Dicalcium hepta­germanate Ca₂Ge₇O₁₆ revised

The structure of dicalcium hepta­germanate, previously described with an ortho­rhom­bic space group, has been redetermined in the tetra­gonal space group . It contains three Ge positions (site symmetry 1, ..2 and 2.22, respectively), one Ca position (..2) and four O atoms, all on general 8i positions (site symmetry 1). A sheet of four-membered rings of Ge tetra­hedra (with Ge on the 8i position) and isolated Ge tetra­hedra (Ge on the 4g position) alternate with a sheet of Ge octa­hedra (Ge on the 2d position) and eightfold-coordinated Ca sites along the c direction in an ABABA... sequence. The three-dimensional framework of Ge sites displays a channel-like structure, evident in a projection on to the ab plane.

S1. Comment

In the system CaO–GeO₂ several phases are reported in the phase-equilibrium studies of Eulenberger et al. (1962) and Shirvinskaya et al. (1966), among them the Ge-rich phase CaGe₄O₉. Another Ge-rich phase is mentioned by Nevskii et al. (1979), namely Ca₂Ge₇O₁₆. While the crystal structure of the first phase appears to be unknown at first glance, the latter was determined by Nevskii et al. (1979) to be orthorhombic, Pba2, a = 11.340 (2) Å, b = 11.340 (2) Å and c = 4.6400 (8) Å. In order to investigate CaGe₄O₉ in more detail and to determine its crystal structure, we attempted to synthesize this compound using ceramic sintering techniques between 1273 and 1473 K. However, we always identified very well crystallized Ca₂Ge₇O₁₆ and small amounts of GeO₂. In addition, under hydrothermal conditions (923 K, 0.2 GPa), the stable phases are Ca₂Ge₇O₁₆ and GeO₂ (when starting with CaGe₄O₉ composition). These findings led us to conclude that, in the phase diagram CaO–GeO₂, the compound CaGe₄O₉ may not exist but has to be replaced by Ca₂Ge₇O₁₆. This is supported by the fact that Cd₂Ge₇O₁₆ was also described as `CdGe₄O₉' in the literature (Wittmann 1966) until Plattner & Völlenkle (1977) evaluated its true chemistry by structure determination. This Cd compound is tetragonal with a = 11.31 Å and c = 4.63 Å, space group P4b2. Germanates with AB₄X₉, such as SrGe₄O₉ (Nishi 1996), BaGe₄O₉ (Shashkov et al., 1984) and PbGe₄O₉ (Shashkov et al., 1981), display similar lattice parameters [e.g. 11.344 (2) and 4.750 (2) Å for SrGe₄O₉] and structural topologies, but have trigonal/rhombohedral symmetry, space group P321.

Nevskii et al. (1979) report that Ca₂Ge₇O₁₆ has Laue symmetry 4/mmm, but the authors were unable to find a structural model in tetragonal symmetry. A reduction of symmetry led to orthorhombic space group Pba2. Nevskii et al. (1979) found a structural model with four Ge, one Ca and eight O positions by a combination of Patterson methods and residual electron density map calculations and refined it down to R = 0.024. Motivated by the availability of small single crystals of the title compound from the hydrothermal experiment (923 K, 0.2 GPa) and large (up to 2 mm-long) prismatic crystals from another synthesis experiment, where the title compound appeared by chance, the structure was reinvestigated and a revised model in tetragonal symmetry is given in here.

The asymmetric unit of the title crystal structure contains one Ca, three Ge and four O positions (Fig. 1). Four-membered rings of Ge1 tetrahedra, isolated Ge3 tetrahedra and Ge2 octahedra make up a three-dimensional framework that builds up two types of channels, which are evident in a projection parallel to the c axis (Fig. 2), viz. four-membered almost quadratic and eight-membered elliptical channels with diameters of ~3.54 and 3.99–6.25 Å, respectively. The large cavities host the eightfold coordinated Ca sites. In analogy to the topologically related AB₄X₉ compounds mentioned above, the title compound may alternatively be described in terms of two different systems of sheets, which are stacked along the c direction in an ABABA··· sequence. The first of these sheets consists of the four-membered ring of Ge1 tetrahedra and the isolated Ge3 tetrahedra (Fig. 3), while the second sheet is composed of isolated Ge2 octahedra and the Ca sites. In contrast to the title compound, the trigonal structures exhibit three-membered rings of GeO₄ tetrahedra but no isolated tetrahedra, while the interconnection to a three-dimensional framework via the Ge octahedra is similar.

The Ge1 site, on general position 8i, is coordinated by four O atoms as a distorted tetrahedron. Polyhedral distortion parameters are intermediately large (Table 2), which becomes evident when comparing especially tetrahedral angle variance (TAV) and tetrahedral quadratic elongation (TQE) parameters (Robinson et al., 1971) with data previously found in other germanate compounds in the literature. The GeO₄ tetrahedron in Cu(Cu_0.44Cr_4.56)Ge₂O₁₂ (Redhammer et al., 2007) is an instance of a regular tetrahedron with distortion parameters TAV = 5.32° and TQE = 1.0013, while distinct distortion is found for tetrahedra in, for example, Ca_7.96Cu_0.04Ge₅O₁₈, with TAV = 79.71° and TQE = 1.0186° for the Ge2 site (Redhammer et al., 2006). The angular distortion of the Ge1 tetrahedron in Ca₂Ge₇O₁₆ mainly results from the large O2—Ge1—O3 bond angle, interconnecting the Ge1 site via corner-sharing to two neighbouring Ge2 octahedra. Via atoms O1 and O1ⁱ [symmetry code (i) -x + 1, y, -z + 1] [should this be the same as i in table 1 and figure 1?] the Ge1 tetrahedron is also connected to two neighbouring Ge1 tetrahedra, being part of the four-membered Ge1₄O₁₂ ring with the 4 axis exactly in the centre of the ring. Within this ring the Ge1—O1—Ge1(y, -x + 1, -z + 1) is 128.9 (2)°, a typical value for Ge—O—Ge angles. In the orthorhombic model of Nevskii et al. (1979), the Ge1 site is split up into two nonequivalent positions (Ge3 and Ge4) differing in average Ge—O bond lengths (1.757 and 1.768 Å) and showing bond-length distortions of 0.91 and 0.98%, respectively. By applying the orthorhombic model of Nevskii et al. (1979) to the present data, these differences in the two Ge sites could not be reproduced but rather the structural parameters are almost identical and differ by less than one standard deviation. Also the differences between the orthorhombic and the tetragonal model are less than one s.u. for the Ge sites of the four-membered ring. This also accounts for the Ge2 and Ge3 sites. In comparing with Cd₂Ge₇O₁₄ (Plattner & Völlenkle 1977) it is evident that the tetrahedron of the four-membered ring displays a smaller average Ge—O bond length but a somewhat larger polyhedral distortion in the Cd compound (Table 2).

The isolated Ge3 tetrahedron is located at the cell edges on special position 2d (site symmetry 2.22) within the same sheet as the four-membered GeO₄ rings. While having four identical bond lengths as a result of symmetry restrictions (Table 1), thus BLD = 0.0, it exhibits distinct angular distortion and quadratic elongation, both being larger than for Ge1 (Table 2). All four corners (O4) are shared with neighbouring Ge2 octahedra (corner-sharing) and the Ca sites. In the Cd compound (Plattner & Völlenkle 1977) the isolated tetrahedron displays somewhat smaller bond and edge lengths and the angular distortion and elongation are lower (Table 2).

The octahedrally coordinated Ge2 site is on special position 4d, site symmetry.. 2. Four of its corners are shared with neighbouring Ge1 and the remaining two with neighbouring Ge3 tetrahedra. The average Ge2—O bond length in the title compound is somewhat larger than that found by Nevskii et al. (1979) but is smaller by ~0.01 Å than that in Cd₂Ge₇O₁₆ (Plattner & Völlenkle 1977). In comparing Ca₂Ge₇O₁₆ and Cd₂Ge₇O₁₆ with the AB₄O₉ compounds it is found that average Ge—O bond lengths and polyhedral distortional parameters are similar. Increasing the size of the eightfold coordinated A cation [Cd = 1.07 Å, Ca = 1.12 Å, Sr = 1.25 Å, Pb = 1.29 Å, Ba = 1.42 Å; Shannon & Prewitt 1969] an almost linear increase of <Ge—O> bond lengths is observable, extending, for example, from 1.746 (2) and 1.762 (2) Å in the title compound to 1.756 (3) and 1.779 (3) Å for the tetrahedral sites in BaGe₄O₉ (Shashkov et al. 1984). The reverse is valid for the polyhedral distortion parameters, which distinctly decrease with increasing size of the A cations within the AB₄O₉ series but also decrease from the title compound to SrGe₄O₉ (Nishi 1996), except the Ge4 tetrahedron, which suffers extreme distortion in SrGe₄O₉ (Nishi 1996) with TAV = 159.9° and TQE = 1.0385. It might be concluded that the trigonal AB₄O₉ structure type is not stable for cations smaller than Sr owing to this large distortion of the above-mentioned tetrahedral site, thus transforming to the similar tetragonal topology of the title compound.

The Ca²⁺ site is eight-coordinated, with six close and two more distant Ca—O bond lengths (Table 1). The two long bonds still contribute 0.08 valence units (v.u.) to the bond valence sum of Ca²⁺, thus being regarded as bonding. While in Ca₂Ge₇O₁₄ the interstitial space hosting the A cation displays an elliptic shape and a nonuniform distribution of Ca—O bond lengths, it is of a more circular shape in SrGe₄O₉, displaying a more uniform distribution of Sr—O bonds between 2.600 (7) and 2.977 (8) Å (Nishi, 1996). It is assumed that the larger space requirement of Sr²⁺ (as compared with Ca²⁺) forces the formation of three-membered GeO₄ rings, while in the title compound four-membered rings are still possible.

Related literature

For related literature, see: Eulenberger et al. (1962); Nevskii et al. (1979); Nishi (1996); Plattner & Völlenkle (1977); Redhammer et al. (2006, 2007); Robinson et al. (1971); Shannon & Prewitt (1969); Shashkov et al. (1981, 1984); Shirvinskaya et al. (1966); Wittmann (1966).

S2. Experimental

The crystal used for crystal structure redetermination, was obtained by chance during attempts to synthesize the clinopyroxene compound CaFeGe₂O₆ under hydrothermal conditions from a highly saturated CaCl₂ solution. Therefore, CaCl₂ was added to a homogenous mixture of CaCO₃, Fe₂O₃ and GeO₂ (with stoichiometry of CaFeGe₂O₆) in a ratio of 1:1. This starting material, together with 10 wt% H₂O, was put into a gold capsule, welded tight and heated under hydrothermal conditions (923 K, 0.2 GPa, redox conditions of the Tuttle-type autoclave being close to nickel–nickel oxide solid-state buffer, 127 h run duration). The synthesis batch consisted of small idiomorphic crystals of Ge andradite Ca₃Fe₂Ge₃O₁₂ (up to 30 µm in size) and large colourless tetragonal prisms of the title compound (up to 2 mm in length and 200 µm in diameter). Ca₂Ge₇O₁₆, however, can also be obtained from stoichiometric mixtures of CaO and GeO₂ using hydrothermal techniques (673–873 K, 0.2 GPa, 10 wt% H₂O added to the Au sample containers). The single crystals obtained here were distinctly smaller (maximum lengths of 80 µm).

S3. Refinement

The highest diffraction symmetry with reasonable R_int values is 4/mmm; thus it was decided to facilitate structure solution using direct methods in tetragonal symmetry. Systematic extinction conditions allow space groups P4/mbm, P4b2 and P4bm. Only in the noncentrosymmetric space group P4b2 was it possible to obtain a good solution with reliable agreement factors and realistic structural topology. For the other two cases it was not possible to get R values below 35%, and also the coordination chemistry of the cations turned out to be highly unrealistic. It should be stressed that a structural model with tetragonal symmetry could be found and refined down to 5.7% in this study, while Nevskii et al. (1979) stated that they were unable to refine the structure with tetragonal symmetry as none of their models refined below 46%. We also tried to refine the structure of the title compound in orthorhombic symmetry. Here space group Pba2 of Nevskii et al. (1979) could be confirmed. The orthorhombic model works well too; the final reliability factors, however, are somewhat higher (wR2 = 6.7%), and thus it was decided that the tetragonal model is valid. In comparing the title compound with Cd₂Ge₇O₁₆ it became evident that there is a typing error in the atomic coordinates of Plattner & Völlenkle (1977) for O2: zO2 should read 0.228 instead of 0.288 given in their Table 2.

Computing details

Data collection: SMART-Plus (Bruker, 2001); cell refinement: SAINT-Plus (Bruker, 2001); data reduction: SAINT-Plus; program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: Diamond (Version 3.0; Pennington,1999); software used to prepare material for publication: WinGX (Version 1.70.01; Farrugia 1999).

Figures

	Fig. 1. View of the asymmetric unit and some symmetry-related atoms of the title compound, showing 95% probability displacement ellipsoids and the atomic nomenclature scheme. [Symmetry codes: (i) -y + 1, x, -z + 1; (ii) -y + 1/2, -x + 1/2, -z; (iii) -y + 1/2, -x + 1/2, -z + 1; (iv) x, y, z - 1; (v) -x, -y + 1, z; (vi) y - 1/2, x + 1/2, -z + 1; (vii) y - 1/2, x + 1/2, -z + 2; (viii) -x + 1/2, y + 1/2, z + 1; (ix) y, -x + 1, -z + 1; (x) x, y, z + 1.]
	Fig. 2. View, along the c direction, of the structure of the title compound.
	Fig. 3. View, along the c direction, of the structure of the title compound, showing the sheet of four-membered rings of Ge1 tetrahedra and isolated Ge3 tetrahedra only.

dicalcium heptagermanate

Crystal data

Ca2Ge7O16	Dx = 4.703 Mg m^−3
Mr = 844.43	Mo Kα radiation, λ = 0.71073 Å
Tetragonal, P4b2	Cell parameters from 7055 reflections
a = 11.3391 (6) Å	θ = 2.5–28.8°
c = 4.6371 (2) Å	µ = 18.37 mm^−1
V = 596.22 (5) Å^3	T = 295 K
Z = 2	Prism, colourless
F(000) = 784	0.15 × 0.08 × 0.07 mm

Data collection

Bruker SMART APEX diffractometer	748 reflections with I > 2σ(I)
rotation, ω scans at 4 different ϕ positions	Rint = 0.060
Absorption correction: numerical via equivalents using X-SHAPE (Stoe & Cie 1996)	θmax = 28.8°, θmin = 2.5°
Tmin = 0.19, Tmax = 0.28	h = −14→14
7055 measured reflections	k = −15→14
764 independent reflections	l = −6→6

Refinement

Refinement on F^2	0 restraints
Least-squares matrix: full	w = 1/[σ^2(Fo^2) + (0.0338P)^2 + 0.6217P] where P = (Fo^2 + 2Fc^2)/3
R[F^2 > 2σ(F^2)] = 0.023	(Δ/σ)max < 0.001
wR(F^2) = 0.057	Δρmax = 0.73 e Å^−3
S = 1.15	Δρmin = −0.81 e Å^−3
764 reflections	Absolute structure: (Flack, 1983), 296 Friedel pairs
60 parameters	Absolute structure parameter: 0.03 (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
Ge1	0.31224 (3)	0.43357 (3)	0.48963 (12)	0.00708 (14)
Ge2	0.13344 (3)	0.36656 (3)	0	0.00658 (15)
Ge3	0	0.5	0.5	0.00700 (18)
Ca	0.16515 (6)	0.66515 (6)	1	0.0105 (2)
O1	0.3594 (3)	0.5680 (3)	0.3397 (7)	0.0116 (7)
O2	0.2653 (3)	0.3302 (3)	0.2311 (7)	0.0092 (6)
O3	0.2192 (3)	0.4722 (3)	0.7748 (6)	0.0087 (6)
O4	0.1160 (3)	0.4989 (3)	0.2524 (6)	0.0082 (6)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ge1	0.0075 (2)	0.0066 (2)	0.0072 (2)	−0.00045 (13)	0.0011 (3)	−0.0004 (2)
Ge2	0.00643 (19)	0.00643 (19)	0.0069 (2)	0.00044 (17)	0.0001 (2)	0.0001 (2)
Ge3	0.0071 (2)	0.0071 (2)	0.0068 (3)	0.0007 (2)	0	0
Ca	0.0099 (3)	0.0099 (3)	0.0116 (5)	−0.0036 (4)	0.0022 (6)	−0.0022 (6)
O1	0.0130 (16)	0.0083 (15)	0.0133 (15)	−0.0047 (12)	0.0014 (12)	−0.0004 (12)
O2	0.0092 (14)	0.0075 (13)	0.0108 (14)	0.0014 (11)	−0.0024 (12)	0.0009 (12)
O3	0.0086 (14)	0.0098 (14)	0.0078 (12)	−0.0011 (12)	0.0023 (12)	0.0003 (11)
O4	0.0050 (13)	0.0100 (14)	0.0097 (15)	−0.0011 (9)	0.0027 (11)	−0.0008 (13)

Geometric parameters (Å, º)

Ge1—O3	1.747 (3)	Ge2—Ca^iv	3.4049 (8)
Ge1—O2	1.758 (3)	Ge3—O4	1.746 (3)
Ge1—O1	1.759 (3)	Ge3—Ca^iv	3.5199 (8)
Ge1—O1^i	1.783 (3)	Ca—O4^v	2.288 (3)
Ge2—O3^ii	1.863 (3)	Ca—O2^vi	2.297 (3)
Ge2—O2	1.886 (3)	Ca—O3	2.500 (3)
Ge2—O4	1.913 (3)	Ca—O1^v	2.924 (3)
Ge2—Ca^iii	3.2297 (11)
O3—Ge1—O2	120.03 (16)	O2^vi—Ca—O2^xi	70.02 (16)
O3—Ge1—O1	105.40 (15)	O4^v—Ca—O3^xii	63.42 (10)
O2—Ge1—O1	113.58 (14)	O4^x—Ca—O3^xii	77.01 (11)
O3—Ge1—O1^i	104.00 (14)	O2^vi—Ca—O3^xii	84.57 (10)
O2—Ge1—O1^i	102.64 (15)	O2^xi—Ca—O3^xii	145.47 (10)
O1—Ge1—O1^i	110.6 (2)	O4^v—Ca—O3	77.01 (11)
O3^ii—Ge2—O3^vii	170.19 (19)	O4^x—Ca—O3	63.42 (10)
O3^ii—Ge2—O2	92.57 (14)	O2^vi—Ca—O3	145.47 (10)
O3^vii—Ge2—O2	94.44 (14)	O2^xi—Ca—O3	84.57 (10)
O2—Ge2—O2^viii	88.67 (19)	O3^xii—Ca—O3	127.13 (14)
O3^ii—Ge2—O4	83.83 (13)	O4^v—Ca—O1^v	66.26 (10)
O3^vii—Ge2—O4	90.01 (13)	O4^x—Ca—O1^v	143.58 (10)
O2—Ge2—O4	84.58 (13)	O2^vi—Ca—O1^v	76.50 (10)
O2^viii—Ge2—O4	172.94 (13)	O2^xi—Ca—O1^v	78.30 (10)
O4—Ge2—O4^viii	102.24 (18)	O3^xii—Ca—O1^v	73.17 (9)
O4^v—Ge3—O4^ix	114.94 (19)	O3—Ca—O1^v	121.78 (9)
O4^v—Ge3—O4	116.3 (2)	O4^v—Ca—O1^x	143.58 (10)
O4^ix—Ge3—O4	97.77 (19)	O4^x—Ca—O1^x	66.26 (10)
O4^v—Ca—O4^x	81.97 (16)	O2^vi—Ca—O1^x	78.30 (10)
O4^v—Ca—O2^vi	136.07 (11)	O2^xi—Ca—O1^x	76.50 (10)
O4^x—Ca—O2^vi	121.09 (10)	O3^xii—Ca—O1^x	121.78 (9)
O4^v—Ca—O2^xi	121.09 (10)	O3—Ca—O1^x	73.17 (9)
O4^x—Ca—O2^xi	136.07 (11)	O1^v—Ca—O1^x	149.11 (13)

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