Supporting information
Crystallographic Information File (CIF) https://doi.org/10.1107/S0108270113025110/ku3106sup1.cif | |
Structure factor file (CIF format) https://doi.org/10.1107/S0108270113025110/ku3106laz1_298K_trsup2.hkl | |
Structure factor file (CIF format) https://doi.org/10.1107/S0108270113025110/ku3106laz1_150K_trsup3.hkl | |
Structure factor file (CIF format) https://doi.org/10.1107/S0108270113025110/ku3106laz1_90k_trsup4.hkl | |
Portable Document Format (PDF) file https://doi.org/10.1107/S0108270113025110/ku3106sup5.pdf | |
Portable Document Format (PDF) file https://doi.org/10.1107/S0108270113025110/ku3106sup6.pdf |
CCDC references: 960142; 960143; 960144
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 Li2-xNaxGe4O9 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 Tc increases monotonically within the Li2-xNaxGe4O9 series up to 270 K at x ~0.3, while for Li1.8Na0.2Ge4O9 Tc = 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 Tc ~190 K in Li2Ge4O9 deviates distinctly from the Tc 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.
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.
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.
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.
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).
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) Å3 | 0.14 × 0.08 × 0.07 mm |
Z = 4 |
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 on F2 | w = 1/[σ2(Fo2) + (0.0253P)2 + 0.056P] where P = (Fo2 + 2Fc2)/3 |
Least-squares matrix: full | (Δ/σ)max = 0.001 |
R[F2 > 2σ(F2)] = 0.019 | Δρmax = 0.71 e Å−3 |
wR(F2) = 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) |
Li2Ge4O9 | V = 681.69 (2) Å3 |
Mr = 448.24 | Z = 4 |
Orthorhombic, P21ca | Mo Kα radiation |
a = 9.31165 (9) Å | µ = 17.50 mm−1 |
b = 4.62854 (5) Å | T = 298 K |
c = 15.81663 (16) Å | 0.14 × 0.08 × 0.07 mm |
Bruker SMART APEX diffractometer | 3223 independent reflections |
Absorption correction: multi-scan (APEX2; Bruker, 2007) | 3036 reflections with I > 2σ(I) |
Tmin = 0.13, Tmax = 0.285 | Rint = 0.026 |
19496 measured reflections |
R[F2 > 2σ(F2)] = 0.019 | 1 restraint |
wR(F2) = 0.047 | Δρmax = 0.71 e Å−3 |
S = 1.06 | Δρmin = −1.04 e Å−3 |
3223 reflections | Absolute structure: Flack (1983), with how many Friedel pairs? |
138 parameters | Absolute structure parameter: 0.357 (11) |
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. |
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) |
U11 | U22 | U33 | U12 | U13 | U23 | |
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) |
Li1—O5 | 1.867 (5) | Ge1—O2 | 1.8900 (14) |
Li1—O6i | 1.899 (5) | Ge2—O6iv | 1.7303 (15) |
Li1—O1i | 1.932 (5) | Ge2—O5 | 1.7332 (14) |
Li1—O4 | 1.959 (5) | Ge2—O8 | 1.7820 (16) |
Li1—O7ii | 2.215 (4) | Ge2—O7 | 1.7874 (16) |
Li2—O2iii | 2.012 (6) | Ge3—O1i | 1.7248 (13) |
Li2—O3iii | 2.039 (5) | Ge3—O2v | 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—O4iii | 1.7259 (14) |
Ge1—O3 | 1.8651 (14) | Ge4—O3vi | 1.7445 (15) |
Ge1—O4 | 1.8671 (17) | Ge4—O9 | 1.7691 (14) |
Ge1—O5 | 1.8780 (15) | Ge4—O8vii | 1.7820 (17) |
Ge1—O6 | 1.8861 (15) | ||
O5—Li1—O6i | 165.6 (3) | O5—Ge1—O2 | 179.87 (9) |
O5—Li1—O1i | 95.71 (18) | O6—Ge1—O2 | 89.41 (7) |
O6i—Li1—O1i | 83.3 (2) | O6iv—Ge2—O5 | 117.84 (6) |
O5—Li1—O4 | 84.5 (2) | O6iv—Ge2—O8 | 109.27 (9) |
O6i—Li1—O4 | 92.65 (18) | O5—Ge2—O8 | 109.15 (7) |
O1i—Li1—O4 | 164.8 (2) | O6iv—Ge2—O7 | 108.40 (7) |
O5—Li1—O7ii | 101.2 (2) | O5—Ge2—O7 | 106.85 (9) |
O6i—Li1—O7ii | 93.11 (18) | O8—Ge2—O7 | 104.48 (7) |
O1i—Li1—O7ii | 99.7 (2) | O1i—Ge3—O2v | 120.76 (10) |
O4—Li1—O7ii | 95.10 (17) | O1i—Ge3—O9 | 104.17 (6) |
O2iii—Li2—O3iii | 79.91 (19) | O2v—Ge3—O9 | 106.85 (6) |
O2iii—Li2—O9 | 96.4 (3) | O1i—Ge3—O7 | 107.58 (7) |
O3iii—Li2—O9 | 92.7 (2) | O2v—Ge3—O7 | 111.19 (7) |
O2iii—Li2—O8 | 88.1 (2) | O9—Ge3—O7 | 104.96 (8) |
O3iii—Li2—O8 | 158.7 (2) | O4iii—Ge4—O3vi | 119.60 (9) |
O9—Li2—O8 | 106.1 (2) | O4iii—Ge4—O9 | 104.66 (7) |
O1—Ge1—O3 | 95.12 (6) | O3vi—Ge4—O9 | 102.59 (7) |
O1—Ge1—O4 | 172.57 (5) | O4iii—Ge4—O8vii | 107.42 (7) |
O3—Ge1—O4 | 91.22 (8) | O3vi—Ge4—O8vii | 112.37 (7) |
O1—Ge1—O5 | 89.02 (6) | O9—Ge4—O8vii | 109.52 (8) |
O3—Ge1—O5 | 92.18 (7) | Ge3viii—O1—Ge1 | 127.92 (9) |
O4—Ge1—O5 | 86.86 (7) | Ge3ix—O2—Ge1 | 118.09 (8) |
O1—Ge1—O6 | 85.89 (7) | Ge4x—O3—Ge1 | 121.54 (8) |
O3—Ge1—O6 | 176.94 (6) | Ge4xi—O4—Ge1 | 126.13 (9) |
O4—Ge1—O6 | 87.97 (7) | Ge2—O5—Ge1 | 125.92 (10) |
O5—Ge1—O6 | 90.72 (5) | Ge2ii—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—Ge4xii | 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. |
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) Å3 | 0.14 × 0.08 × 0.07 mm |
Z = 4 |
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 on F2 | w = 1/[σ2(Fo2) + (0.0172P)2 + 0.1175P] where P = (Fo2 + 2Fc2)/3 |
Least-squares matrix: full | (Δ/σ)max = 0.001 |
R[F2 > 2σ(F2)] = 0.015 | Δρmax = 0.48 e Å−3 |
wR(F2) = 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) |
Li2Ge4O9 | V = 681.72 (8) Å3 |
Mr = 448.24 | Z = 4 |
Orthorhombic, P21ca | Mo Kα radiation |
a = 9.3081 (6) Å | µ = 17.50 mm−1 |
b = 4.6267 (3) Å | T = 150 K |
c = 15.8298 (11) Å | 0.14 × 0.08 × 0.07 mm |
Bruker SMART APEX diffractometer | 1703 independent reflections |
Absorption correction: multi-scan (APEX2; Bruker, 2007) | 1657 reflections with I > 2σ(I) |
Tmin = 0.21, Tmax = 0.355 | Rint = 0.023 |
8631 measured reflections |
R[F2 > 2σ(F2)] = 0.015 | 1 restraint |
wR(F2) = 0.037 | Δρmax = 0.48 e Å−3 |
S = 1.13 | Δρmin = −0.69 e Å−3 |
1703 reflections | Absolute structure: Flack (1983), with how many Friedel pairs? |
138 parameters | Absolute structure parameter: 0.635 (15) |
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. |
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) |
U11 | U22 | U33 | U12 | U13 | U23 | |
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) |
Li1—O5 | 1.881 (6) | Ge1—O2 | 1.890 (2) |
Li1—O6i | 1.897 (6) | Ge2—O6iv | 1.728 (2) |
Li1—O1i | 1.939 (6) | Ge2—O5 | 1.735 (2) |
Li1—O4 | 1.953 (6) | Ge2—O8 | 1.781 (2) |
Li1—O7ii | 2.155 (5) | Ge2—O7 | 1.789 (2) |
Li2—O2iii | 1.985 (7) | Ge3—O1i | 1.732 (2) |
Li2—O3iii | 2.047 (6) | Ge3—O2v | 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—O4iii | 1.725 (2) |
Ge1—O3 | 1.860 (2) | Ge4—O3vi | 1.747 (2) |
Ge1—O5 | 1.871 (2) | Ge4—O9 | 1.771 (2) |
Ge1—O4 | 1.871 (3) | Ge4—O8vii | 1.785 (2) |
Ge1—O6 | 1.885 (2) | ||
O5—Li1—O6i | 164.1 (3) | O4—Ge1—O6 | 87.92 (9) |
O5—Li1—O1i | 95.3 (2) | O1—Ge1—O2 | 90.86 (12) |
O6i—Li1—O1i | 82.9 (3) | O3—Ge1—O2 | 87.61 (7) |
O5—Li1—O4 | 84.4 (3) | O5—Ge1—O2 | 179.87 (9) |
O6i—Li1—O4 | 92.7 (2) | O4—Ge1—O2 | 92.88 (9) |
O1i—Li1—O4 | 163.2 (3) | O6—Ge1—O2 | 89.16 (10) |
O5—Li1—O7ii | 101.9 (3) | O6iv—Ge2—O5 | 117.49 (8) |
O6i—Li1—O7ii | 94.0 (2) | O6iv—Ge2—O8 | 109.88 (13) |
O1i—Li1—O7ii | 100.3 (3) | O5—Ge2—O8 | 109.42 (9) |
O4—Li1—O7ii | 96.2 (2) | O6iv—Ge2—O7 | 108.33 (9) |
O2iii—Li2—O3iii | 80.1 (2) | O5—Ge2—O7 | 106.73 (12) |
O2iii—Li2—O9 | 97.5 (3) | O8—Ge2—O7 | 104.11 (10) |
O3iii—Li2—O9 | 93.1 (3) | O1i—Ge3—O2v | 120.65 (14) |
O2iii—Li2—O8 | 88.8 (2) | O1i—Ge3—O9 | 104.39 (9) |
O3iii—Li2—O8 | 158.5 (3) | O2v—Ge3—O9 | 107.00 (9) |
O9—Li2—O8 | 106.7 (2) | O1i—Ge3—O7 | 107.52 (11) |
O1—Ge1—O3 | 95.44 (9) | O2v—Ge3—O7 | 111.31 (9) |
O1—Ge1—O5 | 89.20 (9) | O9—Ge3—O7 | 104.62 (11) |
O3—Ge1—O5 | 92.50 (11) | O4iii—Ge4—O3vi | 119.56 (13) |
O1—Ge1—O4 | 172.62 (8) | O4iii—Ge4—O9 | 104.76 (9) |
O3—Ge1—O4 | 91.06 (12) | O3vi—Ge4—O9 | 102.46 (10) |
O5—Ge1—O4 | 87.04 (11) | O4iii—Ge4—O8vii | 107.36 (11) |
O1—Ge1—O6 | 85.78 (11) | O3vi—Ge4—O8vii | 112.49 (9) |
O3—Ge1—O6 | 176.56 (9) | O9—Ge4—O8vii | 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. |
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) Å3 | 0.14 × 0.08 × 0.07 mm |
Z = 4 |
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 on F2 | w = 1/[σ2(Fo2) + (0.0179P)2 + 0.329P] where P = (Fo2 + 2Fc2)/3 |
Least-squares matrix: full | (Δ/σ)max = 0.001 |
R[F2 > 2σ(F2)] = 0.015 | Δρmax = 0.57 e Å−3 |
wR(F2) = 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) |
Li2Ge4O9 | V = 681.39 (6) Å3 |
Mr = 448.24 | Z = 4 |
Orthorhombic, P21ca | Mo Kα radiation |
a = 9.3044 (5) Å | µ = 17.50 mm−1 |
b = 4.6253 (2) Å | T = 90 K |
c = 15.8331 (8) Å | 0.14 × 0.08 × 0.07 mm |
Bruker SMART APEX diffractometer | 1705 independent reflections |
Absorption correction: multi-scan (APEX2; Bruker, 2007) | 1664 reflections with I > 2σ(I) |
Tmin = 0.21, Tmax = 0.355 | Rint = 0.023 |
9727 measured reflections |
R[F2 > 2σ(F2)] = 0.015 | 1 restraint |
wR(F2) = 0.038 | Δρmax = 0.57 e Å−3 |
S = 1.13 | Δρmin = −0.74 e Å−3 |
1705 reflections | Absolute structure: Flack (1983), with how many Friedel pairs? |
138 parameters | Absolute structure parameter: 0.623 (14) |
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. |
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) |
U11 | U22 | U33 | U12 | U13 | U23 | |
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) |
Li1—O5 | 1.883 (6) | Ge1—O2 | 1.888 (2) |
Li1—O6i | 1.892 (6) | Ge2—O6iv | 1.729 (2) |
Li1—O1i | 1.941 (6) | Ge2—O5 | 1.735 (2) |
Li1—O4 | 1.954 (6) | Ge2—O8 | 1.777 (2) |
Li1—O7ii | 2.140 (5) | Ge2—O7 | 1.789 (2) |
Li2—O2iii | 1.978 (6) | Ge3—O1i | 1.731 (2) |
Li2—O3iii | 2.054 (6) | Ge3—O2v | 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—O4iii | 1.725 (2) |
Ge1—O3 | 1.864 (2) | Ge4—O3vi | 1.744 (2) |
Ge1—O4 | 1.872 (2) | Ge4—O9 | 1.771 (2) |
Ge1—O5 | 1.873 (2) | Ge4—O8vii | 1.786 (2) |
Ge1—O6 | 1.886 (2) | ||
O5—Li1—O6i | 163.8 (3) | O5—Ge1—O6 | 90.83 (8) |
O5—Li1—O1i | 95.2 (2) | O1—Ge1—O2 | 90.98 (11) |
O6i—Li1—O1i | 83.0 (3) | O3—Ge1—O2 | 87.51 (7) |
O5—Li1—O4 | 84.4 (3) | O4—Ge1—O2 | 92.76 (9) |
O6i—Li1—O4 | 92.7 (2) | O5—Ge1—O2 | 179.75 (13) |
O1i—Li1—O4 | 162.9 (3) | O6—Ge1—O2 | 89.21 (10) |
O5—Li1—O7ii | 102.1 (2) | O6iv—Ge2—O5 | 117.45 (8) |
O6i—Li1—O7ii | 94.1 (2) | O6iv—Ge2—O8 | 109.83 (13) |
O1i—Li1—O7ii | 100.5 (3) | O5—Ge2—O8 | 109.47 (9) |
O4—Li1—O7ii | 96.3 (2) | O6iv—Ge2—O7 | 108.31 (9) |
O2iii—Li2—O3iii | 80.1 (2) | O5—Ge2—O7 | 106.58 (12) |
O2iii—Li2—O9 | 97.7 (3) | O8—Ge2—O7 | 104.33 (10) |
O3iii—Li2—O9 | 93.1 (2) | O1i—Ge3—O2v | 120.61 (14) |
O2iii—Li2—O8 | 89.2 (2) | O1i—Ge3—O9 | 104.46 (9) |
O3iii—Li2—O8 | 158.4 (3) | O2v—Ge3—O9 | 107.00 (9) |
O9—Li2—O8 | 107.0 (2) | O1i—Ge3—O7 | 107.53 (10) |
O1—Ge1—O3 | 95.44 (9) | O2v—Ge3—O7 | 111.27 (9) |
O1—Ge1—O4 | 172.65 (8) | O9—Ge3—O7 | 104.65 (11) |
O3—Ge1—O4 | 91.04 (11) | O4iii—Ge4—O3vi | 119.52 (13) |
O1—Ge1—O5 | 89.27 (9) | O4iii—Ge4—O9 | 104.82 (9) |
O3—Ge1—O5 | 92.44 (10) | O3vi—Ge4—O9 | 102.35 (9) |
O4—Ge1—O5 | 86.99 (11) | O4iii—Ge4—O8vii | 107.24 (11) |
O1—Ge1—O6 | 85.81 (11) | O3vi—Ge4—O8vii | 112.54 (9) |
O3—Ge1—O6 | 176.51 (9) | O9—Ge4—O8vii | 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. |
Experimental details
(laz1_298K_tr) | (laz1_150K_tr) | (laz1_90k_tr) | |
Crystal data | |||
Chemical formula | Li2Ge4O9 | Li2Ge4O9 | Li2Ge4O9 |
Mr | 448.24 | 448.24 | 448.24 |
Crystal system, space group | Orthorhombic, P21ca | Orthorhombic, P21ca | Orthorhombic, P21ca |
Temperature (K) | 298 | 150 | 90 |
a, b, c (Å) | 9.31165 (9), 4.62854 (5), 15.81663 (16) | 9.3081 (6), 4.6267 (3), 15.8298 (11) | 9.3044 (5), 4.6253 (2), 15.8331 (8) |
V (Å3) | 681.69 (2) | 681.72 (8) | 681.39 (6) |
Z | 4 | 4 | 4 |
Radiation type | Mo Kα | Mo Kα | Mo Kα |
µ (mm−1) | 17.50 | 17.50 | 17.50 |
Crystal size (mm) | 0.14 × 0.08 × 0.07 | 0.14 × 0.08 × 0.07 | 0.14 × 0.08 × 0.07 |
Data collection | |||
Diffractometer | Bruker SMART APEX diffractometer | Bruker SMART APEX diffractometer | Bruker SMART APEX diffractometer |
Absorption correction | Multi-scan (APEX2; Bruker, 2007) | Multi-scan (APEX2; Bruker, 2007) | Multi-scan (APEX2; Bruker, 2007) |
Tmin, Tmax | 0.13, 0.285 | 0.21, 0.355 | 0.21, 0.355 |
No. of measured, independent and observed [I > 2σ(I)] reflections | 19496, 3223, 3036 | 8631, 1703, 1657 | 9727, 1705, 1664 |
Rint | 0.026 | 0.023 | 0.023 |
(sin θ/λ)max (Å−1) | 0.836 | 0.678 | 0.678 |
Refinement | |||
R[F2 > 2σ(F2)], wR(F2), S | 0.019, 0.047, 1.06 | 0.015, 0.037, 1.13 | 0.015, 0.038, 1.13 |
No. of reflections | 3223 | 1703 | 1705 |
No. of parameters | 138 | 138 | 138 |
No. of restraints | 1 | 1 | 1 |
Δρmax, Δρmin (e Å−3) | 0.71, −1.04 | 0.48, −0.69 | 0.57, −0.74 |
Absolute structure | Flack (1983), with how many Friedel pairs? | Flack (1983), with how many Friedel pairs? | Flack (1983), with how many Friedel pairs? |
Absolute structure parameter | 0.357 (11) | 0.635 (15) | 0.623 (14) |
Computer programs: APEX2 (Bruker, 2007), SHELXS97 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), DIAMOND (Brandenburg, 1999), WinGX (Farrugia, 2012).
Li2Ge4O9(a) | Li2Ge4O9(a) | Li2Ge4O9(a) | LiNaGe4O9(b) | LiNaGe4O9(c) | |
Space group | P21ca | P21ca | P21ca | P21ca | Pcca |
T (K) | 90 | 150 | 298 | 35 | 298 |
<Li1—O> | 1.962 (5) | 1.965 (5) | 1.974 (5) | 1.989() | 2.169 (134) |
Volume of Li1 | 5.78 | 5.811 | 5.89 | 6.07 | 12.68 |
S(h) (v.u.) | 1.35 (1) | 1.34 (1) | 1.33 (1) | 1.29 (1) | 1.28 (5) |
<Li2—O> | 2.31 (5) | 2.311 (5) | 2.320 (5) | 2.446 | 2.567 (34) |
Volume of Li2 | 9.05 | 9.07 | 9.19 | 9.91 | 20.89 |
S(h) (v.u.) | 0.67 (1) | 0.66 (1) | 0.62 (1) | 0.95 (1) | 0.91 (3) |
<Ge1—O> | 1.871 (2) | 1.871 (2) | 1.873 (2) | 1.866 | 1.866 (20) |
Volume of Ge1 | 8.71 | 8.70 | 8.73 | 8.64 | 8.64 |
OAV(d) Ge1 | 7.65 | 7.68 | 7.38 | 7.21 | 7.21 |
OQE(e) | 1.0022 | 1.0022 | 1.0021 | 1.0021 | 1.0021 |
S(h) (v.u.) | 4.30 (1) | 4.31 (1) | 4.29 (1) | 4.24 (1) | 4.36 (5) |
<Ge2—O> | 1.758 (2) | 1.758 (2) | 1.758 (2) | 1.764 | 1.757 (20) |
Volume of Ge2 | 2.77 | 2.77 | 2.77 | 2.87 | 2.86 |
TAV Ge2 | 19.99 | 20.41 | 20.62 | 31.16 | 28.45 |
TQE Ge2 | 1.0045 | 1.0046 | 1.0046 | 1.0070 | 1.0071 |
S(h) (v.u.) | 3.91 (1) | 3.90 (1) | 3.90 (1) | 3.84 (1) | 3.90 (6) |
<Ge3—O> | 1.756 (2) | 1.756 (2) | 1.754 (2) | 1.751 | 1.757 (20) |
Volume of Ge3 | 2.745 | 2.74 | 2.73 | 2.72 | 2.74 |
TAV Ge3 | 37.09 | 37.54 | 37.87 | 31.03 | 44.01 |
TQE Ge3 | 1.0088 | 1.0089 | 1.0090 | 1.0077 | 1.0104 |
S(h) (v.u.) | 3.92 (1) | 3.93 (1) | 3.95 (1) | 3.98 (1) | 3.91 (6) |
<Ge4—O> | 1.757 (2) | 1.757 (2) | 1.755 (2) | 1.765 | n/a |
Volume of Ge4 | 2.743 | 2.74 | 2.74 | 2.78 | n/a |
TAV Ge4 | 37.58 | 37.33 | 37.15 | 43.98 | n/a |
TQE Ge4 | 1.0097 | 1.0096 | 1.0095 | 1.011 | n/a |
S(h) (v.u.) | 3.92 (1) | 3.91 (1) | 3.93 (1) | 3.83 (1) | n/a |
References: (a) this study; (b) Iwata et al. (1998); (c) Völlenkle et al. (1969). Definitions: (d) octahedral angle variance OAV = Σi=1n(θi - 90)2/11 (Robinson et al., 1971); (e) octahedral quadratic elongation OQE = Σi=16(li/lo)2/6, where lo is the centre-to-vertex distance for a regular octahedron whose volume is equal to that of the undistorted octahedron with bond length li (Robinson et al., 1971); (f) tetrahedral angle variance TAV = Σi=1n(θi - 109.47)2/5 (Robinson et al., 1971); (g) tetrahedral quadratic elongation TQE = Σi=14(li/lt)2/4, where lt is the centre-to-vertex distance for a regular tetrahedron whose volume is equal to that of the undistorted tetrahedron with bond length li (Robinson et al., 1971); (h) S is the bond-valence sum in valence units (Brese & O'Keeffe, 1991). |