O9—Ge4	125.27 (7)

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

(laz1_150K_tr) Dilithium tetragermanate

Crystal data

Li2Ge4O9	F(000) = 824
Mr = 448.24	Dx = 4.367 Mg m^−3
Orthorhombic, P21ca	Mo Kα radiation, λ = 0.71073 Å
a = 9.3081 (6) Å	µ = 17.50 mm^−1
b = 4.6267 (3) Å	T = 150 K
c = 15.8298 (11) Å	Needle, colourless
V = 681.72 (8) Å^3	0.14 × 0.08 × 0.07 mm
Z = 4

Data collection

Bruker SMART APEX diffractometer	1657 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.023
rotation, ω scans at four different φ positions	θmax = 28.8°, θmin = 2.6°
Absorption correction: multi-scan (APEX2; Bruker, 2007)	h = −12→12
Tmin = 0.21, Tmax = 0.355	k = −6→6
8631 measured reflections	l = −21→21
1703 independent reflections

Refinement

Refinement on F^2	w = 1/[σ^2(Fo^2) + (0.0172P)^2 + 0.1175P] where P = (Fo^2 + 2Fc^2)/3
Least-squares matrix: full	(Δ/σ)max = 0.001
R[F^2 > 2σ(F^2)] = 0.015	Δρmax = 0.48 e Å^−3
wR(F^2) = 0.037	Δρmin = −0.69 e Å^−3
S = 1.13	Extinction correction: SHELXL97 (Sheldrick, 2008)
1703 reflections	Extinction coefficient: 0.00163 (16)
138 parameters	Absolute structure: Flack (1983), with how many Friedel pairs?
1 restraint	Absolute structure parameter: 0.635 (15)

Special details

Geometry. All s.u.'s (except the s.u. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell s.u.'s are taken into account individually in the estimation of s.u.'s in distances, angles and torsion angles; correlations between s.u.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell s.u.'s is used for estimating s.u.'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 > 2σ(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
Li1	0.4677 (7)	0.4512 (10)	0.2644 (4)	0.0125 (12)
Li2	0.2706 (6)	0.5785 (13)	0.4764 (4)	0.0222 (13)
Ge1	0.23544 (8)	0.48602 (5)	0.155881 (15)	0.00472 (7)
Ge2	0.23406 (9)	0.99080 (5)	0.295800 (15)	0.00504 (7)
Ge3	0.52526 (4)	1.00156 (5)	0.40174 (3)	0.00538 (10)
Ge4	0.44492 (3)	1.02095 (6)	0.59443 (2)	0.00508 (10)
O1	0.0718 (3)	0.7110 (4)	0.16157 (12)	0.0064 (4)
O2	0.1530 (3)	0.2581 (4)	0.06947 (13)	0.0073 (4)
O3	0.3234 (3)	0.7022 (4)	0.07140 (14)	0.0071 (4)
O4	0.3968 (3)	0.2469 (4)	0.16474 (14)	0.0071 (4)
O5	0.3170 (3)	0.7109 (4)	0.24156 (14)	0.0072 (4)
O6	0.1449 (3)	0.2489 (4)	0.23675 (14)	0.0074 (4)
O7	0.3709 (3)	1.1674 (4)	0.35604 (13)	0.0070 (4)
O8	0.1162 (3)	0.8447 (4)	0.37349 (13)	0.0094 (4)
O9	0.4616 (2)	0.8421 (3)	0.49602 (13)	0.0081 (4)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Li1	0.006 (3)	0.015 (2)	0.017 (4)	−0.001 (2)	−0.001 (2)	−0.001 (2)
Li2	0.020 (3)	0.027 (3)	0.020 (3)	−0.002 (2)	0.012 (2)	0.012 (2)
Ge1	0.00448 (13)	0.00538 (11)	0.00431 (13)	−0.00012 (16)	0.0002 (2)	−0.00008 (9)
Ge2	0.00473 (12)	0.00570 (11)	0.00468 (13)	0.00034 (13)	−0.0005 (2)	0.00009 (9)
Ge3	0.0049 (2)	0.00607 (18)	0.0051 (2)	−0.00011 (10)	0.00016 (17)	−0.00024 (9)
Ge4	0.0051 (2)	0.00578 (16)	0.0043 (2)	0.0002 (2)	0.00010 (18)	0.00018 (9)
O1	0.0057 (12)	0.0070 (8)	0.0065 (10)	0.0035 (8)	0.0000 (8)	0.0013 (7)
O2	0.0072 (11)	0.0087 (8)	0.0060 (10)	−0.0010 (8)	−0.0004 (8)	−0.0014 (7)
O3	0.0078 (12)	0.0073 (8)	0.0062 (10)	−0.0008 (8)	−0.0004 (8)	−0.0001 (7)
O4	0.0077 (11)	0.0075 (9)	0.0062 (11)	0.0010 (8)	−0.0003 (8)	−0.0018 (7)
O5	0.0083 (12)	0.0065 (8)	0.0066 (10)	0.0010 (8)	−0.0004 (8)	−0.0014 (7)
O6	0.0054 (11)	0.0073 (8)	0.0094 (11)	0.0014 (7)	−0.0003 (8)	0.0038 (7)
O7	0.0040 (10)	0.0082 (9)	0.0089 (11)	0.0002 (7)	−0.0017 (8)	−0.0005 (7)
O8	0.0075 (11)	0.0097 (9)	0.0109 (11)	0.0010 (7)	0.0017 (9)	0.0028 (8)
O9	0.0094 (12)	0.0094 (8)	0.0056 (9)	−0.0005 (8)	0.0008 (9)	−0.0004 (7)

Geometric parameters (Å, º)

Li1—O5	1.881 (6)	Ge1—O2	1.890 (2)
Li1—O6^i	1.897 (6)	Ge2—O6^iv	1.728 (2)
Li1—O1^i	1.939 (6)	Ge2—O5	1.735 (2)
Li1—O4	1.953 (6)	Ge2—O8	1.781 (2)
Li1—O7^ii	2.155 (5)	Ge2—O7	1.789 (2)
Li2—O2^iii	1.985 (7)	Ge3—O1^i	1.732 (2)
Li2—O3^iii	2.047 (6)	Ge3—O2^v	1.741 (2)
Li2—O9	2.178 (6)	Ge3—O9	1.767 (2)
Li2—O8	2.497 (6)	Ge3—O7	1.782 (2)
Ge1—O1	1.847 (3)	Ge4—O4^iii	1.725 (2)
Ge1—O3	1.860 (2)	Ge4—O3^vi	1.747 (2)
Ge1—O5	1.871 (2)	Ge4—O9	1.771 (2)
Ge1—O4	1.871 (3)	Ge4—O8^vii	1.785 (2)
Ge1—O6	1.885 (2)
O5—Li1—O6^i	164.1 (3)	O4—Ge1—O6	87.92 (9)
O5—Li1—O1^i	95.3 (2)	O1—Ge1—O2	90.86 (12)
O6^i—Li1—O1^i	82.9 (3)	O3—Ge1—O2	87.61 (7)
O5—Li1—O4	84.4 (3)	O5—Ge1—O2	179.87 (9)
O6^i—Li1—O4	92.7 (2)	O4—Ge1—O2	92.88 (9)
O1^i—Li1—O4	163.2 (3)	O6—Ge1—O2	89.16 (10)
O5—Li1—O7^ii	101.9 (3)	O6^iv—Ge2—O5	117.49 (8)
O6^i—Li1—O7^ii	94.0 (2)	O6^iv—Ge2—O8	109.88 (13)
O1^i—Li1—O7^ii	100.3 (3)	O5—Ge2—O8	109.42 (9)
O4—Li1—O7^ii	96.2 (2)	O6^iv—Ge2—O7	108.33 (9)
O2^iii—Li2—O3^iii	80.1 (2)	O5—Ge2—O7	106.73 (12)
O2^iii—Li2—O9	97.5 (3)	O8—Ge2—O7	104.11 (10)
O3^iii—Li2—O9	93.1 (3)	O1^i—Ge3—O2^v	120.65 (14)
O2^iii—Li2—O8	88.8 (2)	O1^i—Ge3—O9	104.39 (9)
O3^iii—Li2—O8	158.5 (3)	O2^v—Ge3—O9	107.00 (9)
O9—Li2—O8	106.7 (2)	O1^i—Ge3—O7	107.52 (11)
O1—Ge1—O3	95.44 (9)	O2^v—Ge3—O7	111.31 (9)
O1—Ge1—O5	89.20 (9)	O9—Ge3—O7	104.62 (11)
O3—Ge1—O5	92.50 (11)	O4^iii—Ge4—O3^vi	119.56 (13)
O1—Ge1—O4	172.62 (8)	O4^iii—Ge4—O9	104.76 (9)
O3—Ge1—O4	91.06 (12)	O3^vi—Ge4—O9	102.46 (10)
O5—Ge1—O4	87.04 (11)	O4^iii—Ge4—O8^vii	107.36 (11)
O1—Ge1—O6	85.78 (11)	O3^vi—Ge4—O8^vii	112.49 (9)
O3—Ge1—O6	176.56 (9)	O9—Ge4—O8^vii	109.54 (11)
O5—Ge1—O6	90.73 (8)

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

(laz1_90k_tr) Dilithium tetragermanate

Crystal data

Li2Ge4O9	F(000) = 824
Mr = 448.24	Dx = 4.369 Mg m^−3
Orthorhombic, P21ca	Mo Kα radiation, λ = 0.71073 Å
a = 9.3044 (5) Å	µ = 17.50 mm^−1
b = 4.6253 (2) Å	T = 90 K
c = 15.8331 (8) Å	Needle, colourless
V = 681.39 (6) Å^3	0.14 × 0.08 × 0.07 mm
Z = 4

Data collection

Bruker SMART APEX diffractometer	1664 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.023
rotation, ω scans at four different φ positions	θmax = 28.8°, θmin = 2.6°
Absorption correction: multi-scan (APEX2; Bruker, 2007)	h = −12→12
Tmin = 0.21, Tmax = 0.355	k = −6→6
9727 measured reflections	l = −21→21
1705 independent reflections

Refinement

Refinement on F^2	w = 1/[σ^2(Fo^2) + (0.0179P)^2 + 0.329P] where P = (Fo^2 + 2Fc^2)/3
Least-squares matrix: full	(Δ/σ)max = 0.001
R[F^2 > 2σ(F^2)] = 0.015	Δρmax = 0.57 e Å^−3
wR(F^2) = 0.038	Δρmin = −0.74 e Å^−3
S = 1.13	Extinction correction: SHELXL97 (Sheldrick, 2008)
1705 reflections	Extinction coefficient: 0.00155 (15)
138 parameters	Absolute structure: Flack (1983), with how many Friedel pairs?
1 restraint	Absolute structure parameter: 0.623 (14)

Special details

Geometry. All s.u.'s (except the s.u. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell s.u.'s are taken into account individually in the estimation of s.u.'s in distances, angles and torsion angles; correlations between s.u.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell s.u.'s is used for estimating s.u.'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 > 2σ(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
Li1	0.4675 (6)	0.4497 (10)	0.2646 (3)	0.0109 (11)
Li2	0.2706 (6)	0.5814 (13)	0.4764 (4)	0.0197 (12)
Ge1	0.23525 (8)	0.48544 (5)	0.155922 (15)	0.00427 (7)
Ge2	0.23398 (8)	0.99032 (5)	0.295855 (15)	0.00452 (7)
Ge3	0.52529 (4)	1.00110 (5)	0.40166 (2)	0.00486 (10)
Ge4	0.44493 (3)	1.02143 (6)	0.59436 (2)	0.00451 (9)
O1	0.0719 (3)	0.7104 (4)	0.16149 (12)	0.0061 (4)
O2	0.1534 (3)	0.2577 (4)	0.06946 (13)	0.0069 (4)
O3	0.3236 (3)	0.7020 (4)	0.07130 (13)	0.0060 (4)
O4	0.3967 (3)	0.2460 (4)	0.16485 (14)	0.0066 (4)
O5	0.3172 (3)	0.7106 (4)	0.24166 (14)	0.0066 (4)
O6	0.1444 (3)	0.2480 (4)	0.23671 (13)	0.0069 (4)
O7	0.3712 (3)	1.1678 (4)	0.35565 (12)	0.0062 (4)
O8	0.1164 (3)	0.8445 (4)	0.37343 (13)	0.0077 (4)
O9	0.4611 (2)	0.8423 (3)	0.49598 (13)	0.0077 (4)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Li1	0.005 (3)	0.0114 (19)	0.017 (3)	−0.003 (2)	0.003 (2)	−0.002 (2)
Li2	0.016 (3)	0.024 (3)	0.019 (3)	−0.002 (2)	0.008 (2)	0.010 (2)
Ge1	0.00438 (13)	0.00469 (11)	0.00376 (13)	−0.00020 (16)	−0.00032 (19)	0.00000 (9)
Ge2	0.00452 (12)	0.00510 (11)	0.00393 (13)	0.00020 (13)	−0.0001 (2)	0.00006 (9)
Ge3	0.0043 (2)	0.00525 (18)	0.0050 (2)	−0.00006 (10)	−0.00016 (16)	−0.00012 (9)
Ge4	0.0051 (2)	0.00506 (16)	0.00340 (19)	0.0002 (2)	0.00035 (17)	0.00023 (9)
O1	0.0060 (12)	0.0063 (8)	0.0061 (10)	0.0017 (7)	0.0007 (8)	0.0009 (7)
O2	0.0067 (11)	0.0078 (8)	0.0062 (10)	−0.0011 (7)	0.0001 (8)	−0.0005 (7)
O3	0.0058 (11)	0.0063 (8)	0.0057 (10)	−0.0009 (7)	−0.0005 (8)	0.0004 (7)
O4	0.0065 (11)	0.0069 (9)	0.0063 (10)	0.0015 (8)	0.0001 (7)	−0.0020 (7)
O5	0.0063 (12)	0.0069 (8)	0.0066 (10)	0.0008 (8)	0.0004 (8)	−0.0012 (7)
O6	0.0063 (11)	0.0063 (8)	0.0082 (11)	0.0003 (7)	0.0003 (8)	0.0029 (7)
O7	0.0042 (10)	0.0073 (9)	0.0072 (11)	0.0000 (7)	−0.0007 (8)	−0.0019 (7)
O8	0.0068 (11)	0.0087 (9)	0.0075 (10)	0.0008 (7)	0.0024 (8)	0.0018 (7)
O9	0.0083 (12)	0.0091 (8)	0.0056 (9)	−0.0027 (8)	0.0015 (9)	−0.0001 (7)

Geometric parameters (Å, º)

Li1—O5	1.883 (6)	Ge1—O2	1.888 (2)
Li1—O6^i	1.892 (6)	Ge2—O6^iv	1.729 (2)
Li1—O1^i	1.941 (6)	Ge2—O5	1.735 (2)
Li1—O4	1.954 (6)	Ge2—O8	1.777 (2)
Li1—O7^ii	2.140 (5)	Ge2—O7	1.789 (2)
Li2—O2^iii	1.978 (6)	Ge3—O1^i	1.731 (2)
Li2—O3^iii	2.054 (6)	Ge3—O2^v	1.743 (2)
Li2—O9	2.166 (6)	Ge3—O9	1.768 (2)
Li2—O8	2.490 (6)	Ge3—O7	1.783 (2)
Ge1—O1	1.844 (3)	Ge4—O4^iii	1.725 (2)
Ge1—O3	1.864 (2)	Ge4—O3^vi	1.744 (2)
Ge1—O4	1.872 (2)	Ge4—O9	1.771 (2)
Ge1—O5	1.873 (2)	Ge4—O8^vii	1.786 (2)
Ge1—O6	1.886 (2)
O5—Li1—O6^i	163.8 (3)	O5—Ge1—O6	90.83 (8)
O5—Li1—O1^i	95.2 (2)	O1—Ge1—O2	90.98 (11)
O6^i—Li1—O1^i	83.0 (3)	O3—Ge1—O2	87.51 (7)
O5—Li1—O4	84.4 (3)	O4—Ge1—O2	92.76 (9)
O6^i—Li1—O4	92.7 (2)	O5—Ge1—O2	179.75 (13)
O1^i—Li1—O4	162.9 (3)	O6—Ge1—O2	89.21 (10)
O5—Li1—O7^ii	102.1 (2)	O6^iv—Ge2—O5	117.45 (8)
O6^i—Li1—O7^ii	94.1 (2)	O6^iv—Ge2—O8	109.83 (13)
O1^i—Li1—O7^ii	100.5 (3)	O5—Ge2—O8	109.47 (9)
O4—Li1—O7^ii	96.3 (2)	O6^iv—Ge2—O7	108.31 (9)
O2^iii—Li2—O3^iii	80.1 (2)	O5—Ge2—O7	106.58 (12)
O2^iii—Li2—O9	97.7 (3)	O8—Ge2—O7	104.33 (10)
O3^iii—Li2—O9	93.1 (2)	O1^i—Ge3—O2^v	120.61 (14)
O2^iii—Li2—O8	89.2 (2)	O1^i—Ge3—O9	104.46 (9)
O3^iii—Li2—O8	158.4 (3)	O2^v—Ge3—O9	107.00 (9)
O9—Li2—O8	107.0 (2)	O1^i—Ge3—O7	107.53 (10)
O1—Ge1—O3	95.44 (9)	O2^v—Ge3—O7	111.27 (9)
O1—Ge1—O4	172.65 (8)	O9—Ge3—O7	104.65 (11)
O3—Ge1—O4	91.04 (11)	O4^iii—Ge4—O3^vi	119.52 (13)
O1—Ge1—O5	89.27 (9)	O4^iii—Ge4—O9	104.82 (9)
O3—Ge1—O5	92.44 (10)	O3^vi—Ge4—O9	102.35 (9)
O4—Ge1—O5	86.99 (11)	O4^iii—Ge4—O8^vii	107.24 (11)
O1—Ge1—O6	85.81 (11)	O3^vi—Ge4—O8^vii	112.54 (9)
O3—Ge1—O6	176.51 (9)	O9—Ge4—O8^vii	109.74 (11)
O4—Ge1—O6	87.92 (10)

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