Chromium-based clinopyroxene-type germanates NaCrGe₂O₆ and LiCrGe₂O₆ at 298 K

The structure analyses of sodium chromium digermanate, NaCrGe₂O₆, (I), and lithium chromium digermanate, LiCrGe₂O₆, (II), provide important structural information for the clinopyroxene family, and form part of our ongoing studies on the phase transitions and magnetic properties of clinopyroxenes. (I) shows C2/c symmetry at 298 K, contains one Na, one Cr (both site symmetry 2 on special position 4e), one Ge and three O-atom positions (on general positions 8f) and displays the well known clinopyroxene topology. The basic units of the structure of (I) are infinite zigzag chains of edge-sharing Cr³⁺O₆ octa­hedra (M1 site), infinite chains of corner-sharing GeO₄ tetra­hedra, connected to the M1 chains by common corners, and Na sites occupying inter­stitial space. (II) was found to have P2₁/c symmetry at 298 K. The structure contains one Na, one Cr, two distinct Ge and six O-atom positions, all on general positions 4e. The general topology of the structure of (II) is similar to that of (I); however, the loss of the twofold symmetry makes it possible for two distinct tetrahedral chains, having different conformation states, to exist. While sodium is (6+2)-fold coordinated, lithium displays a pure sixfold coordination. Structural details are given and chemical comparison is made between silicate and germanate chromium-based clinopyroxenes.

S1. Comment

The crystal chemistry of the silicate clinopyroxene minerals and their synthetic analogues has been studied in great detail (e.g. Cameron & Papike, 1981; Thompson et al., 2005; Redhammer & Roth, 2002, 2004a,b; Redhammer et al., 2005, 2006). It is now well established that the Li-bearing 1:3 clinopyroxenes (where `1' stands for the monovalent alkali cations Na<sup>+</sup> or Li<sup>+</sup>, and `3' for the trivalent cations such as Al³⁺, Ga³⁺, Cr³⁺, Fe³⁺, V³⁺, Ti³⁺, Sc³⁺or In³⁺) show crystallographic phase transitions as a function of temperature and pressure. Upon cooling, the high-temperature C2/c modification (the most frequently found symmetry for clinopyroxenes) transforms to the low-temperature P2₁/c form as described in detail for LiFeSi₂O₆ (Redhammer et al., 2001) and for LiMSi₂O₆ with M = Cr³⁺, Ga³⁺, Sc³⁺ and V³⁺ (Redhammer & Roth, 2004b). The analogous Na compounds, however, retain C2/c symmetry down to low temperatures (Redhammer & Roth, 2002; Nestola et al., 2007).

While they have been studied in geosciences for decades, the clinopyroxenes are awakening increasing interest in solid-state physics due to their interesting magnetic properties. The titanium-based compounds (Na,Li)Ti³⁺Si₂O₆ show spin-gap behaviour at low temperatures (Isobe et al., 2002), and the dimerization of the chains of TiO₆ octahedra is accompanied by a crystallographic phase transition from C2/c directly to P1 (Redhammer et al. 2003). Recently, multiferroic behaviour has been reported for the clinopyroxenes NaFeSi₂O₆, LiFeSi₂O₆ and LiCrSi₂O₆ (Jodlauk et al., 2007), and this discovery will undoubtedly further increase the interest in this important group of rock-forming minerals/materials.

Among other things, chromium-based pyroxenes are of special interest with respect to their magnetic behaviour – the competitive magnetic interaction within and between the chains of Cr³⁺O₆ octahedra changes from dominating anti-ferromagnetic in LiCrSi₂O₆ and NaCrSi₂O₆ to pure ferromagnetic in NaCrGe₂O₆ (Vasiliev et al., 2003, 2005; Streltsov & Khomskii, 2008). The reason for this must be attributed to the different structural topologies. NaCrSi₂O₆ shows the typical C2/c structure (Origlieri et al., 2003) while LiCrSi₂O₆ has P2₁/c symmetry at room temperature and below, but transforms to the HT [high-temperature?] C2/c structure at 330 K (Redhammer & Roth, 2004b). Except for basic structural data such as lattice parameters and symmetry (Vasiliev et al., 2003, 2005) and the data given in the powder diffraction file, no further structural information is available for the chromium-based germanate clinopyroxenes. As knowledge of the structural topology of a compound is the basis for understanding its physical properties, we undertook the determination of the crystal structures of the chromium-based clinopyroxene-type compounds NaCrGe₂O₆ and LiCrGe₂O₆. Comparison with NaCrSi₂O₆ and LiCrSi₂O₆ is also presented, with the structural parameters of the latter recalculated from atomic coordinates and lattice parameters given by Origlieri et al. (2003) and Redhammer & Roth (2004b).

NaCrGe₂O₆ shows C2/c symmetry at 298 K and the asymmetric unit contains one distinct Na, one Cr, one Ge and three O-atom positions (Fig. 1). The compound adopts the general topology of the clinopyroxenes – infinite chains of corner-sharing GeO₄ tetrahedra (T sites) running parallel to the crystallographic c axis and related to each other by the twofold axis, zigzag chains of edge-sharing Cr³⁺O₆ octahedra (M1 sites), also running parallel to the c axis, and eightfold coordinated M2 sites, hosting Na⁺ in the interstitial space. Compared with NaCrSi₂O₆ (known as the mineral kosmochlor), the replacement of Si⁴⁺ by Ge⁴⁺ causes a distinct increase in lattice parameters in the a and c directions by 3.46 and 5.08%, respectively; b increases by only 1.52%, while the monoclinic angle β remains almost constant. Individual bond lengths and bond angles are in the range typically found for the clinopyroxenes; average bond lengths, polyhedral volumes and distortion parameters are compiled in Table 1.

In NaCrGe₂O₆, the T—O distances range between 1.717 (2) and 1.763 (2) Å, with the average of the two bridging (br) Ge1—O3 bonds <T—O_br> = 1.753 (15) Å, while the average of the two remaining non-bridging (nbr) Ge1—O bonds <T—O_nbr> = 1.735 (26) Å and the difference Δ_br-nbr = 0.018 Å. In NaCrSi₂O₆, the difference Δ_br-nbr = 0.025 Å. According to Ohashi (1981) and Ohashi et al. (1990), the difference Δ_br-nbr is related to the electronegativity of the M³⁺ cation within the series Sc—Ti—V—Cr—Al: Δ_br-nbr decreases with increasing electronegativity of the M³⁺ cation. From this finding, it could be concluded that Cr³⁺ acts as a more electronegative centre in NaCrGe₂O₆ than in NaCrSi₂O₆. The GeO₄ tetrahedra are elongated along a*. This is shown by the angle τ, which is defined as the mean of the three O_basal—T—O_apex bond angles. Ideal tetrahedra have τ = 109.47°, while it is 112.65 (11)° in NaCrGe₂O₆ (Table 1). By nature, the most distinct differences between the germanate NaCrGe₂O₆ and silicate NaCrSi₂O₆ clinopyroxene concern the tetrahedral sites. The <T—O> distance in the germanate is larger by 0.118 Å compared with the silicate; this corresponds well with the difference in ionic radius between Si⁴⁺ and Ge⁴⁺ (0.14 Å; Shannon & Prewitt, 1969). A similar difference of 0.122 Å in <T—O> distances was observed for analogous C2/c CaZnGe₂O₆ and CaZnSi₂O₆ clinopyroxenes (Redhammer & Roth, 2005). The GeO₄ tetrahedra are more elongated along a* compared with the SiO₄ tetrahedron (Table 1) and thus show a distinctly larger tetrahedral quadratic elongation (TQE) and a larger tetrahedral angle variance (TAV, Table 1). From this, it is apparent that NaCrSi₂O₆ possesses a more regular tetrahedral environment than does NaCrGe₂O₆. While bond lengths and bond angles generally show little variation with changes in composition, temperature or pressure, the O3—O3—O3 bridging angle, defining the conformation state of the chains, changes significantly with changes in parameters of state. In NaCrGe₂O₆ the tetrahedral chains show an `O' rotation (O3—O3—O3 < 180°; Redhammer & Roth, 2004b) and the tetrahedral bridging angle = 170.57 (9)°. Compared with NaCrSi₂O₆ (O3—O3—O3 = 172.81°), the tetrahedral chains are more kinked in the germanate as this favours the matching of the larger GeO₄ tetrahedra to the Cr³⁺O₆ octahedral chain. The increased kink of the tetrahedral chains is also responsible for the smaller increase in the b lattice parameter upon substitution of Si⁴⁺ by Ge⁴⁺. As the T—O bonds do not expand as much as might be expected from the different ionic radii of Si⁴⁺ and Ge⁴⁺, this can be regarded (besides tetrahedral chain kinking) as an additional mechanism for maintaining the size comparability between tetrahedral and octahedral chains.

The M2 site shows a [6 + 2]-fold coordination in NaCrGe₂O₆, with six bonds ranging between 2.404 (3) and 2.486 (2) Å; the remaining two Na1—O3^vi and Na1—O3^vii bonds are 2.764 (3) Å, contributing 0.07 valence units (v.u.) to the bond valence sum S of Na⁺ [symmetry codes: (vi) x, y, z + 1; (vii) -x + 1, y, -z + 1/2]. The total bond valence sum (Brese & O'Keeffe, 1991) at the M2 site is S = 1.21 v.u., indicating that the M2 site in NaCrGe₂O₆ is distinctly overbonded. Both the volume of this irregularly shaped M2 polyhedron and the <Na—O> bond lengths are somewhat larger in NaCrGe₂O₆ compared with NaCrSi₂O₆, showing that the available space for the M2 site is larger in NaCrGe₂O₆.

Most interesting in terms of the magnetic properties is the topology of the M1 site. By sharing common edges, the Cr³⁺O₆ octahedra form a quasi-one-dimensional zigzag chain along c (Fig. 2), with an average <Cr³⁺—O> distance of 2.004 (2) Å in NaCrGe₂O₆ (Table 1). Both average and individual Cr1—O bonds are larger by 0.01 Å (~0.5%) in NaCrGe₂O₆ and the CrO₆ octahedra are somewhat more elongated along the c axis compared with isostructural NaCrSi₂O₆. This can be deduced from the larger O1^viii—Cr1—O1ⁱⁱ bond angle of 176.8 (13)° in NaCrGe₂O₆ compared with 173.1 (1)° in NaCrSi₂O₆ [symmetry codes: (ii) x + 1/2, -y + 1/2, z + 1/2; (viii) -x + 1/2, -y + 1/2, -z]. While the bond-length distortion (BLD) is similar in NaCrGe₂O₆ and NaCrSi₂O₆, the germanate compound shows distinctly larger values for the angular variance and the quadratic elongation (OAV and OQE in Table 1). This is mainly due to distinct alterations in octahedral O—O atom edges. Here, the most pronounced changes can be found for the O1^viii—O1^ix and O2—O2^vii edges, which increase by as much as 3.8 and 4.9%, respectively, from NaCrSi₂O₆ to NaCrGe₂O₆. As Cr1—O bond lengths do not alter much, consequently the O—Cr1—O bond angles involving the O1^viii—O1^ixand the O2—O2^vii edges also show marked increases by 4.3 and 5.9% upon the replacement of Si⁴⁺ by Ge⁴⁺ [symmetry code: (ix) -x + 1/2, y + 1/2, -z + 1/2]. The aforementioned O atoms are common to both the CrO₆ octahedra and four neighbouring tetrahedral sites, and thus are sensible [sensitive?] to changes in the tetrahedral cation size. As a third mechanism for maintaining the match between octahedral and tetrahedral chains, octahedral edge-length and bond-angle variation is active at the M1 site, rather than Cr³⁺—O bond-length stretching.

The increased elongation of the CrO₆ octahedra in NaCrGe₂O₆ causes a size reduction of the common O1ⁱⁱ—O1^ix edge between two neighbouring CrO₆ octahedra, from 2.606 (2) Å to 2.578 (2) Å in NaCrSi₂O₆ and NaCrGe₂O₆, respectively; the O1ⁱⁱ—Cr1—O1^ix angle opposite this O1—O1 edge decreases from 80.4 (1)° to 78.76 (10)°. A direct consequence of this is a larger separation of Cr³⁺—Cr³⁺pairs within the chain and a change in the Cr1—O1^{ii, ix}—Cr1^xv angle, which is important for the magnetic super-exchange interaction via the common O1 oxygen: the Cr—Cr^xv interatomic distance within the M1 chain increases from 3.086 (1) Å in NaCrSi₂O₆ to 3.140 (1) Å in NaCrGe₂O₆, and the Cr1—O1^ii,ix—Cr1^xv angle from 99.6 (1)° to 101.2 (1)° [symmetry code: (xv) -x + 1, -y + 1, -z + 1]. Also, the separation between neighbouring M1 chains is distinctly larger in NaCrGe₂O₆: the shortest contact between two Cr³⁺ ions in two different M1 chains is 5.549 (1) Å in NaCrSi₂O₆ but increases to 5.666 (1) Å in the germanate. These differences in bonding topologies certainly influence magnetic properties in chromium-based clinopyroxenes at low temperatures.

LiCrGe₂O₆ adopts P2₁/c symmetry at room temperature with one distinct Li, one Cr, two Ge and six O-atom positions in the asymmetric unit (Fig. 3). The general topology of the P2₁/c structure in LiCrGe₂O₆ is similar to the C2/c structure of NaCrGe₂O₆; the main difference is the presence of two distinct tetrahedral chains, A and B, due to the loss of the twofold axis, with slightly different bond lengths and angles and distinctly different kinking states of the two independent GeO₄ chains (Fig. 4). The A chain is S-rotated, having a tetrahedral bridging angle of 209.7 (1)°, while the B chain is O-rotated with a bridging angle of 136.6 (1)°. It is evident that the tetrahedral chains in LiCrGe₂O₆ exhibit a distinct kinking, which is far larger than in NaCrGe₂O₆ or in the P2₁/c phase of LiCrSi₂O₆ (Table 1). Similar small bridging angles were found in ZnSiO₃ [139.7 (9)° for the B chain; Arlt & Angel, 2000] and clinoenstatite Ca_0.15Mg_1.85Si₂O₆ [143.0 (1)° for the B chain; Tribaudino et al., 2002], but not in 1:3 clinopyroxenes.

In LiCrGe₂O₆,the tetrahedra of the B chain have similar <T—O> and <O—O>_T bond lengths with similar bond-length distortion (BLD_T) values and a similar polyhedral volume (Table 1), while the distortion parameters are smaller compared with the tetrahedra of the A chain; thus, despite the distinct kinked state, the tetrahedra of the B chain appear to be more regular. Both T sites in LiCrGe₂O₆ are elongated along a*; the elongation is smaller for the B-chain tetrahedra and is very similar to that found for the SiO₄ tetrahedra in the B chain of LiCrSi₂O₆. Also, the polyhedral distortions are very similar in both compounds for the B-chain tetrahedra, though there is the size difference due to different tetrahedral cations. The A-chain tetrahedra are distinctly elongated [τ = 111.64 (10)°] and reveal the largest deviations from ideal geometry of the chromium-based 1:3 clinopyroxenes; in particular, the bond-angle variance is high (Table 1). As in all clinopyroxenes, the bridging T—O bond lengths are longer than the two non-bridging bonds; the difference Δ_br-nbr is 0.016 (2) Å for the A and 0.021 (2) Å for the B chain respectively. Bond valence sums S (Brese & O'Keeffe 1991) for the tetrahedral site in LiCrGe₂O₆ are close to the ideal value; the A-site Ge is slightly over-bonded, the B-site Ge slightly under-bonded. The bridging O atom O3A shows a valence sum of S = 2.14 v.u.; in the B-chain S is almost ideal for O3B (2.02 v.u.).

While the M2 site in NaCrGe₂O₆ has a [6 + 2]-fold coordination, in LiCrGe₂O₆ the coordination is purely sixfold. The Li1—O bonds range between 2.038 (6) and 2.369 (6) Å; the next nearest O atoms are 3.144 (6) and 3.478 (6) Å away from Li⁺ and cannot be regarded as bonding atoms. The sixfold O-atom environment of Li⁺in LiCrGe₂O₆, however, is far from being ideal octahedral, and gives rise to extreme values for the distortion parameters OAV = 198.5° and OQE of 1.0576. The coordination of Li⁺ in LiCrGe₂O₆ is different from that in LiCrSi₂O₆ in the P2₁/c form: in the latter, five bonds lie between 2.078 (6) and 2.313 (6) Å, but two O3B atoms are found at somewhat larger distances of 2.678 (6) and 2.891 (6) Å, giving rise to a [5 + 2]-fold coordination in LiCrSi₂O₆. This non-uniform Li1—O bond distribution is related to the conformation state of the tetrahedral chain. The distinct kinking of the B chain in LiCrGe₂O₆ brings one O3B atom closer to the Li⁺ atom, but moves the other one out of the coordination sphere. In addition, the Li1—O2 distances are evidently different in the silicate and the germanate, reflecting the different topologies of the CrO₆ site.

The individual Cr1—O, <Cr1—O> and <O—O>_M1 distances in LiCrGe₂O₆ are similar to the values found in NaCrSi₂O₆ and LiCrSi₂O₆, and are only slightly smaller than those in NaCrGe₂O₆ (Table 1). The CrO₆ octahedra in LiCrGe₂O₆ are again elongated along c (<Cr1—O>_apex/<Cr1—O>_equatorial > 1; Table 1); the angle O1A^v—Cr1—O1Bⁱⁱ is 176.1 (1)° and thus almost identical to LiCrSi₂O₆ and NaCrGe₂O₆ and close to the ideal value of 180° for the undistorted octahedron [symmetry codes: (ii) x, -y + 3/2, z + 1/2; (v) -x, -y + 1, -z]. The bond-length distortion is larger in LiCrGe₂O₆ compared with the sodium pyroxene, while the angular distortion is smaller; however, the latter is still distinctly larger than in the silicates (Table 1). The replacement of Si⁴⁺ by Ge⁴⁺ influences the O—O edges of the CrO₆ octahedron in a different way. An increase in the O—O interatomic distances across octahedral edges is observed e.g. for the O1A^v—O1A^vi, the O2A—O2B^iv or the O1B—O1Bⁱⁱ edges. These increases are in the range 1.0–1.5% (0.03–0.05 Å) and are responses to the increase in the ionic size of the tetrahedral cation; however, there are O—O edges that show a distinct decrease in lengths, among them the O1A^vi—O2A edge which is shortened by 3.0% and the O1A^v—O2B^iv edge, being shorter by 2.7% in the germanate compound [symmetry codes: (iv) -x + 1, y - 1/2, -z + 1/2; (vi) -x, y + 1/2, -z + 1/2]. The latter alterations can be related to the different conformation of the tetrahedral chains in LiCrGe₂O₆ and LiCrSi₂O₆, respectively, which causes, by counter-rotation, a compression of the O—O edges. In contrast, the O2B^iv—O1Bⁱⁱ edge is increased by 3.2% in LiCrGe₂O₆ relative to LiCrSi₂O₆ due to the distinct kinking of the tetrahedral chains.

The common edges between neighbouring octahedra, O1A^v—O1B and O1Bⁱⁱ—O1A^iv, are also shorter in LiCrGe₂O₆ compared with LiCrSi₂O₆ [2.624 (5) and 2.654 (7) Å, respectively], and the angles opposite these edges are smaller in the germanate. The shortest distance between Cr³⁺—Cr³⁺pairs within the M1 chain is increased from 3.064 (1) Å in LiCrSi₂O₆ to 3.098 (1) Å in LiCrGe₂O₆, and thus is also larger than in NaCrSi₂O₆ (Table 1). Within the P2₁/c structure, two different Cr1—O1—Cr1 angles exist: the larger one includes the O1A^vi O atom with Cr—O1A^vi—Cr^x = 100.2 (1)°, the smaller one the O1Bⁱⁱ O atom with Cr—O1Bⁱⁱ—Cr^x= 98.7 (1)° [symmetry codes: (x) x, 1 1/2 - y, 1/2 + z]. In LiCrSi₂O₆ these two corresponding angles are 98.4 (1)° and 98.1 (1)°, respectively. Magnetic super-exchange between Cr³⁺ ions within the M1 chains takes place via the aforementioned two O atoms. The inter-chain separation (nearest distance between two Cr³⁺ ions in different chains) is distinctly larger in LiCrGe₂O₆ and takes a value close to that found in NaCrGe₂O₆ (Table 1). The bond valence sums at the Cr sites are close to the ideal value of 3+ both in LiCrGe₂O₆ and in LiCrSi₂O₆, while in NaCrGe₂O₆ the Cr³⁺ appears to be slightly under-bonded (Table 1). The difference Δ_br-nbr in LiCrGe₂O₆ is somewhat smaller for the GeA site, indicating a more electropositive character; this could indicate that electrons of Cr³⁺ (3 d³ configuration) are delocalized towards the bridging O atoms between the Cr1 and the Ge1A sites, e.g. towards O1A^vi in Fig. 3, the corresponing Ge1A site being Ge1A^vi. Such a localization would result in high screening constants in the direction of O1A^vi and in an increment in the electric charge of the associated O1A atoms. Indeed, the valence sums are largest among the octahedral O atoms for the O1A atoms (S = 2.04 v.u.), while S is 1.98, 1.82 and 1.86 for the O1B, O2A and O2B O atoms, respectively. High screening constants indicate electropositive character and increased charge on oxygen is accompanied by increasing repulsion effects.

From the data presented here, some basic structural conclusions concerning the magnetic properties of chromium-based clinopyroxenes can be derived: NaCrGe₂O₆ with a proposed ferromagnetic (FM) ordering has by far the largest Cr³⁺—Cr³⁺ separation within [3.140 (1) Å] and between [5.666 (1) Å] the M1 chains, and the super-exchange pathway within the M1 chain shows the largest deviation from a 90° Cr—O—Cr angle, which would favour anti-ferromagnetic interactions (Goodenough, 1955). On the other hand, the silicate LiCrSi₂O₆, which shows the highest magnetic ordering temperature and a distinctly negative paramagnetic Curie temperature (standing for an overall anti-ferromagnetic character of the ordering), has the smallest Cr³⁺—Cr³⁺ contacts and the smallest Cr—O—Cr angle. Increasing the inter- and intra-chain separation of Cr³⁺ ions may thus weaken AFM and favour FM interaction. This could be the reason for the change of the overall magnetic property from dominating anti-ferromagnetic in LiCrSi₂O₆ to dominating ferromagnetic in NaCrGe₂O₆. However, the exact spin structure within and between the chains remains unclear and can only be extracted by detailed neutron diffraction experiments.

Related literature

For related literature, see: Arlt & Angel (2000); Brese & O'Keeffe (1991); Cameron & Papike (1981); Goodenough (1955); Isobe et al. (2002); Jodlauk et al. (2007); Nestola et al. (2007); Ohashi (1981); Ohashi et al. (1990); Origlieri et al. (2003); Redhammer & Roth (2002, 2004a, 2005); Redhammer et al. (2001, 2006); Redhammer, Tippelt, Merz, Roth, Treutmann & Amthauer (2005); Shannon & Prewitt (1969); Sheldrick (2008); Streltsov & Khomskii (2008); Thompson et al. (2005); Tribaudino et al. (2002); Vasiliev et al. (2003, 2005).

S2. Experimental

The title compounds were synthesized by the flux growth technique. Mixtures of the oxides Na₂CO₃/Li₂CO₃, Cr₂O₃ and GeO₂ (finely ground and homogenized) in the exact stoichiometry of the title compounds were added to the high-temperature solvent. Tests with molybdate/vanadate fluxes at atmospheric conditions appeared to be unsuccessful, while experiments with a molar mixture of 1 NaF/LiF, 0.5 V₂O₅ and 0.1 PbO as flux turned out to give good yields of high-quality single crystals up to 1 mm in size. A flux-to-nutrient ratio of 2: 1 gave the best results for both compounds. The mixtures were placed into platinum crucibles, covered with a lid, and heated to 1373 K within[for?] 12 h; they were kept at this temperature for 24 h and cooled to 973 K at a rate of 2 K h^-1. The resulting single crystals were emerald green and showed a short prismatic habit.

S3. Refinement

For NaCrGe₂O₆ structure solution using Patterson methods (Sheldrick, 2008) yielded all metal and O positions. Two additional data collections on crystals of different experimental runs gave identical structural parameters. Systematic absences indicate the space group P2₁/c for LiCrGe₂O₆, which is the same as that found for the analogous compound LiCrSi₂O₆ at room temperature. The structure solution for LiCrGe₂O₆ using Patterson methods gave the Ge, Cr and all O positions while Li was located from difference Fourier map analysis.

Computing details

For both compounds, data collection: SMART (Bruker, 2001); cell refinement: SAINT-Plus (Bruker, 2001); data reduction: SAINT-Plus (Bruker, 2001). Program(s) used to solve structure: SHELXL97 (Sheldrick, 2008) for (I); SHELXS97 (Sheldrick, 2008) for (II). For both compounds, program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: DIAMOND (Pennington, 1999); software used to prepare material for publication: WinGX (Farrugia, 1999).

Figures

	Fig. 1. The asymmetric unit and symmetry-related atoms of NaCrGe2O6, with 95% probability displacement ellipsoids [symmetry codes: (i) x, -y, 1/2 + z; (ii) 1/2 - x, 1/2 + y, 1/2 - z; (iii) 1/2 + x, 1/2 - y, 1/2 + z; (iv) 1/2 + x, 1/2 + y, z; (v) 1 - x, y, 1/2 - z; (vi) 1/2 - x, 1/2 - y, -z].
	Fig. 2. Polyhedral representation of the C2/c structure of NaCrGe2O6, displaying the M1 octahedral chains and related GeO4 tetrahedra. Na sites are omitted for clarity.
	Fig. 3. The asymmetric unit and symmetry-related atoms of LiCrGe2O6, showing 95% probability displacement ellipsoids [symmetry codes: (i) x, 1/2 - y, -1/2 + z; (ii) -x, 1 - y, 1 - z; (iii) 1 - x, -1/2 + y, 1 1/2 - z; (iv) x, 1 1/2 - y, 1/2 + z; (v) 1 - x, 1 - y, 1 - z; (vi) -x, 1/2 + y, 1/2 - z; (vii) 1 - x, -1/2 + y, 1/2 - z; (viii) -x, 1 - y, -z; (ix) x, 1 1/2 - y, -1/2 + z].
	Fig. 4. Polyhedral representation of the P21/c structure of LiCrGe2O6, displaying the M1 octahedral chains and related GeO4 tetrahedra. Li sites are omitted for clarity. A similar orientation as in Fig. 2 was chosen to facilitate comparison.

(I) sodium chromium digermanate

Crystal data

NaCrGe2O6	F(000) = 588
Mr = 316.17	Dx = 4.601 Mg m^−3
Monoclinic, C2/c	Mo Kα radiation, λ = 0.71073 Å
a = 9.9151 (8) Å	Cell parameters from 6821 reflections
b = 8.8441 (7) Å	θ = 3.2–28.7°
c = 5.4595 (4) Å	µ = 15.47 mm^−1
β = 107.548 (1)°	T = 295 K
V = 456.47 (6) Å^3	Cuboid, green
Z = 4	0.14 × 0.12 × 0.08 mm

Data collection

SMART APEX diffractometer	548 reflections with I > 2σ(I)
rotation, ω–scans at 4 different ϕ positions	Rint = 0.043
Absorption correction: numerical via equivalents using X-SHAPE (Stoe & Cie, 1996)	θmax = 28.7°, θmin = 3.2°
Tmin = 0.13, Tmax = 0.285	h = −12→12
2696 measured reflections	k = −11→11
559 independent reflections	l = −7→7

Refinement

Refinement on F^2	0 restraints
Least-squares matrix: full	w = 1/[σ^2(Fo^2) + (0.0242P)^2 + 1.6562P] where P = (Fo^2 + 2Fc^2)/3
R[F^2 > 2σ(F^2)] = 0.021	(Δ/σ)max < 0.001
wR(F^2) = 0.056	Δρmax = 0.73 e Å^−3
S = 1.19	Δρmin = −0.58 e Å^−3
559 reflections	Extinction correction: SHELXL, Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
48 parameters	Extinction coefficient: 0.0030 (5)

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.

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

	x	y	z	Uiso*/Ueq
Na1	0.5	0.1976 (2)	0.75	0.0148 (4)
Cr1	0.5	0.41226 (8)	0.25	0.00588 (19)
Ge1	0.29050 (3)	0.09627 (4)	0.22762 (6)	0.00649 (16)
O1	0.1055 (2)	0.0813 (2)	0.1284 (4)	0.0073 (5)
O2	0.3597 (2)	0.2738 (3)	0.3085 (5)	0.0111 (5)
O3	0.3629 (2)	0.0127 (3)	0.0069 (4)	0.0108 (5)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Na1	0.0171 (9)	0.0110 (9)	0.0140 (9)	0	0.0012 (8)	0
Cr1	0.0059 (4)	0.0053 (4)	0.0064 (4)	0	0.0019 (3)	0
Ge1	0.0061 (2)	0.0064 (2)	0.0068 (2)	−0.00074 (11)	0.00184 (14)	−0.00032 (11)
O1	0.0059 (10)	0.0083 (11)	0.0072 (11)	−0.0009 (8)	0.0014 (9)	0.0001 (8)
O2	0.0116 (11)	0.0080 (11)	0.0140 (11)	−0.0041 (9)	0.0042 (9)	−0.0017 (9)
O3	0.0093 (11)	0.0137 (12)	0.0095 (11)	−0.0003 (9)	0.0031 (9)	−0.0041 (9)

Geometric parameters (Å, º)

Na1—O1^i	2.404 (3)	Cr1—O1^vi	2.047 (2)
Na1—O3^ii	2.446 (3)	Ge1—O2	1.717 (2)
Na1—O2^iii	2.486 (2)	Ge1—O3	1.742 (2)
Na1—O3^iv	2.764 (3)	Ge1—O1	1.754 (2)
Cr1—O2	1.951 (2)	Ge1—O3^ii	1.763 (2)
Cr1—O1^v	2.016 (2)
O1^i—Na1—O1^vii	71.13 (12)	O2—Cr1—O2^ix	102.24 (14)
O1^i—Na1—O3^ii	123.48 (7)	O2—Cr1—O1^v	90.57 (10)
O1^vii—Na1—O3^ii	133.30 (7)	O2—Cr1—O1^vii	91.47 (9)
O3^ii—Na1—O3^viii	80.97 (12)	O2^ix—Cr1—O1^vii	90.57 (10)
O1^i—Na1—O2^iii	71.01 (8)	O1^v—Cr1—O1^vii	176.75 (13)
O1^vii—Na1—O2^iii	83.35 (9)	O2—Cr1—O1^vi	86.89 (9)
O3^ii—Na1—O2^iii	142.15 (10)	O2^ix—Cr1—O1^vi	166.21 (10)
O3^viii—Na1—O2^iii	67.85 (7)	O1^v—Cr1—O1^vi	98.83 (9)
O2^iii—Na1—O2	148.53 (14)	O1^vii—Cr1—O1^vi	78.76 (10)
O1^i—Na1—O3^iv	91.12 (7)	O1^vi—Cr1—O1^x	86.17 (13)
O1^vii—Na1—O3^iv	160.58 (9)	O2—Ge1—O3	110.47 (11)
O3^ii—Na1—O3^iv	63.10 (5)	O2—Ge1—O1	116.61 (11)
O3^viii—Na1—O3^iv	63.42 (9)	O3—Ge1—O1	111.40 (11)
O2^iii—Na1—O3^iv	83.42 (7)	O2—Ge1—O3^ii	104.52 (11)
O2—Na1—O3^iv	115.82 (7)	O3—Ge1—O3^ii	102.76 (7)
O1^i—Na1—O3^ix	160.58 (9)	O1—Ge1—O3^ii	109.94 (10)
O3^iv—Na1—O3^ix	107.46 (12)

Symmetry codes: (i) −x+1/2, −y+1/2, −z+1; (ii) x, −y, z+1/2; (iii) −x+1, y, −z+3/2; (iv) x, y, z+1; (v) −x+1/2, −y+1/2, −z; (vi) −x+1/2, y+1/2, −z+1/2; (vii) x+1/2, −y+1/2, z+1/2; (viii) −x+1, −y, −z+1; (ix) −x+1, y, −z+1/2; (x) x+1/2, y+1/2, z.

(II) lithium chromium digermanate

Crystal data

LiCrGe2O6	F(000) = 556
Mr = 300.12	Dx = 4.618 Mg m^−3
Monoclinic, P21/c	Mo Kα radiation, λ = 0.71073 Å
a = 9.7989 (7) Å	Cell parameters from 5160 reflections
b = 8.7190 (7) Å	θ = 3.2–28.8°
c = 5.3410 (4) Å	µ = 16.25 mm^−1
β = 108.905 (4)°	T = 295 K
V = 431.70 (6) Å^3	Prismatic, green
Z = 4	0.14 × 0.13 × 0.07 mm

Data collection

SMART APEX diffractometer	1001 reflections with I > 2σ(I)
rotation, ω–scans at 4 different ϕ positions	Rint = 0.051
Absorption correction: numerical via equivalents using X-SHAPE (Stoe & Cie, 1996)	θmax = 28.8°, θmin = 3.2°
Tmin = 0.12, Tmax = 0.295	h = −13→13
5160 measured reflections	k = −11→11
1064 independent reflections	l = −7→6

Refinement

Refinement on F^2	0 restraints
Least-squares matrix: full	w = 1/[σ^2(Fo^2) + (0.0363P)^2 + 0.6726P] where P = (Fo^2 + 2Fc^2)/3
R[F^2 > 2σ(F^2)] = 0.026	(Δ/σ)max < 0.001
wR(F^2) = 0.068	Δρmax = 1.35 e Å^−3
S = 1.12	Δρmin = −0.71 e Å^−3
1064 reflections	Extinction correction: SHELXL, Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
92 parameters	Extinction coefficient: 0.0509 (18)

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
Li1	0.2571 (6)	0.4859 (8)	0.7210 (12)	0.0173 (14)
Cr1	0.25128 (5)	0.65992 (6)	0.21270 (11)	0.00447 (17)
Ge1A	0.04680 (3)	0.34443 (4)	0.27339 (7)	0.00566 (15)
Ge1B	0.55421 (3)	0.84164 (4)	0.22963 (7)	0.00545 (15)
O1A	−0.1427 (2)	0.3325 (2)	0.1732 (5)	0.0060 (5)
O2A	0.1142 (3)	0.5259 (3)	0.2830 (5)	0.0124 (5)
O3A	0.1176 (2)	0.2906 (3)	0.6079 (4)	0.0091 (4)
O1B	0.3641 (3)	0.8321 (2)	0.1050 (5)	0.0071 (5)
O2B	0.6308 (3)	1.0072 (2)	0.3861 (4)	0.0087 (5)
O3B	0.6129 (2)	0.6891 (3)	0.4552 (4)	0.0081 (5)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Li1	0.017 (3)	0.014 (3)	0.020 (3)	0.001 (2)	0.004 (3)	0.000 (2)
Cr1	0.0052 (3)	0.0043 (3)	0.0040 (3)	−0.00009 (15)	0.0017 (2)	0.00018 (15)
Ge1A	0.0060 (2)	0.0059 (2)	0.0051 (2)	−0.00082 (10)	0.00172 (15)	−0.00021 (10)
Ge1B	0.0061 (2)	0.0056 (2)	0.0044 (2)	−0.00078 (10)	0.00129 (14)	−0.00029 (10)
O1A	0.0040 (10)	0.0076 (10)	0.0056 (12)	−0.0015 (7)	0.0005 (9)	−0.0001 (7)
O2A	0.0139 (12)	0.0090 (11)	0.0166 (13)	−0.0042 (9)	0.0081 (10)	−0.0021 (9)
O3A	0.0107 (10)	0.0115 (11)	0.0048 (10)	−0.0015 (8)	0.0020 (8)	0.0025 (9)
O1B	0.0068 (10)	0.0079 (10)	0.0059 (12)	−0.0021 (8)	0.0011 (9)	0.0006 (8)
O2B	0.0109 (10)	0.0086 (10)	0.0068 (11)	−0.0041 (8)	0.0033 (9)	−0.0017 (8)
O3B	0.0097 (10)	0.0087 (10)	0.0066 (11)	0.0027 (8)	0.0037 (9)	0.0037 (8)

Geometric parameters (Å, º)

Li1—O2B^i	2.038 (6)	Cr1—O1A^vii	2.047 (2)
Li1—O1B^ii	2.103 (7)	Cr1—O1B	2.054 (2)
Li1—O1A^iii	2.119 (7)	Ge1A—O2A	1.709 (2)
Li1—O3A	2.145 (7)	Ge1A—O3A^viii	1.745 (2)
Li1—O2A	2.331 (7)	Ge1A—O3A	1.758 (2)
Li1—O3B^iv	2.369 (7)	Ge1A—O1A	1.761 (2)
Cr1—O2A	1.907 (2)	Ge1B—O2B	1.714 (2)
Cr1—O2B^v	1.944 (2)	Ge1B—O3B^ix	1.760 (2)
Cr1—O1A^vi	1.991 (2)	Ge1B—O3B	1.761 (2)
Cr1—O1B^ii	2.029 (2)	Ge1B—O1B	1.765 (2)
O2B^i—Li1—O1B^ii	94.6 (3)	O2A—Cr1—O1A^vii	85.68 (10)
O2B^i—Li1—O1A^iii	79.2 (2)	O2B^v—Cr1—O1A^vii	175.01 (9)
O1B^ii—Li1—O1A^iii	82.7 (3)	O1A^vi—Cr1—O1A^vii	97.42 (9)
O2B^i—Li1—O3A	116.4 (3)	O1B^ii—Cr1—O1A^vii	80.15 (10)
O1B^ii—Li1—O3A	148.1 (3)	O2A—Cr1—O1B	168.60 (10)
O1A^iii—Li1—O3A	108.9 (3)	O2B^v—Cr1—O1B	90.18 (10)
O2B^i—Li1—O2A	165.5 (4)	O1A^vi—Cr1—O1B	80.88 (10)
O1B^ii—Li1—O2A	77.6 (2)	O1B^ii—Cr1—O1B	95.82 (9)
O1A^iii—Li1—O2A	87.6 (2)	O1A^vii—Cr1—O1B	85.69 (10)
O3A—Li1—O2A	73.5 (2)	O2A—Ge1A—O3A^viii	115.26 (11)
O2B^i—Li1—O3B^iv	106.7 (3)	O2A—Ge1A—O3A	101.27 (12)
O1B^ii—Li1—O3B^iv	89.1 (2)	O3A^viii—Ge1A—O3A	104.13 (8)
O1A^iii—Li1—O3B^iv	170.3 (3)	O2A—Ge1A—O1A	115.01 (11)
O3A—Li1—O3B^iv	75.7 (2)	O3A^viii—Ge1A—O1A	111.05 (10)
O2A—Li1—O3B^iv	85.6 (2)	O3A—Ge1A—O1A	108.85 (11)
O2A—Cr1—O2B^v	98.76 (11)	O2B—Ge1B—O3B^ix	108.93 (10)
O2A—Cr1—O1A^vi	92.86 (10)	O2B—Ge1B—O3B	107.96 (11)
O2B^v—Cr1—O1A^vi	84.66 (10)	O3B^ix—Ge1B—O3B	109.41 (8)
O2A—Cr1—O1B^ii	90.04 (10)	O2B—Ge1B—O1B	117.73 (10)
O2B^v—Cr1—O1B^ii	97.51 (9)	O3B^ix—Ge1B—O1B	105.56 (11)
O1A^vi—Cr1—O1B^ii	176.08 (10)	O3B—Ge1B—O1B	107.04 (10)

Symmetry codes: (i) −x+1, y−1/2, −z+3/2; (ii) x, −y+3/2, z+1/2; (iii) −x, −y+1, −z+1; (iv) −x+1, −y+1, −z+1; (v) −x+1, y−1/2, −z+1/2; (vi) −x, −y+1, −z; (vii) −x, y+1/2, −z+1/2; (viii) x, −y+1/2, z−1/2; (ix) x, −y+3/2, z−1/2.