The tetra­germanates A₂Ge₄O₉ (A = Na, K and Rb)

The crystal structures of three alkali tetra­germanates A₂Ge₄O₉ (A = Na, K and Rb) [namely disodium tetra­germanate, Na₂Ge₄O₉, dipotassium tetra­germanate, K₂Ge₄O₉, and dirubidium tetra­germanate, Rb₂Ge₄O₉] are trigonal (space group Pc1). The main building units are a three-membered ring of tetra­hedra, oriented within the (001) plane and forming tetra­hedral sheets. These sheets are connected to each other by two different regular isolated GeO₆ octa­hedra via corner-sharing to build up a tetra­hedral-octa­hedral framework. The alkali cations are located in cavities within this framework and are sevenfold coordinated. The increasing size of the A-site cation is accommodated by twist deformations of the tetra­hedral rings and alterations in the Ge-O-Ge angles. With increasing size of the A-site cation, both the tetra­hedral and octa­hedral sites become more regular, with slightly decreasing <Ge-O> distances from Na₂Ge₄O₉ to Rb₂Ge₄O₉. This goes hand-in-hand with a more uniform distribution of bonds around the A-site cation. All these observations make Rb₂Ge₄O₉ the most regular member of this A₂Ge₄O₉ octa­hedral-tetra­hedral framework structure series.

S1. Introduction

Structures containing Ge in both tetra­hedral and o­cta­hedral coordinations are rare, but are of inter­est as analogue structures for high-pressure silicate materials. Among them are garnet-type CaGeO₃ (Nakatsuka et al., 2005), Ca₂Ge₇O₁₆ (Redhammer et al., 2007a) and A₂B(T₃O₉)-type compounds. Fleet & Muthupari (1998) noted that three structure types are known for this last class of materials: (i) wadeite-type materials with the space group P6₃/m, a structure type which is favoured by silicates such as wadeite K₂ZrSi₃O₉, K₂TiSi₃O₉, Cs₂ZrSi₃O₉ or the high-pressure silicate K₂SiSi₃O₉ (Swanson & Prewitt, 1983); (ii) the alkali germanates Na₂Ge₄O₉, K₂Ge₄O₉ and Rb₂Ge₄O₉ with the space group P3c1 (Fleet & Muthupari, 1998; Völlenkle & Wittmann, 1971; Goreaud & Raveau, 1976); and (iii) Na₂Si₄O₉ with the space group P2₁/n. All these structures show a tetra­hedral–o­cta­hedral framework, in which three-membered rings of TO₄ tetra­hedra are inter­connected by BO₆ o­cta­hedra. In contrast with this, the alkali tetra­germanates Li₂Ge₄O₉ and NaLiGe₄O₉ show orthorhombic symmetry, with space group P2₁ca or Pcca depending on composition and temperature (Völlenkle et al., 1969; Redhammer & Tippelt, 2013). Their structures are based on crumbled [Ge₃O₉]_n chains of GeO₄ tetra­hedra which are inter­connected by GeO₆ o­cta­hedra, and no ring structure is present.

The structures of A₂Ge₄O₉-type materials are known in principle. Sodium tetra­germanate Na₂Ge₄O₉ was resolved, after long-standing uncertainties, by Fleet & Muthupari (1998), who determined the space group to be P3c1 rather than wadeite-type P6₃/m. The latter authors also noted close similarities between Na₂Ge₄O₉, K₂Ge₄O₉ and Rb₂Ge₄O₉. The structure of K₂Ge₄O₉ was first determined by Völlenkle & Wittmann (1971) using intensity data from visual inspection of Weissenberg photographic films, so no anisotropic refinement of the atomic displacement parameters is available and the uncertainties in the primary and secondary structural parameters are large. For Rb₂Ge₄O₉, the structure was determined by Goreaud & Raveau (1976) using intensity data from photographic precession film exposures; again, only isotropic atomic displacement parameters are given, and the estimated standard uncertainties on e.g. the bond lengths are in the range of 0.05 Å, i.e. at least ten times larger than would be expected from a modern high-quality structure refinement based on single-crystal X-ray data. Within the isotpyic series A₂Ge₄O₉, two further compositions exist, namely Ag₂Ge₄O₉ and Tl₂Ge₄O₉. Due to the similarities in their powder X-ray diffraction patterns, Wittmann & Modern (1965) concluded that they also belong to the isotypic series of P3c1 tetra­germanates A₂Ge₄O₉ (A = Na, K and Rb); only the lattice parameters are available for the Ag₂Ge₄O₉ and Tl₂Ge₄O₉ compounds up to now. In this study, we report a redetermination and structure refinement of three A₂Ge₄O₉ (A = Na, K and Rb) compounds, giving full anisotropic atomic displacement parameters and much better precision in the bond lengths and angles than were possible in the older literature.

S2. Experimental

S2.1. Synthesis and crystallization

Na₂Ge₄O₉ and K₂Ge₄O₉ were obtained by chance when attempting to grow feldspar-type materials NaAlGe₃O₈ and KAlGe₃O₈, using the flux method with Na₂MoO₄ and K₂MoO₄ as the high-temperature solvent. A finely ground mixture of K₂CO₃ (Na₂CO₃), Al₂O₃ and GeO₂ in the stoichiometry of the feldspars, together with the flux (flux to nutrient ratio of 10:1) were put into platinum crucibles, covered with a lid, and placed in a chamber furnace, which was then heated to 1373 K at a rate of 3 K min^-1, held at this temperature for 24 h and cooled to 973 K at a rate of 0.02 K min^-1. After dissolving the flux in hot water, for nominal KAlGe₃O₈ composition the experimental yield consisted of small colourless needles of the title compound [K₂Ge₄O₉?], up to 2 mm in length, compact fine-grained aggregates of tetra­gonal KAlGe₂O₆ and K₂Ge₄O₉, and finally glass spheres up to 0.5 mm. Chemical analysis of the needles using EDX analysis with scanning electron microscopy showed only oxygen, potassium and germanium were present, with no aluminium. For nominal NaAlGe₃O₈ composition the synthesis batch showed plates of NaAlGe₃O₈ feldspar and about 15% of large needles up to 1 mm in length of the title compound [Na₂Ge₄O₉?]. Additionally, some glass was found.

Rb₂Ge₄O₉ was first obtained by sinter­ing a stoichiometric mixture of Rb₂CO₃ and GeO₂ at 1123 K, followed by melting this material at 1273 K for 2 h in a platinum crucible and slow cooling to 873 K at a rate of 0.05 K min^-1. By this procedure a solidified material was obtained, consisting of thin needles of the title compound [Rb₂Ge₄O₉?], about 3 to 4 mm in length and 0.1 mm in diameter.

S2.2. Refinement

Crystal data, data collection and structure refinement details are summarized in Table 1. Analysis of the systematic absences yielded possible space groups P3c1 and P3c1 for all three compounds. Intensity statistics suggested strong evidence for a centrosymmetric space group. No evidence was found for higher symmetry, e.g. P6₃/m derivative wadeite type. Structure solution using direct methods was carried out for K₂Ge₄O₉ in space group P3c1, yielding all the Ge-atom positions. For the O-atom positions, one turned out to be K and the remaining two O-atom positions were identified from a difference Fourier analysis. For the other two compounds, the structures were refined using the atomic coordinates obtained for K₂Ge₄O₉. The structural model obtained is identical to that given by Völlenkle & Wittmann (1971), Goreaud & Raveau (1976) and Fleet & Muthupari (1998), but was transformed to give a full connectivity set with the Ge1 site at (0,0,1/2). The Ge1, Ge2, Ge3 and Ge4 sites of Fleet & Muthupari (1998) correspond to the Ge1, Ge4, Ge2 and Ge3 sites of this study, respectively, and the O1, O2, O3, O4 and O5 sites of Fleet & Muthupari (1998) correspond to the O5, O1, O2, O3 and O4 sites of this study, respectively.

S3. Results and discussion

All three A₂Ge₄O₉ (A = Na, K and Rb) compounds exhibit the space group P3c1, thus confirming the findings of the literature. The general structure topology consists of the sevenfold coordinated A site (general position 12g, site symmetry 1), the o­cta­hedrally coordinated Ge1 and Ge4 sites (special positions 2b and 4d, site symmetries 3 and 3, respectively), and two tetra­hedrally coordinated Ge2 and Ge3 sites (special and general positions 6f and 12g with site symmetries 2 and 1, respectively). There are five independent O-atom positions, four of them on general positions 12g and the fifth on special position 6f, site symmetry 2. This is in good agreement with the findings from the literature, confirming the older structure determinations of K₂Ge₄O₉ (Völlenkle & Wittmann, 1971) and Rb₂Ge₄O₉ (Goreaud & Raveau, 1976). The results for Na₂Ge₄O₉ perfectly match those obtained by Fleet & Muthupari (1998). Fig. 1 shows an anisotropic displacement plot for K₂Ge₄O₉, with the atomic nomenclature. It is evident that the A-site cations in particular, but also the O atoms, exhibit distinct anisotropic atomic displacement parameters, justifying the need for new structure refinements.

Within the A₂Ge₄O₉ series, the Na⁺ compound naturally shows the smallest unit-cell dimensions and unit-cell volume, while the largest are found for Rb₂Ge₄O₉. This variation corresponds well with the variations in ionic radii of the monovalent cations (1.18 Å for Na⁺, 1.51 Å for K⁺ and 1.61 Å for Rb⁺ in eightfold coordination; Shannon & Prewitt, 1969). For ease of comparison, the lattice parameters, selected bond lengths and angles, and distortion parameters, recalculated from the literature data, are given in Table 2 together with the data from this study. As can be seen, the lattice parameters for Na₂Ge₄O₉ are in excellent agreement with those given by Fleet & Muthupari (1998). The lattice parameters of Völlenkle & Wittmann (1971) for K₂Ge₂O₉ are confirmed in this study, albeit with a much better precision. The present data for Rb₂Ge₄O₉ are somewhat larger than those given by Goreaud & Raveau (1976), but again the precision of the new data is better by two orders of magnitude.

The dominant building unit of the title compounds is a three-membered [Ge₃O₉] ring consisting of two Ge3O₄ and one Ge2O₄ tetra­hedra, and having an intrinsic twofold symmetry (Fig. 2) with the twofold axis passing through atoms Ge2 and O5. Within the ab plane, the [Ge₃O₉] units are oriented in layers. Within each layer these are related to each other by the threefold axes in 3d, while from layer to layer they are related to each other by the 3-fold axes in the 2b position. The tetra­hedral [Ge₃O₉] rings are not coplanar within such a layer. The planes through atom Ge2 and the two Ge3 atoms of an individual ring are inclined to each other by a tilt angle of 31.40 (2)–17.29 (2)°, depending on chemistry. Very similar values were calculated from the literature data (Table 2), with the best agreement being observed for the high-quality data for Na₂Ge₄O₉ (Fleet & Muthupari, 1998) and the worst with the data for Rb₂Ge₄O₉ (Goreaud & Raveau, 1976). The smallest tilts are found in the Rb compound; the angle between the plane through atoms Ge2 and Ge3 and the (001) plane decreases from 18.3 (1)° in Na₂Ge₄O₉ to 10.0 (1)° in Rb₂Ge₄O₉ (Table 2), i.e. the larger the A-site cation, the more coplanar are the tetra­hedral rings aligned to each other with respect to the Ge2–Ge3–Ge2 plane. Within the [Ge₃O₉] rings, the Ge—O—Ge angles all increase with increasing size of the alkaline cation, causing the tetra­hedral faces to be more crimped to each other within the ring. In Na₂Ge₄O₉, for example, the angle between the O2–O4–O5 faces of the neighbouring Ge3 sites is 2.4 (1)°, while it increases to 13.17 (7)° in Rb₂Ge₄O₉. However, this crimp brings atom Ge3 closer to the plane through bridging atoms O2–O2–O5 of the ring. While in Na₂Ge₄O₉ atom Ge3 is displaced out of this plane by 0.704 (1) Å, it is 0.519 (1) Å away in Rb₂Ge₄O₉; atom Ge2 is within this plane. For comparison, in the related structure of wadeite K₂Zr(Si₃O₉), the [Si₃O₉] rings have ideal geometry, with the Si atoms being coplanar to the bridging O atoms of the ring.

The layers of [Ge₃O₉] rings pass through the unit cell at z \sim 0.25 and z ~3/4, although they are not stacked up on each other but are displaced as a consequence of the 3 [3-fold axis?]. This is different to wadeite, which has three-membered rings of SiO₄ tetra­hedra and where the layers of [Si₃O₉] rings are superimposed on each other parallel to the c axis due to the higher P6₃/m symmetry. The Ge2O₄ tetra­hedron with site symmetry 2 shows an average <Ge2—O> bond length of 1.776 (3) Å for Na₂Ge₄O₉, in perfect agreement with the data given by Fleet & Muthupari (1972 1998?). While for K₂Ge₄O₉ the data of this study are similar to those given in the literature, for the Rb₂Ge₄O₉ compound in particular some distinct deviations in individual bond lengths are found. Goreaud & Raveau (1976) reported two quite small (1.69 Å) and two quite long (1.81 Å) Ge—O bonds, which are at the limit for Ge—O bonds in a tetra­hedral coordination. However, these bonds are no longer valid on the basis of the new structure refinement of this study. The Ge2 tetra­hedron generally shows larger <Ge—O> bond lengths and also a larger polyhedral volume compared with the Ge3O₄ tetra­hedron, but it shows a smaller polyhedral distortion, as expressed by the values of TAV (tetra­hedral angle variance) and TQE (tetra­hedral quadratic elongation; Table 2). Nevertheless, the tetra­hedral distortion is large compared with e.g. Li₂Ge₄O₉. Here, the most distorted GeO₄ tetra­hedron has TAV values of ~37°, and the average Ge—O distances range between 1.755 and 1.778 Å (Redhammer & Tippelt, 2013). The tetra­hedral distortion of the title compounds is among the largest found in the literature and similar high values are valid only in e.g. lanthanide pyrogermanates with Ge₂O₇ groups (Redhammer et al., 2007b). Within the A₂Ge₄O₉ series, a significant decrease of <Ge—O> distances, polyhedral volume and distortion with increasing size of the A-site cation is observed (Table 2). This suggests that the Rb compound represents the most stable and regular member of the A₂Ge₄O₉ series and that the long Ge—O bonds in Na₂Ge₄O₉ are energetically unfavourable. The bond-valence sums (BVS; Brese & O'Keeffe, 1991; Table 2) also increase from Na to Rb compounds, thereby becoming closer to the ideal value of 4.0 valence units (v.u.). But even in Rb₂Ge₄O₉ the Ge2 site appears to be underbonded. For the Ge3O₄ tetra­hedra, <Ge—O> is smaller than for Ge2 and remains constant across the A₂Ge₄O₉ series. The polyhedral volume increases slightly towards Rb₂Ge₄O₉ but is also smaller than for the Ge2 site. For the Ge3 site, the data of this study fit well with the data from the literature, except for Rb₂Ge₄O₉; besides the large estimated standard uncertainties there is again more spread in the individual bond lengths, with somewhat unrealistically long Ge3—O5 bond lengths in the Goreaud & Raveau (1976) data; these are mended by the present structure determination. The largest distortion of all the tetra­hedral sites in the A₂Ge₄O₉ compounds is found for the Ge3 site in Na₂Ge₄O₉. With increasing size of the A-site cation, the Ge3 tetra­hedra become more regular but are still distinctly distorted. In wadeite, the SiO₄ tetra­hedron shows a TAV value of only 38.8° (recalculated from Swanson & Prewitt, 1983). The BVS for the Ge3 tetra­hdron are almost ideal and do not change from the Na to the Rb compound, neither in the literature nor in this study (Table 2).

Two different GeO₆ o­cta­hedra (Ge1 and Ge4) connect the tetra­hedral layers to each other to build up the tetra­hedral-o­cta­hedral framework. Thus, three corners of a triangular o­cta­hedral face belong to an upper layer and three to a lower tetra­hedral layer (see Fig. 3 for a graphical illustration). The Ge1O₆ o­cta­hedron at the origin of the unit cell with site symmetry 3 has a regular O-atom coordination, with a <Ge—O> distance of 1.920 (2) Å for the sodium compound, in perfect accordance with Fleet & Muthupari (1998). This is a typical value found for Ge in an o­cta­hedral coordination. With increasing size of the A-site cation a decrease in <Ge—O> is again observed towards Rb₂Ge₄O₉, accompanied by a decrease in the o­cta­hedral volume and, in particular, of the o­cta­hedral distortion (Table 2). This is not observable from the literature data, as Rb₂Ge₄O₉ in particular deviates from the data of this study. Also, the large estimated standard uncertainties for both K₂Ge₄O₉ and Rb₂Ge₄O₉ would not allow the extraction of such small alterations with composition on a meaningful basis. While atom Ge1 is distinctly underbonded in Na₂Ge₄O₉, the BVS approaches the ideal value of 4.00 in the Rb compound. The Ge1O₆ site has common corners with six Ge2O₄ tetra­hedra, and additionally each O-atom corner is shared with an A site. The second o­cta­hedral site within the structure of the A₂Ge₄O₉ series is the Ge4 site. It exhibits distinctly shorter <Ge—O> bond lengths and also a smaller polyhedral volume than the Ge1 site; both are similar across the series. From Table 2 a good agreement between the data from this study and the literature is observable, except for the longer Ge4—O bond lengths in the Goreaud & Raveau (1976) data for Rb₂Ge₄O₉. The Ge4 site represents an almost-perfect o­cta­hedron with respect to polyhedral distortion, which does not change as a function of A-site composition; a similar situation exists for the polyhedral volume. The BVS of the Ge4 site show this Ge atom to be overbonded, with BVS of 4.29–4.19 v.u., decreasing with increasing size of the A-site cation. The O-atom corners of the Ge4O₆ site are common to one Ge3O₄ tetra­hedron and an A-site cation each.

The cavities within the tetra­hedral–o­cta­hedral framework are filled with the medium-to-large sized extra-framework alkaline cations Na⁺, K⁺ or Rb⁺. It is the bonding topology of the monovalent cations which marks the essential difference between the title compounds. The Na⁺ cation is in a 5+2 coordination, with five bonds between 2.442 (4) and 2.633 (4) Å, the two others being 2.722 (4) and 2.860 (4), showing a near square-pyramidal coordination. This distorted coordination is reflected in the large value of the bond-length distortion (deviation of individual A—O bonds from the mean value) of 4.18%. The low BVS of sodium (0.84 v.u.) suggests that the Na⁺ cation is nearly too small (and consequently has too long Na—O bonds) to fit into the cavities. This is supported by the large equivalent isotropic and anisotropic atomic displacement parameters in Na₂Ge₄O₉ and by the fact that Li₂Ge₄O₉ shows a different crystal structure, even though the chemical composition would fit the A₂Ge₄O₉ series. K₂Ge₄O₉ shows a more uniform K—O bond distribution which is close to a 6+1 coordination, a bond-length distortion of 2.06% and a less pronounced anisotropic atomic displacement. The BVS is 1.14 v.u., reflecting some overbonding of the A site. This is even more pronounced in Rb₂Ge₄O₉ (1.19 v.u.), where the Rb⁺ shows a sevenfold coordination with bond lengths between 2.823 (1) and 3.013 (1) Å and a bond-length distortion of 1.92%; the coordination polyhedron may be described as a distorted prism with a triangular and a quadrangular covering face. The Rb⁺ cation itself shows the smallest equivalent and anisotropic atomic displacement parameters of all three compounds. The different size requirements of the alkali cations within the cavity are adjusted by a twist deformation of the tetra­hedral rings and altered Ge—O—Ge angles between tetra­hedral and o­cta­hedral sites. The latter angles increase distinctly by a mean of 11° between the Na and Rb compounds, while the increase in the twist of the Ge—O—Ge angles within the tetra­hedral rings is 6.7° on the average (Table 2). The literature data show similar behaviour and the differences in bonding topology are valid, especially for the Rb₂Ge₄O₉ compound.

In conclusion, our data for Na₂Ge₄O₉ fit perfectly with the high-quality structure refinement of Fleet & Muthupari (1998). The redetermination of the crystal structures of K₂Ge₄O₉ and Rb₂Ge₄O₉ in this study using modern equipment confirms their space group symmetries and atomic positions, extracted by Völlenkle & Wittmann (1971) and Goreaud & Raveau (1976), respectively. We pay respect to these works as their data, obtained from film methods and visual estimates of intensity data, fit those determined here using automated methods, and the authors were able to report the principal structural features of the A₂Ge₄O₉ compounds correctly. With the capabilities of modern diffractometers we have here given more precise data with much smaller estimated standard uncertainties and anisotropic refinements of atomic displacement parameters. This is especially important for the A-site cation and the O atoms, and may explain the large differences in A-site geometry in Rb₂Ge₄O₉ between the Goreaud & Raveau (1976) data and those of this study.

Generally, among all three compounds, the literature data for Rb₂Ge₄O₉ show the largest deviation in bond lengths, bond angles and distortion parameters from the data determined in this study (Table 2). The unrealistically small (1.69 Å) and/or large (1.81 Å) Ge—O distances for tetra­hedral coordination in the Rb₂Ge₄O₉ data of Goreaud & Raveau (1976) indicate the deficiencies in their structural model. These problems, together with the large uncertainties and the isotropic refinement of atomic displacements, are overcome in this study. The structural model for K₂Ge₄O₉ given by Völlenkle & Wittmann (1971) is confirmed to a large extent and our new data `only' contribute much smaller uncertainties in the structural parameters and give full anisotropic refinement of atomic displacements. Direct comparison of the three A₂Ge₄O₉ compounds allows the extraction of some systematic deviations with chemistry. Both tetra­hedral sites are distinctly distorted but become more regular towards the Rb₂Ge₄O₉ compound, which is associated with a decrease in the tetra­hedral <Ge—O> distances with increasing A-site cation. Also for the o­cta­hedral sites, the distortion becomes smaller from the Na to the Rb compound, especially for the larger Ge1 site. This, together with the more regular A-site geometry (smaller bond length distortion), shows Rb₂Ge₄O₉ to be the most regular and geometrically most stable member of the A₂Ge₄O₉ series.

Related literature

For related literature, see: Brese & O'Keeffe (1991); Fleet & Muthupari (1998); Goreaud & Raveau (1976); Nakatsuka et al. (2005); Redhammer & Tippelt (2013); Redhammer et al. (2007a, 2007b); Shannon & Prewitt (1969); Swanson & Prewitt (1983); Völlenkle (1969); Völlenkle & Wittmann (1971); 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 K₂Ge₄O₉, showing 95% probability atomic displacement ellipsoids and the atomic numbering scheme. [Symmetry codes: (i) -x + y, -x, z; (ii) -y, x - y, z; (iii) -x, -y, -z + 1; (iv) x - y, x, -z + 1; (v) y, -x + y, -z + 1; (vi) y, x, -z + 1/2; (vii) -y + 1, x - y, z; (viii) -x + y + 1, -x + 1, z; (ix) -x + 1, y, z + 1/2; (x) -y + 1, -x + 1, z - 1/2; (xi) x, x - y, z - 1/2; (xii) -x + 1, -y + 1, -z + 1; (xiii) x, x - y, z + 1/2.]

Fig. 2. A polyhedral representation of a layer of tetrahedral [Ge₃O₉] rings in K₂Ge₄O₉ at z ~ 0.25, in a view parallel to the c axis.

Fig. 3. Polyhedral representations of the full structure of K₂Ge₄O₉, (a) in a view parallel to the c axis and (b) in a view parallel to the b axis.

(Na2Ge4O9) Disodium tetragermanate

Crystal data

Na2Ge4O9	F(000) = 1332
Mr = 480.34	Dx = 4.447 Mg m^−3
Trigonal, P3c1	Mo Kα radiation, λ = 0.71073 Å
a = 11.3216 (10) Å	µ = 16.75 mm^−1
c = 9.6946 (18) Å	T = 295 K
V = 1076.2 (3) Å^3	Prism, colourless
Z = 6	0.22 × 0.07 × 0.06 mm

Data collection

Bruker SMART APEX diffractometer	924 independent reflections
Radiation source: three-circle diffractometer	853 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.041
ω scan at four different ϕ positions	θmax = 28.7°, θmin = 2.1°
Absorption correction: empirical (using intensity measurements) [multiscan absorption correction using APEX2 (Bruker, 2007)]	h = −15→15
Tmin = 0.441, Tmax = 0.748	k = −14→14
12328 measured reflections	l = −13→12

Refinement

Refinement on F^2	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.028	w = 1/[σ^2(Fo^2) + (0.0118P)^2 + 1.8181P] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.055	(Δ/σ)max < 0.001
S = 1.21	Δρmax = 0.78 e Å^−3
924 reflections	Δρmin = −0.95 e Å^−3
71 parameters	Extinction correction: SHELXL97 (Sheldrick, 2008)
0 restraints	Extinction coefficient: 0.00065 (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
Na1	0.3355 (2)	0.3294 (2)	0.5763 (2)	0.0284 (5)
Ge1	0	0	0.5	0.0090 (2)
Ge2	0.17623 (6)	0.17623 (6)	0.25	0.01015 (16)
Ge3	0.49387 (4)	0.34451 (4)	0.29968 (4)	0.00891 (14)
Ge4	0.6667	0.3333	0.05427 (7)	0.00812 (18)
O1	0.0592 (3)	0.1546 (3)	0.3803 (3)	0.0112 (6)
O2	0.3252 (3)	0.2245 (3)	0.3532 (3)	0.0140 (6)
O3	0.5126 (3)	0.2500 (3)	0.1700 (3)	0.0133 (6)
O4	0.5922 (3)	0.4152 (3)	0.4454 (3)	0.0130 (6)
O5	0.4939 (4)	0.4939 (4)	0.25	0.0131 (9)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Na1	0.0364 (13)	0.0201 (10)	0.0200 (9)	0.0077 (10)	0.0071 (9)	−0.0017 (8)
Ge1	0.0098 (3)	0.0098 (3)	0.0075 (5)	0.00490 (16)	0	0
Ge2	0.0100 (2)	0.0100 (2)	0.0094 (3)	0.0042 (3)	0.00118 (11)	−0.00118 (11)
Ge3	0.0096 (2)	0.0091 (2)	0.0082 (2)	0.00484 (18)	−0.00050 (15)	−0.00039 (15)
Ge4	0.0091 (2)	0.0091 (2)	0.0061 (3)	0.00456 (12)	0	0
O1	0.0143 (15)	0.0114 (14)	0.0098 (13)	0.0079 (13)	0.0022 (11)	0.0011 (11)
O2	0.0092 (15)	0.0163 (16)	0.0127 (14)	0.0035 (13)	0.0005 (11)	0.0010 (12)
O3	0.0140 (15)	0.0118 (15)	0.0115 (13)	0.0044 (13)	0.0059 (12)	−0.0004 (11)
O4	0.0175 (16)	0.0126 (15)	0.0096 (13)	0.0080 (13)	−0.0045 (12)	−0.0015 (12)
O5	0.0115 (15)	0.0115 (15)	0.018 (2)	0.0066 (18)	−0.0006 (8)	0.0006 (8)

Geometric parameters (Å, º)

Na1—O2	2.442 (4)	Ge2—O1	1.757 (3)
Na1—O1^i	2.443 (4)	Ge2—O2	1.795 (3)
Na1—O5^ii	2.589 (4)	Ge2—O2^viii	1.795 (3)
Na1—O4^ii	2.589 (4)	Ge3—O4	1.727 (3)
Na1—O3^iii	2.633 (4)	Ge3—O3	1.732 (3)
Na1—O2^iv	2.722 (4)	Ge3—O5	1.758 (2)
Na1—O4	2.860 (4)	Ge3—O2	1.780 (3)
Ge1—O1^i	1.920 (3)	Ge4—O4^ix	1.862 (3)
Ge1—O1^iv	1.920 (3)	Ge4—O4^x	1.862 (3)
Ge1—O1^v	1.920 (3)	Ge4—O4^xi	1.862 (3)
Ge1—O1^vi	1.920 (3)	Ge4—O3^xii	1.883 (3)
Ge1—O1	1.920 (3)	Ge4—O3^xiii	1.883 (3)
Ge1—O1^vii	1.920 (3)	Ge4—O3	1.883 (3)
Ge2—O1^viii	1.757 (3)
O2—Na1—O1^i	79.30 (11)	O1^iv—Ge1—O1^vii	180.00 (13)
O2—Na1—O5^ii	141.97 (13)	O1^v—Ge1—O1^vii	87.26 (12)
O1^i—Na1—O5^ii	128.56 (12)	O1^vi—Ge1—O1^vii	92.74 (12)
O2—Na1—O4^ii	112.49 (12)	O1—Ge1—O1^vii	87.26 (12)
O1^i—Na1—O4^ii	148.28 (14)	O1^viii—Ge2—O1	126.9 (2)
O5^ii—Na1—O4^ii	59.54 (9)	O1^viii—Ge2—O2	112.72 (14)
O2—Na1—O3^iii	91.37 (12)	O1—Ge2—O2	99.76 (13)
O1^i—Na1—O3^iii	88.56 (12)	O1^viii—Ge2—O2^viii	99.76 (13)
O5^ii—Na1—O3^iii	67.46 (9)	O1—Ge2—O2^viii	112.72 (14)
O4^ii—Na1—O3^iii	119.20 (13)	O2—Ge2—O2^viii	103.1 (2)
O2—Na1—O2^iv	113.86 (14)	O4—Ge3—O3	129.09 (15)
O1^i—Na1—O2^iv	69.86 (11)	O4—Ge3—O5	95.04 (13)
O5^ii—Na1—O2^iv	101.26 (10)	O3—Ge3—O5	117.02 (10)
O4^ii—Na1—O2^iv	78.52 (11)	O4—Ge3—O2	108.21 (14)
O3^iii—Na1—O2^iv	141.79 (12)	O3—Ge3—O2	99.00 (14)
O2—Na1—O4	64.24 (10)	O5—Ge3—O2	107.34 (16)
O1^i—Na1—O4	127.11 (13)	O4^ix—Ge4—O4^x	91.02 (13)
O5^ii—Na1—O4	77.73 (10)	O4^ix—Ge4—O4^xi	91.02 (13)
O4^ii—Na1—O4	83.37 (11)	O4^x—Ge4—O4^xi	91.02 (13)
O3^iii—Na1—O4	57.33 (10)	O4^ix—Ge4—O3^xii	91.06 (13)
O2^iv—Na1—O4	159.25 (12)	O4^x—Ge4—O3^xii	89.76 (13)
O1^i—Ge1—O1^iv	87.26 (12)	O4^xi—Ge4—O3^xii	177.78 (14)
O1^i—Ge1—O1^v	180.00 (16)	O4^ix—Ge4—O3^xiii	177.78 (14)
O1^iv—Ge1—O1^v	92.74 (12)	O4^x—Ge4—O3^xiii	91.06 (13)
O1^i—Ge1—O1^vi	87.26 (12)	O4^xi—Ge4—O3^xiii	89.76 (13)
O1^iv—Ge1—O1^vi	87.26 (12)	O3^xii—Ge4—O3^xiii	88.14 (13)
O1^v—Ge1—O1^vi	92.74 (12)	O4^ix—Ge4—O3	89.76 (13)
O1^i—Ge1—O1	92.74 (12)	O4^x—Ge4—O3	177.78 (14)
O1^iv—Ge1—O1	92.74 (12)	O4^xi—Ge4—O3	91.06 (13)
O1^v—Ge1—O1	87.26 (12)	O3^xii—Ge4—O3	88.14 (13)
O1^vi—Ge1—O1	180.00 (14)	O3^xiii—Ge4—O3	88.14 (13)
O1^i—Ge1—O1^vii	92.74 (12)

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

(K2Ge4O9) Dipotassium tetragermanate

Crystal data

K2Ge4O9	Dx = 4.287 Mg m^−3
Mr = 512.56	Mo Kα radiation, λ = 0.71073 Å
Trigonal, P3c1	Cell parameters from 12842 reflections
a = 11.8461 (4) Å	θ = 2.0–28.9°
c = 9.8009 (4) Å	µ = 16.08 mm^−1
V = 1191.10 (7) Å^3	T = 295 K
Z = 6	Prism, colourless
F(000) = 1428	0.17 × 0.09 × 0.08 mm

Data collection

Bruker SMART APEX diffractometer	1026 independent reflections
Radiation source: three-circle diffractometer	984 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.026
ω scan at four different ϕ positions	θmax = 28.9°, θmin = 2.0°
Absorption correction: empirical (using intensity measurements) [multiscan absorption correction using APEX2 (Bruker, 2007)]	h = −15→15
Tmin = 0.441, Tmax = 0.748	k = −15→15
12842 measured reflections	l = −13→13

Refinement

Refinement on F^2	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.014	w = 1/[σ^2(Fo^2) + (0.0151P)^2 + 1.1161P] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.035	(Δ/σ)max = 0.001
S = 1.14	Δρmax = 0.39 e Å^−3
1026 reflections	Δρmin = −0.58 e Å^−3
71 parameters	Extinction correction: SHELXL97 (Sheldrick, 2008)
0 restraints	Extinction coefficient: 0.00549 (16)

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
K1	0.33657 (4)	0.33480 (4)	0.57196 (4)	0.01681 (10)
Ge1	0	0	0.5	0.00634 (10)
Ge2	0.17619 (2)	0.17619 (2)	0.25	0.00681 (8)
Ge3	0.486079 (17)	0.335234 (16)	0.285931 (18)	0.00685 (7)
Ge4	0.6667	0.3333	0.03798 (3)	0.00632 (8)
O1	0.06988 (12)	0.14984 (12)	0.38487 (12)	0.0097 (2)
O2	0.32552 (11)	0.21187 (12)	0.33163 (12)	0.0103 (2)
O3	0.51615 (12)	0.26357 (12)	0.14830 (12)	0.0118 (2)
O4	0.58170 (12)	0.39769 (12)	0.43018 (12)	0.0104 (2)
O5	0.47618 (14)	0.47618 (14)	0.25	0.0123 (3)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
K1	0.01542 (19)	0.0153 (2)	0.01793 (19)	0.00635 (15)	0.00248 (15)	−0.00298 (15)
Ge1	0.00647 (13)	0.00647 (13)	0.00609 (19)	0.00323 (6)	0	0
Ge2	0.00662 (10)	0.00662 (10)	0.00681 (13)	0.00302 (9)	0.00038 (4)	−0.00038 (4)
Ge3	0.00664 (10)	0.00724 (10)	0.00699 (11)	0.00371 (7)	−0.00026 (6)	−0.00011 (6)
Ge4	0.00655 (10)	0.00655 (10)	0.00585 (15)	0.00328 (5)	0	0
O1	0.0113 (6)	0.0086 (6)	0.0094 (5)	0.0050 (5)	0.0036 (5)	0.0017 (5)
O2	0.0062 (5)	0.0113 (6)	0.0109 (6)	0.0025 (5)	0.0002 (4)	0.0025 (5)
O3	0.0107 (6)	0.0115 (6)	0.0107 (5)	0.0037 (5)	0.0038 (5)	−0.0019 (5)
O4	0.0124 (6)	0.0112 (6)	0.0091 (5)	0.0071 (5)	−0.0031 (5)	−0.0005 (4)
O5	0.0093 (6)	0.0093 (6)	0.0194 (9)	0.0053 (7)	−0.0019 (3)	0.0019 (3)

Geometric parameters (Å, º)

K1—O2	2.7377 (13)	Ge2—O1	1.7428 (12)
K1—O1^i	2.7401 (13)	Ge2—O2	1.7889 (12)
K1—O2^ii	2.7547 (13)	Ge2—O2^viii	1.7889 (12)
K1—O4^iii	2.8128 (13)	Ge3—O3	1.7232 (12)
K1—O5^iii	2.8305 (14)	Ge3—O4	1.7295 (12)
K1—O3^iv	2.8471 (13)	Ge3—O5	1.7667 (8)
K1—O4	2.9588 (13)	Ge3—O2	1.7816 (12)
Ge1—O1^i	1.9078 (12)	Ge4—O4^ix	1.8649 (12)
Ge1—O1^v	1.9078 (12)	Ge4—O4^x	1.8649 (12)
Ge1—O1^vi	1.9078 (12)	Ge4—O4^xi	1.8649 (12)
Ge1—O1^ii	1.9078 (12)	Ge4—O3^xii	1.8862 (12)
Ge1—O1^vii	1.9078 (12)	Ge4—O3^xiii	1.8862 (12)
Ge1—O1	1.9078 (12)	Ge4—O3	1.8862 (12)
Ge2—O1^viii	1.7428 (12)
O2—K1—O1^i	75.48 (4)	O1^v—Ge1—O1^vii	88.58 (5)
O2—K1—O2^ii	118.94 (5)	O1^vi—Ge1—O1^vii	91.42 (5)
O1^i—K1—O2^ii	70.93 (4)	O1^ii—Ge1—O1^vii	180
O2—K1—O4^iii	119.39 (4)	O1^i—Ge1—O1	91.42 (5)
O1^i—K1—O4^iii	151.15 (4)	O1^v—Ge1—O1	88.58 (5)
O2^ii—K1—O4^iii	80.25 (4)	O1^vi—Ge1—O1	180.00 (6)
O2—K1—O5^iii	139.58 (3)	O1^ii—Ge1—O1	91.42 (5)
O1^i—K1—O5^iii	131.15 (3)	O1^vii—Ge1—O1	88.58 (5)
O2^ii—K1—O5^iii	100.17 (3)	O1^viii—Ge2—O1	126.40 (8)
O4^iii—K1—O5^iii	54.64 (3)	O1^viii—Ge2—O2	107.98 (6)
O2—K1—O3^iv	83.65 (4)	O1—Ge2—O2	104.11 (5)
O1^i—K1—O3^iv	84.96 (4)	O1^viii—Ge2—O2^viii	104.11 (5)
O2^ii—K1—O3^iv	139.60 (4)	O1—Ge2—O2^viii	107.98 (6)
O4^iii—K1—O3^iv	119.49 (4)	O2—Ge2—O2^viii	104.45 (8)
O5^iii—K1—O3^iv	71.61 (3)	O3—Ge3—O4	126.74 (6)
O2—K1—O4	60.64 (3)	O3—Ge3—O5	115.93 (4)
O1^i—K1—O4	120.00 (4)	O4—Ge3—O5	95.59 (5)
O2^ii—K1—O4	166.33 (4)	O3—Ge3—O2	101.04 (6)
O4^iii—K1—O4	88.35 (4)	O4—Ge3—O2	110.34 (6)
O5^iii—K1—O4	78.94 (3)	O5—Ge3—O2	106.09 (6)
O3^iv—K1—O4	53.31 (4)	O4^ix—Ge4—O4^x	91.06 (5)
O2—K1—O1	53.31 (3)	O4^ix—Ge4—O4^xi	91.06 (5)
O1^i—K1—O1	52.13 (4)	O4^x—Ge4—O4^xi	91.06 (5)
O2^ii—K1—O1	65.79 (3)	O4^ix—Ge4—O3^xii	90.53 (5)
O4^iii—K1—O1	114.43 (3)	O4^x—Ge4—O3^xii	88.02 (5)
O5^iii—K1—O1	164.71 (3)	O4^xi—Ge4—O3^xii	178.18 (5)
O3^iv—K1—O1	122.80 (4)	O4^ix—Ge4—O3^xiii	178.18 (5)
O4—K1—O1	113.17 (3)	O4^x—Ge4—O3^xiii	90.53 (5)
O1^i—Ge1—O1^v	180	O4^xi—Ge4—O3^xiii	88.02 (5)
O1^i—Ge1—O1^vi	88.58 (5)	O3^xii—Ge4—O3^xiii	90.41 (5)
O1^v—Ge1—O1^vi	91.42 (5)	O4^ix—Ge4—O3	88.02 (5)
O1^i—Ge1—O1^ii	88.58 (5)	O4^x—Ge4—O3	178.18 (5)
O1^v—Ge1—O1^ii	91.42 (5)	O4^xi—Ge4—O3	90.53 (5)
O1^vi—Ge1—O1^ii	88.58 (5)	O3^xii—Ge4—O3	90.41 (5)
O1^i—Ge1—O1^vii	91.42 (5)	O3^xiii—Ge4—O3	90.41 (5)

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

(Rb2Ge4O9) Dirubidium tetragermanate

Crystal data

Rb2Ge4O9	F(000) = 1644
Mr = 605.3	Dx = 4.817 Mg m^−3
Trigonal, P3c1	Mo Kα radiation, λ = 0.71073 Å
a = 12.1008 (6) Å	µ = 25.89 mm^−1
c = 9.8722 (5) Å	T = 295 K
V = 1251.91 (11) Å^3	Prism, colourless
Z = 6	0.14 × 0.05 × 0.04 mm

Data collection

Bruker SMART APEX diffractometer	1091 independent reflections
Radiation source: three-circle diffractometer	1027 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.048
ω scan at four different ϕ positions	θmax = 28.9°, θmin = 1.9°
Absorption correction: empirical (using intensity measurements) [multiscan absorption correction using APEX2 (Bruker, 2007)]	h = −16→16
Tmin = 0.298, Tmax = 0.746	k = −16→15
13739 measured reflections	l = −13→13

Refinement

Refinement on F^2	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.017	w = 1/[σ^2(Fo^2) + (0.0186P)^2 + 0.9217P] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.042	(Δ/σ)max = 0.001
S = 1.20	Δρmax = 0.62 e Å^−3
1091 reflections	Δρmin = −0.89 e Å^−3
71 parameters	Extinction correction: SHELXL97 (Sheldrick, 2008)
0 restraints	Extinction coefficient: 0.00650 (19)

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
Rb1	0.337178 (18)	0.335293 (17)	0.56932 (2)	0.01206 (9)
Ge1	0	0	0.5	0.00325 (12)
Ge2	0.17740 (2)	0.17740 (2)	0.25	0.00375 (9)
Ge3	0.48398 (2)	0.333022 (18)	0.27825 (2)	0.00399 (9)
Ge4	0.6667	0.3333	0.02886 (4)	0.00335 (10)
O1	0.07656 (13)	0.14755 (13)	0.38704 (14)	0.0069 (3)
O2	0.32683 (13)	0.20855 (13)	0.31913 (14)	0.0077 (3)
O3	0.51870 (14)	0.27242 (13)	0.13727 (15)	0.0090 (3)
O4	0.57704 (13)	0.38950 (13)	0.42159 (15)	0.0077 (3)
O5	0.46957 (16)	0.46957 (16)	0.25	0.0101 (4)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Rb1	0.00989 (12)	0.01141 (13)	0.01378 (14)	0.00451 (8)	0.00190 (7)	−0.00279 (7)
Ge1	0.00249 (15)	0.00249 (15)	0.0048 (2)	0.00124 (7)	0	0
Ge2	0.00267 (12)	0.00267 (12)	0.00533 (17)	0.00091 (11)	0.00028 (5)	−0.00028 (5)
Ge3	0.00293 (12)	0.00353 (12)	0.00574 (14)	0.00179 (8)	−0.00012 (7)	0.00007 (7)
Ge4	0.00280 (12)	0.00280 (12)	0.00445 (18)	0.00140 (6)	0	0
O1	0.0076 (6)	0.0053 (6)	0.0082 (7)	0.0034 (5)	0.0045 (5)	0.0025 (5)
O2	0.0037 (6)	0.0077 (7)	0.0102 (7)	0.0017 (6)	−0.0003 (5)	0.0019 (5)
O3	0.0065 (6)	0.0101 (7)	0.0085 (7)	0.0026 (6)	0.0038 (5)	−0.0019 (5)
O4	0.0089 (7)	0.0077 (7)	0.0082 (7)	0.0055 (6)	−0.0033 (5)	−0.0008 (5)
O5	0.0061 (7)	0.0061 (7)	0.0185 (11)	0.0034 (8)	−0.0021 (4)	0.0021 (4)

Geometric parameters (Å, º)

Rb1—O2^i	2.8228 (14)	Ge2—O1^v	1.7346 (14)
Rb1—O2	2.8768 (14)	Ge2—O1	1.7346 (14)
Rb1—O1^ii	2.8881 (13)	Ge2—O2	1.7878 (14)
Rb1—O5^iii	2.9503 (16)	Ge2—O2^v	1.7878 (14)
Rb1—O4^iii	2.9528 (14)	Ge3—O3	1.7203 (14)
Rb1—O3^iv	2.9667 (14)	Ge3—O4	1.7228 (14)
Rb1—O4	3.0130 (14)	Ge3—O5	1.7682 (9)
Rb1—O1	3.3437 (14)	Ge3—O2	1.7842 (14)
Rb1—O3^v	3.3820 (15)	Ge4—O4^ix	1.8700 (14)
Ge1—O1^vi	1.9067 (13)	Ge4—O4^x	1.8700 (14)
Ge1—O1^ii	1.9067 (13)	Ge4—O4^xi	1.8700 (14)
Ge1—O1^vii	1.9067 (13)	Ge4—O3^xii	1.8908 (14)
Ge1—O1	1.9067 (13)	Ge4—O3^xiii	1.8908 (14)
Ge1—O1^i	1.9067 (13)	Ge4—O3	1.8908 (14)
Ge1—O1^viii	1.9067 (13)
O2^i—Rb1—O2	121.71 (5)	O4^iii—Rb1—O2^iv	132.37 (4)
O2^i—Rb1—O1^ii	71.94 (4)	O3^iv—Rb1—O2^iv	48.29 (4)
O2—Rb1—O1^ii	74.87 (4)	O4—Rb1—O2^iv	99.83 (3)
O2^i—Rb1—O5^iii	98.46 (3)	O1—Rb1—O2^iv	101.44 (3)
O2—Rb1—O5^iii	138.73 (3)	O3^v—Rb1—O2^iv	165.44 (3)
O1^ii—Rb1—O5^iii	132.00 (4)	O5—Rb1—O2^iv	142.79 (2)
O2^i—Rb1—O4^iii	79.83 (4)	O1^vi—Ge1—O1^ii	180.00 (7)
O2—Rb1—O4^iii	121.63 (4)	O1^vi—Ge1—O1^vii	89.25 (6)
O1^ii—Rb1—O4^iii	151.77 (4)	O1^ii—Ge1—O1^vii	90.75 (6)
O5^iii—Rb1—O4^iii	52.26 (3)	O1^vi—Ge1—O1	89.25 (6)
O2^i—Rb1—O3^iv	138.62 (4)	O1^ii—Ge1—O1	90.75 (6)
O2—Rb1—O3^iv	80.99 (4)	O1^vii—Ge1—O1	89.25 (6)
O1^ii—Rb1—O3^iv	83.50 (4)	O1^vi—Ge1—O1^i	90.75 (6)
O5^iii—Rb1—O3^iv	73.71 (3)	O1^ii—Ge1—O1^i	89.25 (6)
O4^iii—Rb1—O3^iv	119.74 (4)	O1^vii—Ge1—O1^i	180
O2^i—Rb1—O4	168.84 (4)	O1—Ge1—O1^i	90.75 (6)
O2—Rb1—O4	58.73 (4)	O1^vi—Ge1—O1^viii	90.75 (6)
O1^ii—Rb1—O4	117.31 (4)	O1^ii—Ge1—O1^viii	89.25 (6)
O5^iii—Rb1—O4	80.02 (3)	O1^vii—Ge1—O1^viii	90.75 (6)
O4^iii—Rb1—O4	90.69 (4)	O1—Ge1—O1^viii	180.00 (7)
O3^iv—Rb1—O4	51.75 (4)	O1^i—Ge1—O1^viii	89.25 (6)
O2^i—Rb1—O1	68.66 (4)	O1^v—Ge2—O1	125.76 (9)
O2—Rb1—O1	53.19 (4)	O1^v—Ge2—O2	106.20 (6)
O1^ii—Rb1—O1	51.00 (5)	O1—Ge2—O2	106.15 (6)
O5^iii—Rb1—O1	165.94 (2)	O1^v—Ge2—O2^v	106.15 (6)
O4^iii—Rb1—O1	117.58 (4)	O1—Ge2—O2^v	106.20 (6)
O3^iv—Rb1—O1	119.54 (4)	O2—Ge2—O2^v	104.65 (9)
O4—Rb1—O1	111.47 (4)	O3—Ge3—O4	125.67 (7)
O2^i—Rb1—O3^v	74.81 (4)	O3—Ge3—O5	115.46 (5)
O2—Rb1—O3^v	82.50 (4)	O4—Ge3—O5	96.27 (6)
O1^ii—Rb1—O3^v	120.01 (4)	O3—Ge3—O2	101.98 (7)
O5^iii—Rb1—O3^v	100.97 (3)	O4—Ge3—O2	111.01 (7)
O4^iii—Rb1—O3^v	49.03 (4)	O5—Ge3—O2	105.25 (7)
O3^iv—Rb1—O3^v	146.22 (3)	O4^ix—Ge4—O4^x	91.08 (6)
O4—Rb1—O3^v	94.55 (4)	O4^ix—Ge4—O4^xi	91.08 (6)
O1—Rb1—O3^v	70.86 (3)	O4^x—Ge4—O4^xi	91.08 (6)
O2^i—Rb1—O5	124.40 (3)	O4^ix—Ge4—O3^xii	89.92 (6)
O2—Rb1—O5	50.91 (4)	O4^x—Ge4—O3^xii	87.90 (6)
O1^ii—Rb1—O5	124.58 (4)	O4^xi—Ge4—O3^xii	178.58 (6)
O5^iii—Rb1—O5	100.094 (8)	O4^ix—Ge4—O3^xiii	178.58 (6)
O4^iii—Rb1—O5	71.72 (3)	O4^x—Ge4—O3^xiii	89.92 (6)
O3^iv—Rb1—O5	96.93 (3)	O4^xi—Ge4—O3^xiii	87.90 (6)
O4—Rb1—O5	45.87 (3)	O3^xii—Ge4—O3^xiii	91.11 (6)
O1—Rb1—O5	83.64 (4)	O4^ix—Ge4—O3	87.90 (6)
O3^v—Rb1—O5	50.37 (2)	O4^x—Ge4—O3	178.58 (6)
O2^i—Rb1—O2^iv	90.96 (4)	O4^xi—Ge4—O3	89.92 (6)
O2—Rb1—O2^iv	103.031 (11)	O3^xii—Ge4—O3	91.11 (6)
O1^ii—Rb1—O2^iv	50.52 (3)	O3^xiii—Ge4—O3	91.11 (6)
O5^iii—Rb1—O2^iv	83.86 (3)

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