Pyroxene-type compounds NaM³⁺Ge₂O₆, with M = Ga, Mn, Sc and In

The four title compounds, namely sodium gallium germanate, NaGaGe₂O₆, sodium manganese vanadate germanate, NaMnV_0.1Ge_1.9O₆, sodium scandium germanate, NaScGe₂O₆, and sodium indium germanate, NaInGe₂O₆, adopt the high-temperature structure of the pyroxene-type chain germanates, with monoclinic symmetry and space group C2/c. The lattice parameters, the individual and average bond lengths involving M1, and the distortion parameters scale well with the ionic radius of the M1 cation. NaGaGe₂O₆ has more distorted M1 sites and more extended tetra­hedral chains than NaInGe₂O₆, in which a high degree of kinking is required to maintain the connection between the octa­hedral and tetra­hedral building units of the pyroxene structure. An exceptional case is NaMnGe₂O₆, in which the strong Jahn-Teller effect of Mn³⁺ results in more distorted octa­hedral sites than expected according to linear extrapolation from the other NaM³⁺Ge₂O₆ pyroxenes. In contrast with the literature, minor incorporations of V⁵⁺ in the tetra­hedral site and a corresponding reduction of Mn³⁺ to Mn²⁺ in the octa­hedral sites in the present sample lower the Jahn-Teller distortion and stabilize the Mn-bearing pyroxene, even allowing its synthesis at ambient pressure.

S1. Introduction

The pyroxene family shows a wide range of chemical compositions, in both naturally occurring and synthetic systems. The general formula is given as M2M1T₂O₆, in which M2 stands for divalent or monovalent cations such as, among others, Ca²⁺, Na⁺ and Li⁺, M1 stands for Mg²⁺, Al³⁺ and di- and trivalent transition metal cations, and T stands for Si⁴⁺ and Ge⁴⁺, the latter in the synthetic system only. The variety in composition is also reflected in the different space-group symmetries, with C2/c, P2₁/c, P2/n and Pbca being the most frequently occurring (Cameron & Papike 1981), P1 being found for the low-temperature phase of NaTiSi₂O₆ (Redhammer et al., 2003) and P2₁/n being recently reported for a new pyroxene structure type in LiAlGe₂O₆ (Redhammer et al., 2012).

For the sodium–silicate pyroxenes with space-group symmetry C2/c, M1 can be Al³⁺, Ga³⁺, Fe³⁺, Mn³⁺, V³⁺, Ti³⁺, Sc³⁺ or In³⁺, as summarized, for example, by Redhammer et al. (2003). In pyroxene research, Si⁴⁺ is frequently replaced by Ge⁴⁺ to tune the M1 chain distances, with the aim of studying magnetic properties at low temperature (Redhammer et al., 2011, 2013), but also of shifting structural phase transitions, e.g. from P2₁/c to C2/c, to higher temperatures or lower pressures, as demonstrated e.g. for LiFeGe₂O₆ (Redhammer et al., 2010; Nestola et al., 2009). For the NaM³⁺Ge₂O₆ system, the structures of NaFeGe₂O₆ (Redhammer et al., 2011), NaCrGe₂O₆ (Redhammer, Roth, Topa & Amthauer, 2008; Nenert et al., 2009), NaVGe₂O₆ (Emirdag-Eanes & Kolis, 2004), NaMnGe₂O₆ (synthesized at high pressure; Chen et al., 2013) and NaScGe₂O₆ (Genkina et al., 1985) have been reported. For the last compound, only isotropic atomic displacement parameters were given. In this contribution, we present the structure determinations of NaGaGe₂O₆ and NaInGe₂O₆, and also a redetermination and refinement of the structure of NaScGe₂O₆. Together with new data on NaMnGe₂O₆, synthesized at ambient pressure, a crystal chemical comparison among the NaM³⁺Ge₂O₆ compounds and with the corresponding sodium–silicate pyroxenes is provided. The synthesis of NaMnGe₂O₆ at ambient pressure has not been reported previously.

S2. Experimental

S2.1. Synthesis and crystallization

NaScGe₂O₆ and NaInGe₂O₆ were grown from stoichiometric mixtures of Na₂CO₃, GeO₂ and Sc₂O₃ or In₂O₃ using a flux-growth synthesis route, with Na₂MoO₄ (eight parts) and NaVO₃ (two parts) as the high-temperature solvent. The nutrient–flux ratio was 1:10. Oxide mixtures and flux were ground together, placed in platinum crucibles, covered with lids, heated to 1473 K at a rate of 3 K min^-1 and held at this temperature for 24 h to allow the melt to homogenize. Afterwards, the temperature was lowered at a rate of 0.03 K min^-1 to 973 K. Cooling to room temperature was accelerated by shutting down the furnace. After dissolving the flux in hot distilled water, transparent colourless idiomorphic crystals up to 2 mm in size were found for both compounds.

NaGaGe₂O₆ could not be grown using flux methods, but was synthesized from a stoichiometric mixture of Na₂CO₃, Ga₂O₃ and GeO₂ at 20 GPa and 1473 K over a period of 70 h in a piston cylinder apparatus at the Institute of Crystallography, RWTH Aachen, Germany. Small single crystals up to 100 µm in size were obtained.

NaMnGe₂O₆ was obtained by chance during attempts to synthesize the pyroxene compound SrMn²⁺Ge₂O₆ using the Na₂MoO₄/NaVO₃ flux. One part of a stoichiometric mixture of SrCO₃, MnO and GeO₂ was mixed with ten parts of the flux, heated to 1473 K and cooled slowly to 1128 K at a rate of 0.02 K min^-1. After dissolving the flux, brown needle-like [Prismatic given in CIF tables - please clarify] single crystals of NaMnGe₂O₆, plates of an as yet unidentified and unknown Na–Mn–Ge phase and crystals of transparent SrWO₃ were obtained. Semi-qu­anti­tative energy dispersive X-ray (EDX) analysis on the pyroxene phase yielded a low content of vanadium, besides dominating Na, Mn and Ge. Electron microprobe analysis of the single crystals, among them those used for the X-ray diffraction work, yielded an average chemical composition of Na_1.02Mn_0.95V_0.10Ge_1.95O₆ (based on seven grains, with five to six points per grain), with an Na content varying in the range 1.00–1.04, Mn 0.94–0.97, Ge 1.93–1.97 and V 0.07–0.13.

When the synthesis was repeated starting with a stoichiometric mixture of Na₂CO₃, Mn₂O₃ and GeO₂ with the Na₂WO₄ flux (1:10), but without the addition of NaVO₃, a Ge-rich aenigmatite type compound (Redhammer, Roth & Amthauer, 2008) and NaGe₉O₂₀, but no pyroxene phase, were obtained. In contrast, addition of NaVO₃ to the flux gave plate-to-needle-shaped NaMnGe₂O₆ upon cooling from 1373 to 1223 K; these crystals were not sufficiently large for intensity data collection. These results prove that NaMnGe₂O₆ can also be synthesized at ambient pressure; small amounts of vanadium and, associated with this, reduction of Mn³⁺ to Mn²⁺, are obviously necessary to stabilize the pyroxene structure.

S2.2. Refinement

Crystal data, data collection parameters and structure refinement details are summarized in Table 1, while Table 2 contains selected geometric and distortion parameters of the title compounds. Initial structure determinations were carried out using direct methods; after confirming the C2/c pyroxene structure, the atomic coordinates of NaCrGe₂O₆ (Redhammer, Roth & Amthauer, 2008 OR Redhammer, Roth, Topa & Amthauer, 2008 ?) were used as the starting point for further structure refinements. Structural data for NaScGe₂O₆ obtained in this study agree to within four standard uncertainties with those reported by Genkina et al. (1985); our data generally exhibit smaller standard uncertainties. However, our data for NaMnGe₂O₆ differ significantly from those given by Chen et al. (2013); this difference may arise from the different pressures used during the syntheses (ambient versus high pressure) and from the small content of vanadium in our sample, as discussed above. Based on the results of microprobe analysis for this NaMnGe₂O₆ crystal, a fractional occupancy of vanadium was introduced at the Ge site and the occupancy was allowed to vary with the restraint Ge + V = 1.00. Refinement based on intensity data sets for five different crystals yielded V contents of 0.08–0.11 atoms per formula unit (apfu) at the tetra­hedral sites, in good agreement with the microprobe results. In the final refinement, the V content at the tetra­hedral site was constrained to 0.1 apfu; the valence state is most likely V⁵⁺. Due to their similar scattering factors, our laboratory X-ray data do not allow a meaningful site-occupancy refinement of V versus Mn at the M1 position; full occupancy with Mn was assumed for simplicity.

S3. Results and discussion

The title compounds are all monoclinic, space group C2/c, and adopt the so-called high-temperature form of the two possible but distinct C2/c polymorphs of pyroxene topology (the second is the high-pressure C2/c structure; compare with, for example, Nestola et al., 2009). The asymmetric unit contains one Na position on 4e, one M³⁺ position, also on 4e, and one Ge and three O atoms, all on general position 8f. The transition metal cations occupy the hexacoordinated M1 site and share edges with their neighbours, thus forming infinite zigzag chains of o­cta­hedra parallel to the crystallographic c axis. The corner-sharing GeO₄ tetra­hedra also make up infinite chains parallel to the c axis, giving rise to the name `chain germanates' for this group of materials. The tetra­hedral chains are related to each other by the twofold axis. Sodium occupies the 6+2-fold coordinated M2 position, filling the inter­stitial space between the M1O₆ and GeO₄ chains. Figs. 1 and 2 give representations of the NaGaGe₂O₆ structure.

Structural variations across the NaM³⁺Ge₂O₆ series are largely controlled by the size of the metal cation at the M1 site. The unit-cell volume increases from NaGaGe₂O₆ [r(Ga³⁺) = 0.62 Å; Shannon & Prewitt, 1969] to NaInGe₂O₆ [r(In³⁺) = 0.79 Å; Shannon & Prewitt, 1969]. The substitution of Si⁴⁺ by Ge⁴⁺ causes an increase in volume of 9%. Similar to the silicates, an almost linear variation of volume with ionic radius is observed from Ga³⁺- to Sc³⁺-bearing pyroxenes. It is evident that our data for NaMnGe₂O₆ deviate much less from this linear variation than those of Chen et al. (2013), whose sample was synthesized at high pressure, similar to the NaMnSi₂O₆ sample (Ohashi et al., 1987). The latter [Could refer to either of two, or even three. Would be clearer to give explicit compound name here] also deviates significantly from the linear trend defined by the silicates. The unit-cell volume of NaInGe₂O₆ is smaller than expected from the linear variation, but the observation is consistent with results for the silicates (see Fig. 3) and was also reported for LiM³⁺Si₂O₆ by Redhammer & Roth (2004a). The lattice parameters a, b, c and β show similar trends, again with the data for NaMn(Si,Ge)₂O₆, synthesized at high pressure, deviating more than the other pyroxenes. However, the lattice parameters of the V-containing ambient-pressure NaMnGe₂O₆ are once again closer to the common trend defined by the other pyroxenes.

The mean <M1—O> distance increases almost linearly with ionic radius in both Na–silicate and Na–germanate pyroxenes, with <M1—O> generally being somewhat larger in the germanate pyroxenes. The data for NaMn³⁺Ge₂O₆ obtained in this study again match the general trend more closely than those from Chen et al. (2013). This is also reflected by the individual Mn—O bond lengths, which are distinctly different in the sample of Chen et al. (2013) and those of this study, especially for the Mn—O1^vi bonds within the equatorial plane of the o­cta­hedron (for symmetry codes in the following discussion, see Table 2). These are larger in the ambient-pressure NaMnGe₂O₆ by 0.061 Å, while the Mn—O1^v bond to the apex O atoms of the o­cta­hedra is smaller by 0.046 Å, giving rise to a more regular and less elongated o­cta­hedron at ambient pressure compared with the high-pressure Mn pyroxene. Within the complete NaM³⁺Ge₂O₆ series, the individual M1—O bond lengths all increase to the same extent from Ga³⁺ to In³⁺.

Generally, the M1 o­cta­hedra are slightly elongated along the c axis, with ratios of <M1—O_equ>/M1—O_apex \sim 0.98–0.99, except for NaMnGe₂O₆. Here, values of 0.93 are calculated for ambient-pressure NaMnGe₂O₆ in this study and 0.88 for the high-pressure NaMnGe₂O₆ of Chen et al. (2013). This exceptional case is also expressed by the bond-length distortion (BLD; Table 2), which is distinctly more pronounced in high-pressure NaMnGe₂O₆ compared with the other compounds (Fig. 4). Here, again, data for ambient-pressure NaMnGe₂O₆ behave differently and are closer to the values of NaFeGe₂O₆, while the BLD is generally similar in silicates and germanates, especially for Ga³⁺, Sc³⁺ and In³⁺. Chen et al. (2013) suggested that the large BLD in high-pressure NaMnGe₂O₆ might be the result of the strong Jahn–Teller effect of Mn³⁺, and that high pressure could be mandatory to overcome it during the synthesis of NaMnGe₂O₆. To some extent, this contrasts with the results of this study. Obviously, the incorporation of small amounts of vanadium reduces the Jahn–Teller distortion and stabilizes the Mn-bearing pyroxene at ambient pressure. Additionally, the incorporation of V⁵⁺ on the tetra­hedral site requires some reduction of Mn³⁺ to Mn²⁺ to maintain charge balance. The low content of Mn²⁺, which has a fully symmetric 3d⁵ electron-shell configuration, could then be seen as a possible reason for the less pronounced polyhedral distortion. As Mn²⁺ is distinctly larger (r = 0.82 Å) than Mn³⁺ (r = 0.65 Å; Shannon & Prewitt, 1969), this explains to some extent the differences between ambient- and high-pressure NaMnGe₂O₆. When compared with the data of Chen et al. (2013), the increase in the Mn—O1^vi bond lengths within the equatorial plane of the o­cta­hedron in the ambient-pressure NaMnGe₂O₆ sample may be an indicator of the substitution of Mn³⁺ by Mn²⁺. The shorter Mn—O1^v bond length to the apex atom is probably due to a smaller Jahn–Teller distortion. Also, the volume of the M1 site is slightly larger in the Mn pyroxene of this study compared with the high-pressure structure of Chen et al. (2013), again an indication of small amounts of larger Mn²⁺ on the M1 site due to the V⁵⁺ substitution on the tetra­hedral sites.

Generally, the germanate pyroxenes display larger angular distortions of the o­cta­hedra than the comparable silicate compounds, and the angles O1^v_apex—M1—O1^xi_apex at the same point are closer to the ideal value of 180°. This is related to the larger space requirement and altered kinking state of the tetra­hedral chain. The O1_apex atom common to the o­cta­hedral and tetra­hedral chains plays a pivotal role in maintaining the connection between these two building units of the pyroxene structure. It was noted by Redhammer & Roth (2004a) and Redhammer et al. (2003) that the o­cta­hedral angle variance (OAV) and the O1^v—M1—O1^xi angle behave differently for compounds having a spherical outer electron shell (Ga³⁺, Fe³⁺, Sc³⁺, In³⁺) than for those with a nonspherical electron configuration (Cr³⁺, V³⁺, Mn³⁺, Ti³⁺). This also holds true for the structures of the Na–germanates reported here, with NaGaGe₂O₆ having the most distorted o­cta­hedra in terms of the angular distortion (largest OAV; Table 2). The O1^v—M1—O1^xi angle here is 173.206 (16)°, deviating significantly from the ideal value of 180°, whereas NaCrGe₂O₆, with a comparable ionic radius, has an O1^v—M1—O1^xi angle of 178.752 (18)° (Redhammer, Roth & Amthauer, 2008 OR Redhammer, Roth, Topa & Amthauer, 2008 ?). Pyroxenes containing transition metals with nonspherical electron configurations have more stretched O1^v—M1—O1^xi geometries closer to 180° and thus lower angular distortions.

Similar observations are made for the variation in the M1—O1^v—M1^xiv angle, an important structural parameter with respect to magnetic superexchange (Fig. 5 and Table 2). The M1—O1^v—M1^xiv angles deviate distinctly from the ideal value of 90° in the Na–germanate series, but they follow a linear trend for the transition metals with spherical electron configurations, for both silicates and germanates. Thus, the M1—O1^v—M1^xiv values are larger by ~1.5° compared with the analogous silicates. The Cr, V, Ti and Mn members deviate from these trends. Also, the M1—M1^xiv distances are smaller for the latter compounds [The analogue silicates or the Cr, V, Ti and Mn members?]. As the sum of the M1—O1^v—M1^xiv and the O1^v—M1—O1^xi angles is 180° (Ohashi et al., 1987), smaller M1—O1^v—M1^xiv angles correspond to larger O1^v—M1—O1^xi angles. These larger values may then be due to repulsion between the O1 atoms and the unpaired electrons of the above-mentioned transition metals. These observations underline the fact that not only steric considerations but also electronic configurations represent important factors for controlling the M1 site geometry.

Within a coordination sphere of 3.0 Å, the Na atom is surrounded by eight O atoms, six of them associated with Na—O bonds in the range 2.4–2.6 Å and the other two more distant, in the range 2.75–2.92 Å. The Na⁺ cation can thus be regarded as 6+2 coordinated. In particular, the long M2—O3ⁱⁱⁱ bonds show a large variation with the radius of the M1 cation, which is a consequence of the altered kinking state of the tetra­hedral chain. The O3 atoms not only belong to the coordination of the M2 cation, but also represent the bridging O atoms in the tetra­hedral chain. The longest M2—O3ⁱⁱⁱ bond is found in NaScGe₂O₆ [2.9124 (14) Å]. In NaInGe₂O₆ with an even larger M1 cation, this value is reduced, while the smaller Na—O3ⁱ is increased. This is a direct consequence of the kinking of the tetra­hedra. The shortest Na—O bond is that to the O1 atom, giving a connection of the M1 and M2 polyhedra along a common edge perpendicular to the b axis (with the bond thus being parallel to b). The average <Na—O> bond length increases from Ga³⁺ to the Sc³⁺ member, with some deviations observed for the V³⁺- and Mn-bearing pyroxenes. However, these deviations from the general Na pyroxene trends are much less pronounced for the M2 than for the M1 site. Generally, the Na germanates show larger individual and average Na—O bond lengths in the germanates compared with the silicates, a direct consequence of the replacement of the smaller Si⁴⁺ by the larger Ge⁴⁺ cation.

In all members of the Na–germanate pyroxenes, the tetra­hedral chains display an `opposite' (O) rotation sense of the chains (cf. Redhammer & Roth, 2004a). This kinking of the tetra­hedral chains is one of the effective mechanisms to overcome geometric differences between o­cta­hedral and tetra­hedral chains in pyroxenes. The kinking state, defined by the O3—O3^vii—O3^xv bridging angle, is 172.747 (14)° in NaGaGe₂O₆ and decreases with increasing size of the M1 cation to 166.21 (5)° in NaInGe₂O₆ (Table 2). The most stretched tetra­hedral chains are found in NaFeGe₂O₆, with O3—O3^vii—O3^xv = 175.17 (7)°. However, not only does the kinking state change, but also a stretching of the Ge—O bond lengths takes place, with increasing size of the M1 cation. Here, especially, the two Ge1—O3 bonds running in the c direction become elongated, while the Ge1—O1 and Ge1—O2 bonds remain constant or are slightly shortened. Most prominent are the alterations in O—O edge lengths and O—Ge—O bond angles. Here, the O3—O3^vii edge increases from 2.7395 (13) Å in NaGaGe₂O₆ to 2.8167 (17) Å in NaInGe₂O₆ and the corresponding O3—Ge1—O3^vii angle opens up from 102.782 (11) to 105.54 (5)°. Also, the Ge1—O3—Ge1^xiii angle changes by nearly 1° from 133.1 (2) to 133.96 (7)°. This all increases the size of the tetra­hedral chain, especially along the c axis, and maintains the fit with the o­cta­hedral chain.

The BLD increases slightly from the Ga³⁺ to the In³⁺ member, whereas the angular distortion decreases. For the latter, the GeO₄ tetra­hedron exhibits a more distorted geometry than the SiO₄ tetra­hedron in the pyroxenes. However, the slopes of the variation are very similar and of the same order of magnitude.

The most significant deviation from the ideal geometry of a tetra­hedron is observed for NaGaGe₂O₆. The substantial angular distortion is mainly a consequence of a large O1—Ge1—O2 angle, which is 116.88 (19)°; the O1—O2 edge opposite this angle is the longest of the tetra­hedron, at 2.9613 (12) Å. The tetra­hedral chain is laterally connected to the o­cta­hedral chain via the O1 atom (see Fig. 2). The fit of the large GeO₄ tetra­hedron to the small GaO₆ o­cta­hedron can only be maintained by distortion and elongation of the tetra­hedra. Replacing Ga³⁺ by the smaller Al³⁺ needs even larger distortions and causes higher structural strain, so the syntheses of both NaAlGe₂O₆ and NaGaGe₂O₆ are thus only possible at high pressures. The incorporation of larger M1 cations reduces the structural strain along the b axis, the O1—Ge1—O2 angle and O1—O2 edge length decreasing from 114.89 (6)° and 2.9193 (17) Å in NaInGe₂O₆, respectively. Generally, the tetra­hedra are stretched along the c axis.

The average of the three O—Ge—O bonds involving the apex O1 atom is 112.81 (6)° in the Ga³⁺ member and decreases slightly to 112.00 (6)° in In³⁺. The basal planes of the tetra­hedra within a chain are almost coplanar to each other, the tilt being 1.66° in the Ga³⁺ sample and 1.26° in the In³⁺ end member.

The data for the Mn-bearing pyroxenes, both ambient- and high-pressure synthesized samples, do not deviate much from each other and fit well into the trend defined by the whole NaM³⁺Ge₂O₆ series.

Related literature

For related literature, see: Cameron & Papike (1981); Chen et al. (2013); Emirdag-Eanes & Kolis (2004); Genkina et al. (1985); Nenert et al. (2009); Nestola et al. (2009); Ohashi et al. (1987); Redhammer & Roth (2004a); Redhammer et al. (2003, 2010, 2011, 2012, 2013); Redhammer, Roth & Amthauer (2008); Redhammer, Roth, Topa & Amthauer (2008); Shannon & Prewitt (1969).

Computing details

For all compounds, data collection: APEX2 (Bruker, 2012); cell refinement: APEX2 (Bruker, 2012); data reduction: APEX2 (Bruker, 2012); program(s) used to solve structure: SHELXS2012 (Sheldrick, 2008); program(s) used to refine structure: SHELXL2012 (Sheldrick, 2008). Molecular graphics: DIAMOND (Brandenburg,2006) for NGaG; DIAMOND (Brandenburg, 2006) for NMnG, NScG, NInG. For all compounds, software used to prepare material for publication: WinGX (Farrugia, 2012).

Figures

	Fig. 1. The asymmetric unit and symmetry-related atoms of NaGaGe2O6, shown with 95% probability displacement ellipsoids. [Symmetry codes: (ii) x - 1/2, -y + 1/2, z - 1/2; (iii) -x + 1/2, -y + 1/2, -z; (iv) x - 1/2, y + 1/2, z; (v) x, -y + 1, z + 1/2; (vii) x, -y, z + 1/2; (viii) -x, y, -z + 1/2; (ix) -x + 1/2, -y + 1/2, -z + 1; (x) x - 1/2, -y + 1/2, z + 1/2; (xi) -x, -y + 1, -z; (xiii) x, -y, z - 1/2; (xvi) -x + 1/2, y + 1/2, -z + 1/2; (xvii) -x, -y, -z; (xviii) x - 1/2, y - 1/2, z; (xix) -x + 1/2, y - 1/2, -z + 1/2; (xx) x, y - 1, z.] [Codes ix and xiii are not used in either figure - can they be omitted?]
	Fig. 2. Polyhedral representation of the C2/c structure of NaGaGe2O6, displaying the M1 octahedral chain and related tetrahedral chains. For clarity, no polyhedra are shown for Na atoms. [Symmetry codes as in Fig. 1; in addition: (i) -x + 1/2, y + 1/2, -z + 1/2; (vi) x, y + 1, z; (xii) -x, y + 1, -z + 1/2; (xiv) -x, -y + 2, -x + 1; (xv) x, y, z + 1.]
	Fig. 3. The unit-cell volume of NaM^3+(Si,Ge)2O6 pyroxenes. Filled red squares represent the data from this study, and filled blue triangles represent the data for NaM^3+Ge2O6 from the literature, for Cr^3+ taken from Redhammer, Roth & Amthauer (2008) OR Redhammer, Roth, Topa & Amthauer (2008) ? and Nenert et al. (2009), for V^3+ from Emirdag-Eanes & Kolis (2004), for Fe^3+ from Redhammer et al. (2011) and for Mn^3+ from Chen et al. (2013). Data for silicates (crossed squares) are taken from Redhammer et al. (2003, and reference therein).
	Fig. 4. Variation of the octahedral bond-length distortion (BLD) of NaM^3+(Si,Ge)2O6 pyroxenes with ionic radius of M1. The symbols are as in Fig. 3.
	Fig. 5. Variation of the M1—O1—M1 bond angle of NaM^3+(Si,Ge)2O6 pyroxenes with ionic radius of M1. Filled squares and triangles represent data for elements with spherical and nonspherical electron configurations, respectively, for the Na–germanate pyroxenes, and filled and open circles represent data for the Na–silicate pyroxenes. References to the literature are as in Fig. 3.

(NGaG) Sodium gallium germanate

Crystal data

NaGaGe2O6	F(000) = 616
Mr = 333.93	Dx = 4.839 Mg m^−3
Monoclinic, C2/c	Mo Kα radiation, λ = 0.71073 Å
a = 9.9279 (9) Å	Cell parameters from 2544 reflections
b = 8.8550 (8) Å	θ = 3.2–26.6°
c = 5.4680 (6) Å	µ = 18.91 mm^−1
β = 107.5419 (11)°	T = 293 K
V = 458.35 (8) Å^3	Isometric, colourless
Z = 4	0.11 × 0.09 × 0.08 mm

Data collection

Bruker SMART APEX diffractometer	382 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.048
rotation, ω scans at four different φ positions	θmax = 26.6°, θmin = 3.2°
Absorption correction: multi-scan (APEX2; Bruker, 2012)	h = −12→12
Tmin = 0.359, Tmax = 0.746	k = −11→11
2544 measured reflections	l = −6→6
489 independent reflections

Refinement

Refinement on F^2	47 parameters
Least-squares matrix: full	0 restraints
R[F^2 > 2σ(F^2)] = 0.029	w = 1/[σ^2(Fo^2) + (0.0237P)^2 + 0.9355P] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.056	(Δ/σ)max < 0.001
S = 1.03	Δρmax = 0.85 e Å^−3
489 reflections	Δρmin = −0.81 e Å^−3

Special details

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

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

	x	y	z	Uiso*/Ueq
Na1	0	0.3016 (4)	0.25	0.0150 (8)
Ga1	0	0.90672 (11)	0.25	0.0061 (2)
Ge1	0.28868 (6)	0.09561 (7)	0.22575 (12)	0.00600 (19)
O2	0.3580 (4)	0.2737 (5)	0.3025 (8)	0.0105 (9)
O1	0.1039 (4)	0.0798 (5)	0.1262 (8)	0.0062 (9)
O3	0.3617 (4)	0.0098 (5)	0.0076 (8)	0.0089 (9)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Na1	0.018 (2)	0.011 (2)	0.0131 (19)	0	0.0000 (16)	0
Ga1	0.0061 (5)	0.0063 (5)	0.0060 (5)	0	0.0019 (4)	0
Ge1	0.0052 (3)	0.0067 (3)	0.0063 (3)	−0.0003 (3)	0.0020 (2)	0.0000 (3)
O2	0.011 (2)	0.008 (2)	0.012 (2)	−0.0050 (19)	0.0030 (18)	−0.0009 (18)
O1	0.007 (2)	0.007 (2)	0.005 (2)	−0.0013 (18)	0.0025 (17)	0.0000 (18)
O3	0.005 (2)	0.015 (2)	0.006 (2)	0.0003 (19)	0.0002 (16)	−0.004 (2)

Geometric parameters (Å, º)

Na1—O1	2.409 (5)	Ga1—O1^vi	2.072 (4)
Na1—O3^i	2.438 (5)	Ge1—O2	1.721 (4)
Na1—O2^ii	2.518 (4)	Ge1—O3	1.746 (4)
Na1—O3^iii	2.797 (5)	Ge1—O1	1.754 (4)
Ga1—O2^iv	1.924 (4)	Ge1—O3^vii	1.760 (4)
Ga1—O1^v	2.008 (4)
O1^viii—Na1—O1	70.8 (2)	O2^ii—Na1—O3^x	115.55 (13)
O1^viii—Na1—O3^i	133.04 (14)	O2^ix—Na1—O3^x	83.39 (13)
O1—Na1—O3^i	123.40 (13)	O3^iii—Na1—O3^x	106.7 (2)
O1^viii—Na1—O3^iv	123.40 (13)	O2^iv—Ga1—O2^i	104.5 (3)
O1—Na1—O3^iv	133.04 (14)	O2^iv—Ga1—O1^v	93.27 (17)
O3^i—Na1—O3^iv	81.8 (2)	O2^i—Ga1—O1^v	90.89 (16)
O1^viii—Na1—O2^ii	83.99 (16)	O2^iv—Ga1—O1^xi	90.89 (16)
O1—Na1—O2^ii	70.90 (15)	O2^i—Ga1—O1^xi	93.27 (17)
O3^i—Na1—O2^ii	141.93 (18)	O1^v—Ga1—O1^xi	173.2 (2)
O3^iv—Na1—O2^ii	67.24 (14)	O2^iv—Ga1—O1^vi	163.96 (17)
O1^viii—Na1—O2^ix	70.90 (15)	O2^i—Ga1—O1^vi	86.83 (18)
O1—Na1—O2^ix	83.99 (16)	O1^v—Ga1—O1^vi	97.94 (15)
O3^i—Na1—O2^ix	67.24 (14)	O1^xi—Ga1—O1^vi	76.96 (17)
O3^iv—Na1—O2^ix	141.93 (18)	O2^iv—Ga1—O1^xii	86.83 (18)
O2^ii—Na1—O2^ix	149.3 (3)	O2^i—Ga1—O1^xii	163.96 (17)
O1^viii—Na1—O3^iii	160.96 (16)	O1^v—Ga1—O1^xii	76.96 (17)
O1—Na1—O3^iii	91.62 (12)	O1^xi—Ga1—O1^xii	97.94 (15)
O3^i—Na1—O3^iii	62.67 (9)	O1^vi—Ga1—O1^xii	84.6 (2)
O3^iv—Na1—O3^iii	63.66 (16)	O2—Ge1—O3	110.3 (2)
O2^ii—Na1—O3^iii	83.39 (13)	O2—Ge1—O1	116.88 (19)
O2^ix—Na1—O3^iii	115.55 (13)	O3—Ge1—O1	111.34 (19)
O1^viii—Na1—O3^x	91.62 (12)	O2—Ge1—O3^vii	104.10 (19)
O1—Na1—O3^x	160.96 (16)	O3—Ge1—O3^vii	102.78 (13)
O3^i—Na1—O3^x	63.66 (16)	O1—Ge1—O3^vii	110.22 (18)
O3^iv—Na1—O3^x	62.67 (9)	Ge1—O3—Ge1^xiii	133.1 (2)

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

(NMnG) Sodium manganese vanadate germanate

Crystal data

NaMnV0.1Ge1.9O6	F(000) = 588
Mr = 316.95	Dx = 4.471 Mg m^−3
Monoclinic, C2/c	Mo Kα radiation, λ = 0.71073 Å
a = 9.9611 (13) Å	Cell parameters from 2505 reflections
b = 8.8630 (11) Å	θ = 3.1–28.2°
c = 5.5598 (7) Å	µ = 14.93 mm^−1
β = 106.3818 (13)°	T = 293 K
V = 470.92 (10) Å^3	Prismatic, brown
Z = 4	0.17 × 0.09 × 0.07 mm

Data collection

Bruker SMART APEX diffractometer	558 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.019
rotation, ω scans at four different φ positions	θmax = 28.7°, θmin = 3.1°
Absorption correction: multi-scan (APEX2; Bruker, 2012)	h = −12→13
Tmin = 0.359, Tmax = 0.746	k = −11→11
2505 measured reflections	l = −7→7
585 independent reflections

Refinement

Refinement on F^2	47 parameters
Least-squares matrix: full	0 restraints
R[F^2 > 2σ(F^2)] = 0.021	w = 1/[σ^2(Fo^2) + (0.0288P)^2 + 2.9044P] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.058	(Δ/σ)max < 0.001
S = 1.12	Δρmax = 0.84 e Å^−3
585 reflections	Δρmin = −0.75 e Å^−3

Special details

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

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Na1	0	0.30110 (18)	0.25	0.0111 (3)
Mn1	0	0.90765 (7)	0.25	0.00847 (16)
Ge1	0.28982 (3)	0.09350 (3)	0.23556 (6)	0.01186 (14)	0.95
V1	0.28982 (3)	0.09350 (3)	0.23556 (6)	0.01186 (14)	0.05
O2	0.3585 (3)	0.2713 (3)	0.3065 (5)	0.0233 (5)
O1	0.1080 (3)	0.0806 (3)	0.1442 (5)	0.0188 (5)
O3	0.3622 (2)	0.0100 (3)	0.0145 (4)	0.0183 (5)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Na1	0.0156 (8)	0.0057 (7)	0.0095 (7)	0	−0.0006 (6)	0
Mn1	0.0100 (3)	0.0081 (3)	0.0072 (3)	0	0.0023 (2)	0
Ge1	0.0118 (2)	0.0114 (2)	0.0124 (2)	−0.00043 (11)	0.00355 (14)	−0.00162 (11)
V1	0.0118 (2)	0.0114 (2)	0.0124 (2)	−0.00043 (11)	0.00355 (14)	−0.00162 (11)
O2	0.0318 (15)	0.0142 (11)	0.0249 (12)	−0.0040 (10)	0.0096 (11)	−0.0022 (10)
O1	0.0137 (11)	0.0216 (12)	0.0207 (12)	0.0027 (9)	0.0044 (9)	−0.0050 (9)
O3	0.0164 (12)	0.0247 (13)	0.0140 (11)	0.0010 (9)	0.0045 (9)	−0.0047 (8)

Geometric parameters (Å, º)

Na1—O1	2.383 (3)	Mn1—O1^vi	2.154 (3)
Na1—O3^i	2.452 (3)	Ge1—O2	1.719 (2)
Na1—O2^ii	2.553 (3)	Ge1—O1	1.742 (3)
Na1—O3^iii	2.826 (3)	Ge1—O3	1.754 (2)
Mn1—O2^iv	1.948 (3)	Ge1—O3^vii	1.771 (2)
Mn1—O1^v	2.052 (3)
O1—Na1—O1^viii	69.81 (13)	O2^ii—Na1—O3^x	82.13 (8)
O1—Na1—O3^i	121.84 (8)	O2^ix—Na1—O3^x	115.77 (8)
O1^viii—Na1—O3^i	135.32 (8)	O3^iii—Na1—O3^x	107.35 (11)
O1—Na1—O3^iv	135.32 (8)	O2^iv—Mn1—O2^i	103.31 (15)
O1^viii—Na1—O3^iv	121.84 (8)	O2^iv—Mn1—O1^v	166.24 (11)
O3^i—Na1—O3^iv	81.93 (12)	O2^i—Mn1—O1^v	87.46 (10)
O1—Na1—O2^ii	73.74 (9)	O2^iv—Mn1—O1^xi	87.46 (10)
O1^viii—Na1—O2^ii	82.40 (9)	O2^i—Mn1—O1^xi	166.24 (11)
O3^i—Na1—O2^ii	141.16 (9)	O1^v—Mn1—O1^xi	83.32 (13)
O3^iv—Na1—O2^ii	66.47 (8)	O2^iv—Mn1—O1^vi	92.42 (10)
O1—Na1—O2^ix	82.40 (9)	O2^i—Mn1—O1^vi	91.02 (11)
O1^viii—Na1—O2^ix	73.74 (9)	O1^v—Mn1—O1^vi	95.97 (9)
O3^i—Na1—O2^ix	66.47 (8)	O1^xi—Mn1—O1^vi	79.85 (10)
O3^iv—Na1—O2^ix	141.16 (9)	O2^iv—Mn1—O1^xii	91.02 (11)
O2^ii—Na1—O2^ix	150.88 (13)	O2^i—Mn1—O1^xii	92.42 (10)
O1—Na1—O3^iii	158.98 (9)	O1^v—Mn1—O1^xii	79.85 (10)
O1^viii—Na1—O3^iii	92.19 (8)	O1^xi—Mn1—O1^xii	95.97 (9)
O3^i—Na1—O3^iii	63.62 (9)	O1^vi—Mn1—O1^xii	174.46 (13)
O3^iv—Na1—O3^iii	63.24 (5)	O2—Ge1—O1	116.18 (12)
O2^ii—Na1—O3^iii	115.77 (8)	O2—Ge1—O3	109.36 (12)
O2^ix—Na1—O3^iii	82.13 (8)	O1—Ge1—O3	111.54 (11)
O1—Na1—O3^x	92.19 (8)	O2—Ge1—O3^vii	103.69 (12)
O1^viii—Na1—O3^x	158.98 (9)	O1—Ge1—O3^vii	110.76 (11)
O3^i—Na1—O3^x	63.24 (5)	O3—Ge1—O3^vii	104.40 (8)
O3^iv—Na1—O3^x	63.62 (9)	Ge1—O3—Ge1^xiii	133.29 (14)

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

(NScG) Sodium scandium germanate

Crystal data

NaScGe2O6	F(000) = 576
Mr = 309.13	Dx = 4.146 Mg m^−3
Monoclinic, C2/c	Mo Kα radiation, λ = 0.71073 Å
a = 10.1705 (7) Å	Cell parameters from 3175 reflections
b = 9.1545 (7) Å	θ = 3.1–29.9°
c = 5.5715 (4) Å	µ = 13.43 mm^−1
β = 107.3051 (7)°	T = 293 K
V = 495.26 (6) Å^3	Prismatic, colourless
Z = 4	0.22 × 0.21 × 0.13 mm

Data collection

Bruker SMART APEX diffractometer	672 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.028
rotation, ω scans at four different φ positions	θmax = 29.9°, θmin = 3.1°
Absorption correction: multi-scan (APEX2; Bruker, 2012)	h = −13→14
Tmin = 0.359, Tmax = 0.746	k = −12→12
3175 measured reflections	l = −7→7
680 independent reflections

Refinement

Refinement on F^2	0 restraints
Least-squares matrix: full	w = 1/[σ^2(Fo^2) + (0.0135P)^2 + 0.7625P] where P = (Fo^2 + 2Fc^2)/3
R[F^2 > 2σ(F^2)] = 0.014	(Δ/σ)max = 0.001
wR(F^2) = 0.037	Δρmax = 0.52 e Å^−3
S = 1.20	Δρmin = −0.69 e Å^−3
680 reflections	Extinction correction: SHELXL2012 (Sheldrick, 2008)
48 parameters	Extinction coefficient: 0.0561 (13)

Special details

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

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

	x	y	z	Uiso*/Ueq
Na1	0	0.30340 (12)	0.25	0.0164 (2)
Sc1	0	0.90134 (4)	0.25	0.00433 (11)
Ge1	0.28988 (2)	0.09154 (2)	0.24018 (3)	0.00447 (10)
O2	0.35888 (13)	0.26275 (13)	0.3104 (2)	0.0099 (2)
O1	0.11062 (13)	0.07983 (12)	0.1369 (2)	0.0056 (2)
O3	0.35954 (12)	0.00987 (15)	0.0190 (2)	0.0097 (3)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Na1	0.0203 (6)	0.0122 (5)	0.0123 (5)	0	−0.0021 (4)	0
Sc1	0.0044 (2)	0.0041 (2)	0.0044 (2)	0	0.00121 (16)	0
Ge1	0.00404 (13)	0.00478 (13)	0.00464 (13)	−0.00096 (5)	0.00137 (8)	−0.00026 (5)
O2	0.0113 (6)	0.0064 (5)	0.0127 (6)	−0.0048 (4)	0.0048 (5)	−0.0022 (4)
O1	0.0035 (5)	0.0066 (5)	0.0058 (6)	−0.0010 (4)	0.0001 (4)	0.0002 (4)
O3	0.0073 (6)	0.0141 (6)	0.0075 (5)	−0.0001 (4)	0.0020 (4)	−0.0049 (4)

Geometric parameters (Å, º)

Na1—O3^i	2.4852 (16)	Sc1—O1^vi	2.1804 (12)
Na1—O1	2.5046 (15)	Ge1—O2	1.7144 (12)
Na1—O2^ii	2.5165 (13)	Ge1—O1	1.7442 (13)
Na1—O3^iii	2.9124 (14)	Ge1—O3	1.7605 (11)
Sc1—O2^iv	2.0176 (12)	Ge1—O3^vii	1.7669 (12)
Sc1—O1^v	2.1214 (12)
O3^i—Na1—O3^iv	80.97 (7)	O2^ii—Na1—O3^x	82.27 (4)
O3^i—Na1—O1^viii	136.32 (4)	O2^ix—Na1—O3^x	114.64 (4)
O3^iv—Na1—O1^viii	121.32 (4)	O3^iii—Na1—O3^x	108.12 (6)
O3^i—Na1—O1	121.32 (4)	O2^iv—Sc1—O2^i	102.07 (7)
O3^iv—Na1—O1	136.32 (4)	O2^iv—Sc1—O1^v	94.02 (5)
O1^viii—Na1—O1	70.40 (6)	O2^i—Sc1—O1^v	91.84 (5)
O3^i—Na1—O2^ii	139.52 (5)	O2^iv—Sc1—O1^xi	91.84 (5)
O3^iv—Na1—O2^ii	66.76 (4)	O2^i—Sc1—O1^xi	94.02 (5)
O1^viii—Na1—O2^ii	83.07 (5)	O1^v—Sc1—O1^xi	170.68 (6)
O1—Na1—O2^ii	74.18 (4)	O2^iv—Sc1—O1^vi	166.73 (5)
O3^i—Na1—O2^ix	66.76 (4)	O2^i—Sc1—O1^vi	88.24 (5)
O3^iv—Na1—O2^ix	139.52 (5)	O1^v—Sc1—O1^vi	93.98 (4)
O1^viii—Na1—O2^ix	74.19 (4)	O1^xi—Sc1—O1^vi	78.98 (5)
O1—Na1—O2^ix	83.07 (5)	O2^iv—Sc1—O1^xii	88.24 (5)
O2^ii—Na1—O2^ix	152.15 (7)	O2^i—Sc1—O1^xii	166.73 (5)
O3^i—Na1—O3^iii	65.26 (5)	O1^v—Sc1—O1^xii	78.98 (5)
O3^iv—Na1—O3^iii	61.69 (3)	O1^xi—Sc1—O1^xii	93.98 (4)
O1^viii—Na1—O3^iii	91.40 (4)	O1^vi—Sc1—O1^xii	82.92 (6)
O1—Na1—O3^iii	159.20 (5)	O2—Ge1—O1	116.63 (6)
O2^ii—Na1—O3^iii	114.64 (4)	O2—Ge1—O3	108.99 (6)
O2^ix—Na1—O3^iii	82.27 (4)	O1—Ge1—O3	109.99 (5)
O3^i—Na1—O3^x	61.69 (3)	O2—Ge1—O3^vii	104.46 (6)
O3^iv—Na1—O3^x	65.26 (5)	O1—Ge1—O3^vii	111.35 (5)
O1^viii—Na1—O3^x	159.20 (5)	O3—Ge1—O3^vii	104.63 (4)
O1—Na1—O3^x	91.40 (4)	Ge1—O3—Ge1^xiii	134.34 (7)

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

(NInG) Sodium indium germanate

Crystal data

NaInGe2O6	Z = 4
Mr = 378.99	F(000) = 688
Monoclinic, C2/c	Dx = 5.019 Mg m^−3
a = 10.2215 (7) Å	Mo Kα radiation, λ = 0.71073 Å
b = 9.1814 (6) Å	µ = 16.65 mm^−1
c = 5.5931 (4) Å	T = 293 K
β = 107.1333 (7)°	Prismatic, colourless
V = 501.61 (6) Å^3	0.19 × 0.10 × 0.09 mm

Data collection

Bruker SMART APEX diffractometer	679 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.023
rotation, ω scans at four different φ positions	θmax = 29.9°, θmin = 3.1°
Absorption correction: multi-scan (APEX2; Bruker, 2012)	h = −13→14
Tmin = 0.359, Tmax = 0.746	k = −12→12
3250 measured reflections	l = −7→7
687 independent reflections

Refinement

Refinement on F^2	0 restraints
Least-squares matrix: full	w = 1/[σ^2(Fo^2) + (0.0143P)^2 + 0.2607P] where P = (Fo^2 + 2Fc^2)/3
R[F^2 > 2σ(F^2)] = 0.012	(Δ/σ)max = 0.001
wR(F^2) = 0.033	Δρmax = 0.41 e Å^−3
S = 1.2	Δρmin = −0.52 e Å^−3
687 reflections	Extinction correction: SHELXL2012 (Sheldrick, 2008)
48 parameters	Extinction coefficient: 0.0159 (4)

Special details

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

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

	x	y	z	Uiso*/Ueq
Na1	0	0.30410 (12)	0.25	0.0174 (2)
In1	0	0.89946 (2)	0.25	0.00576 (8)
Ge1	0.29111 (2)	0.09083 (2)	0.24432 (4)	0.00570 (8)
O2	0.35674 (13)	0.26117 (14)	0.3295 (2)	0.0112 (3)
O1	0.11216 (13)	0.08163 (13)	0.1420 (2)	0.0075 (3)
O3	0.35909 (12)	0.01841 (17)	0.0138 (2)	0.0107 (3)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Na1	0.0218 (6)	0.0135 (5)	0.0125 (5)	0	−0.0020 (4)	0
In1	0.00537 (12)	0.00618 (11)	0.00548 (12)	0	0.00121 (8)	0
Ge1	0.00481 (12)	0.00645 (12)	0.00549 (12)	−0.00085 (5)	0.00099 (8)	−0.00023 (5)
O2	0.0131 (6)	0.0088 (6)	0.0131 (6)	−0.0052 (5)	0.0061 (5)	−0.0023 (5)
O1	0.0050 (6)	0.0094 (6)	0.0069 (6)	−0.0017 (4)	−0.0001 (5)	−0.0003 (4)
O3	0.0085 (6)	0.0151 (7)	0.0082 (7)	−0.0006 (4)	0.0023 (5)	−0.0042 (4)

Geometric parameters (Å, º)

Na1—O2^i	2.4505 (14)	In1—O1^vi	2.2102 (12)
Na1—O1	2.5019 (16)	Ge1—O2	1.7131 (13)
Na1—O3^ii	2.5633 (17)	Ge1—O1	1.7503 (13)
Na1—O3^iii	2.8565 (14)	Ge1—O3	1.7649 (12)
In1—O2^iv	2.0829 (12)	Ge1—O3^vii	1.7731 (13)
In1—O1^v	2.1610 (13)
O2^i—Na1—O2^viii	151.69 (8)	O3^ii—Na1—O3^x	62.35 (3)
O2^i—Na1—O1	75.84 (5)	O3^iv—Na1—O3^x	65.68 (5)
O2^viii—Na1—O1	81.10 (5)	O3^iii—Na1—O3^x	110.43 (7)
O2^i—Na1—O1^ix	81.10 (5)	O2^iv—In1—O2^ii	104.88 (7)
O2^viii—Na1—O1^ix	75.84 (5)	O2^iv—In1—O1^v	91.64 (5)
O1—Na1—O1^ix	70.55 (6)	O2^ii—In1—O1^v	93.98 (5)
O2^i—Na1—O3^ii	140.22 (5)	O2^iv—In1—O1^xi	93.98 (5)
O2^viii—Na1—O3^ii	66.86 (4)	O2^ii—In1—O1^xi	91.64 (5)
O1—Na1—O3^ii	121.55 (4)	O1^v—In1—O1^xi	170.78 (6)
O1^ix—Na1—O3^ii	136.90 (4)	O2^iv—In1—O1^vi	166.82 (5)
O2^i—Na1—O3^iv	66.86 (4)	O2^ii—In1—O1^vi	87.07 (5)
O2^viii—Na1—O3^iv	140.22 (5)	O1^v—In1—O1^vi	93.08 (4)
O1—Na1—O3^iv	136.90 (4)	O1^xi—In1—O1^vi	79.90 (5)
O1^ix—Na1—O3^iv	121.55 (4)	O2^iv—In1—O1^xii	87.07 (5)
O3^ii—Na1—O3^iv	79.71 (7)	O2^ii—In1—O1^xii	166.82 (5)
O2^i—Na1—O3^iii	112.68 (4)	O1^v—In1—O1^xii	79.90 (5)
O2^viii—Na1—O3^iii	83.89 (4)	O1^xi—In1—O1^xii	93.08 (4)
O1—Na1—O3^iii	158.00 (5)	O1^vi—In1—O1^xii	81.65 (7)
O1^ix—Na1—O3^iii	90.25 (4)	O2—Ge1—O1	114.89 (6)
O3^ii—Na1—O3^iii	65.68 (5)	O2—Ge1—O3	109.94 (6)
O3^iv—Na1—O3^iii	62.35 (3)	O1—Ge1—O3	109.95 (6)
O2^i—Na1—O3^x	83.89 (4)	O2—Ge1—O3^vii	104.87 (7)
O2^viii—Na1—O3^x	112.68 (4)	O1—Ge1—O3^vii	111.15 (6)
O1—Na1—O3^x	90.25 (4)	O3—Ge1—O3^vii	105.54 (4)
O1^ix—Na1—O3^x	158.00 (5)	Ge1—O3—Ge1^xiii	133.96 (7)

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