Trigonal sodium cal­cium germanate, Na_2.54Ca_1.73Ge₃O₉

Single crystals of a new germanate, Na_2.54Ca_1.73Ge₃O₉, have been synthesized. The structure has a six-membered ring of GeO₄ tetrahedra, which is similar to the rings of the silicate analogue Na₂Ca₂Si₃O₉, and both structures contain pseudo-cubic subcells with an edge length of 3.8 Å. The details of the two compounds are slightly different, however. For example, two O atoms are statistically distributed about twofold axes in the title compound, while the silicate analogue has no such O-atom distributions. In addition, the title germanate has an extra partially populated metal site containing 54 (4)% Na, with no equivalent site in the silicate analogue.

S1. Comment

In the ternary system Na₂O-CaO-SiO₂, Koppen & Padurow (1958) identified the compound Na₂Ca₂Si₃O₉ as having a rhombohedral lattice (a = 7.41 Å, α = 89.7°), by means of Debye-Scherrer photography. Glasser & Mileson (1968) studied the same compound by means of a Weissenberg method and found that its structure had a trigonal space group, P3₁21 or P3₂21. Maki & Sugimura (1968) studied solid solutions of the Na₂O-CaO-SiO₂ system, and found a clear phase boundary between the compounds Na₂Ca₂Si₃O₉ (low-temperature modification) and Na₂CaSi₂O₆ (high-temperature modification). Their results were confirmed by Moir & Glasser (1974). The crystal structures of two minerals, both having a composition close to Na₂Ca₂Si₃O₉, were studied by Fischer & Tillmanns (1983). One was combeite from Zaire, with the space group R3 m, and the other was an unknown mineral from Eifel, with the space group P3₁ or P3₂. They thought that this compound had two modifications, with the former probably corresponding to the quenched high-temperature modification, while the latter corresponded to the low-temperature phase of Maki & Sugimura (1968). Single crystals of Na₂CaSi₂O₆ (high-temperature modification) and Na₂Ca₂Si₃O₉ (low-temperature modification) were synthesized and studied in detail by Ohsato et al. in 1985 and 1986, respectively. These authors reported some interesting structural characteristics, such as the disorder of the Na/Ca atoms and the splitting of the O and metal atoms.

The silicates and their germanate analogues are being investigated here in order to find the common rules and principles among these compounds. The Na₂O-CaO-GeO₂ system has been studied and three different types of single-crystal have been synthesized. The first was Na_3.70Ca_1.15Ge₃O₉, which has a 12-membered ring (Nishi & Takeuchi, 1988), while the second was Na₂CaGe₂O₆, which has a six-membered ring (Nishi & Takeuchi, 1990), analogous to Na₂CaSi₂O₆ (high-temperature modification; Ohsato et al., 1985). The crystal structure of the third compound, Na_2.54Ca_1.73Ge₃O₉, corresponding to Na₂Ca₂Si₃O₉ (low-temperature modification; Ohsato et al., 1986), is the subject of the present paper.

After the least-squares refinement two O atoms (O1 and O2), which were located on twofold axes, showed abnormal atomic displacement parameters. In addition, the bond lengths between Ge and these O atoms were abnormal. Consequently, atoms O1 and O2 were assigned to general positions and split into two components about their twofold axes, with each component separated by 0.87 (2) and 0.93 (2) Å for O1 and O2, respectively.

The trigonal unit cell basically includes pseudo-cubic sub-cells with an edge length of 3.8 Å, similar to related compounds such as Na_3.70Ca_1.15Ge₃O₉ (Nishi & Takeuchi, 1988), Na₂CaGe₂O₆ (Nishi & Takeuchi, 1990), the silicate analogue Na₂CaSi₂O₆ (Ohsato et al., 1985) and Na₂Ca₂Si₃O₉ (Ohsato et al., 1986).

The six-membered ring of the title germanate, which is very similar to that of the silicate analogue Na₂Ca₂Si₃O₉ (Ohsato et al., 1986), is a little deformed in comparison with the regular six-membered ring of Na₂CaGe₂O₆ (Nishi & Takeuchi, 1990) and the silicate analogue Na₂CaSi₂O₆ (Ohsato et al., 1985). The arrangement of the six-membered rings is shown in Fig. 1.

The refined site occupancies of the disordered Na and Ca atoms over the sites M1—M6 are as follows: M1 = 0.56 (2) Na + 0.44 (2) Ca, M2 = 0.93 (2) Na + 0.07 (2) Ca, M3 = 0.54 (4) Na, M4 = 0.72 (2) Na + 0.28 (2) Ca, M5 = 0.12 (4) Na + 0.88 (4) Ca and M6 = Ca. Thus it can be seen that the site occupancies of the Na atoms range from 0% (site M6) to 93 (2)% (site M2). Judging from the average M—O distances for each M polyhedron, we can conclude that the greater the Na atom population of a given M site, the larger is the average value of the M—O distances. The average value of the M3—O distances is abnormally large, on account of the M3 site vacancy [46 (4)%]. The M3 site itself constitutes the fundamental difference between this germanate and the silicate analogue Na₂Ca₂Si₃O₉ (Ohsato et al., 1986). The former has Na atoms with an occupancy of 54 (4)% in this site, but there is no equivalent populated site in the latter.

The total numbers of Na and Ca atoms for the title germanate and Na₂Ca₂Si₃O₉ (Ohsato et al., 1986) are 4.27 (= 2.54 + 1.73) and 4 (= 2 + 2). Accordingly, this germanate requires extra sites to accommodate the excess Na atoms. The new M3 site, located at one of the vertices of the pseudo-cubic sub-cells, plays precisely this role. In Fig. 2, the M1—M6 polyhedra are shown.

Related literature

For related literature, see: Fischer & Tillmanns (1983); Glasser & Mileson (1968); Koppen & Padurow (1958); Maki & Sugimura (1968); Moir & Glasser (1974); Nishi & Takeuchi (1988, 1990); Ohsato et al. (1985, 1986).

S2. Experimental

Single crystals of sodium calcium germanate were synthesized from a mixture of Na₂CO₃, CaCO₃ and GeO₂ at 1500 K. The electron microprobe analyses of the crystals showed that the chemical formula is Na_2.54Ca_1.73Ge₃O₉. The intensities of the reflections were measured at the X-ray laboratory of Nihon University, Japan.

Computing details

Data collection: MSC/AFC Diffractometer Control Software (Molecular Structure Corporation, 1992); cell refinement: MSC/AFC Diffractometer Control Software; data reduction: TEXSAN (Molecular Structure Corporation, 1992); program(s) used to solve structure: ORFFE (Busing et al., 1964); program(s) used to refine structure: LINUS (Coppens & Hamilton, 1970); molecular graphics: Please provide details.

Figures

	Fig. 1. The arrangement of six-membered rings in the unit cell. The hatched tetrahedra are at z ≈ 7/6, the dotted ones at z ≈ 5/6 and those without patterns at z ≈ 3/6. Atoms O1 and O2 are drawn at the average positions of each split half.
	Fig. 2. The arrangement of polyhedra about the cation sites. M1 polyhedra are at z ≈ 0.09, M2 at z ≈ 0.0, M3 at z = 0, M4 at z ≈ 0.16, M5 at z = 1/6 and M6 at z = 0. Atoms O1 and O2 are drawn as in Fig. 1. The refined site occupancies are given in the text.

(I)

Crystal data

Ca1.73Ge3Na2.54O9	Dx = 3.60 Mg m^−3
Mr = 489.5	Mo Kα radiation, λ = 0.71073 Å
Trigonal, P3121	Cell parameters from 20 reflections
a = 10.780 (2) Å	θ = 10.5–20.5°
c = 13.449 (2) Å	µ = 11.07 mm^−1
V = 1353.5 (3) Å^3	T = 293 K
Z = 6	Sphere, colourless
F(000) = 2937.0	0.14 mm (radius)

Data collection

Rigaku AFC-5 diffractometer	Rint = 0.063
ω/2θ scans	θmax = 40.0°
Absorption correction: for a sphere International Tables, Vol. 2, Table 5.3.6B	h = −16→16
Tmin = 0.114, Tmax = 0.158	k = 0→19
4377 measured reflections	l = 0→24
3108 independent reflections	3 standard reflections every 150 reflections
2142 reflections with I > 3σ(I)	intensity decay: 1.1%

Refinement

Refinement on F	w = 1/(σ^2(F) + 0.0001F^2)
Least-squares matrix: full	(Δ/σ)max = 0.04
R[F^2 > 2σ(F^2)] = 0.062	Δρmax = 1.1 e Å^−3
wR(F^2) = 0.068	Δρmin = −0.1 e Å^−3
S = 1.34	Extinction correction: isotropic (Zachariasen, 1963)
2142 reflections	Extinction coefficient: 0.000050 (2)
117 parameters

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Ge1	0.1968 (1)	0.1495 (1)	0.77072 (8)	0.012 (1)
Ge2	0.4984 (1)	0.3237 (1)	0.89852 (7)	0.011 (1)
Ge3	0.6278 (1)	0.1484 (1)	0.76144 (7)	0.011 (1)
M1(Na)	0.3154 (4)	−0.0136 (4)	0.5848 (3)	0.027 (2)	0.56 (2)
M1(Ca)	0.3154 (4)	−0.0136 (4)	0.5848 (3)	0.027 (2)	0.44 (2)
M2(Na)	0.5057 (9)	0.3419 (8)	0.6642 (4)	0.035 (2)	0.93 (2)
M2(Ca)	0.5057 (9)	0.3419 (8)	0.6642 (4)	0.035 (2)	0.07 (2)
M3(Na)	0.815 (1)	0.0	0.33333	0.032 (2)	0.54 (4)
M4(Na)	0.5198 (6)	0.3589 (6)	0.1596 (3)	0.037 (2)	0.72 (2)
M4(Ca)	0.5198 (6)	0.3589 (6)	0.1596 (3)	0.037 (2)	0.28 (2)
M5(Na)	0.8241 (3)	0.0	0.83333	0.020 (1)	0.12 (4)
M5(Ca)	0.8241 (3)	0.0	0.83333	0.020 (1)	0.88 (4)
M6(Ca)	0.3074 (3)	0.0	0.33333	0.019 (1)
O1	0.183 (2)	0.018 (2)	0.863 (1)	0.023 (3)*	0.5
O2	0.568 (2)	0.023 (2)	0.864 (1)	0.022 (3)*	0.5
O3	0.349 (2)	0.283 (2)	0.827 (1)	0.051 (3)*
O4	0.599 (1)	0.274 (1)	0.822 (1)	0.048 (4)*
O5	0.258 (1)	0.156 (1)	0.6511 (8)	0.032 (3)*
O6	0.433 (1)	0.238 (1)	0.0095 (8)	0.039 (3)*
O7	0.549 (1)	0.079 (1)	0.6546 (8)	0.033 (3)*
O8	0.060 (1)	0.185 (1)	0.7912 (7)	0.027 (3)*
O9	0.596 (1)	0.508 (1)	0.8871 (8)	0.031 (4)*
O10	0.810 (1)	0.214 (1)	0.7724 (7)	0.029 (3)*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ge1	0.0185 (9)	0.0242 (9)	0.0331 (7)	0.0100 (7)	−0.0037 (7)	−0.0082 (6)
Ge2	0.0281 (9)	0.0269 (9)	0.0195 (7)	0.0196 (7)	−0.0036 (7)	−0.0043 (5)
Ge3	0.0185 (9)	0.0183 (8)	0.0261 (7)	0.0122 (7)	0.0028 (5)	0.0004 (6)
M1	0.067 (5)	0.045 (5)	0.058 (3)	0.037 (4)	−0.021 (12)	−0.016 (5)
M2	0.070 (4)	0.106 (7)	0.047 (4)	0.054 (5)	0.006 (4)	0.028 (5)
M3	0.052 (7)	0.136 (9)	0.030 (3)	0.068 (4)	0.022 (6)	0.044 (11)
M4	0.062 (6)	0.134 (7)	0.055 (4)	0.073 (5)	−0.023 (3)	−0.042 (7)
M5	0.039 (4)	0.038 (4)	0.040 (3)	0.019 (2)	0.0035 (7)	0.0069 (14)
M6	0.038 (4)	0.028 (4)	0.040 (3)	0.014 (2)	0.0001 (6)	0.0002 (11)

Geometric parameters (Å, º)

M1—O6^i	2.31 (1)	M4—O9^ix	2.900 (9)
M1—O5	2.38 (1)	M5—O5^vii	2.27 (1)
M1—O7	2.39 (1)	M5—O5^ii	2.27 (1)
M1—O9^ii	2.41 (1)	M5—O8^xi	2.386 (8)
M1—O8^iii	2.520 (8)	M5—O8^xii	2.386 (8)
M1—O10^iv	2.73 (1)	M5—O10	2.52 (1)
M2—O5	2.41 (1)	M5—O10^xiii	2.52 (1)
M2—O7^v	2.39 (1)	M5—O2	2.92 (2)
M2—O4	2.60 (2)	M5—O2^xiii	2.92 (2)
M2—O3	2.64 (2)	M6—O10^iv	2.274 (9)
M2—O2^iv	2.24 (1)	M6—O10^xiv	2.274 (9)
M2—O2^v	3.16 (2)	M6—O9^ix	2.30 (1)
M2—O6^vi	2.915 (8)	M6—O9^ii	2.30 (1)
M2—O4^iv	2.85 (1)	M6—O8^iii	2.412 (8)
M2—O7	3.09 (2)	M6—O8^x	2.412 (8)
M3—O6^vii	2.44 (1)	Ge1—O8	1.721 (13)
M3—O6^viii	2.44 (1)	Ge1—O5	1.727 (11)
M3—O1^ix	2.57 (1)	Ge1—O3	1.725 (15)
M3—O1^ii	2.57 (1)	Ge1—O1	1.833 (16)
M3—O3^ix	2.79 (2)	Ge1—O1^xiii	1.719 (18)
M3—O3^ii	2.79 (2)	Ge2—O9	1.728 (10)
M3—O8^ix	3.115 (9)	Ge2—O6^xv	1.711 (10)
M3—O8^ii	3.115 (9)	Ge2—O3	1.734 (19)
M4—O6	2.33 (1)	Ge2—O4	1.762 (13)
M4—O7^iv	2.37 (1)	Ge3—O7	1.646 (10)
M4—O4^ix	2.43 (1)	Ge3—O2	1.809 (15)
M4—O3^x	2.51 (2)	Ge3—O2^xiii	1.694 (17)
M4—O9^x	2.70 (1)	Ge3—O10	1.729 (10)
M4—O10^ix	2.821 (8)	Ge3—O4	1.736 (13)
O1—Ge1—O1^xiii	28.0 (14)	O6^xv—Ge2—O3	105.5 (6)
O8—Ge1—O5	119.5 (6)	O6^xv—Ge2—O4	119.7 (6)
O8—Ge1—O3	107.9 (9)	O3—Ge2—O4	103.5 (8)
O8—Ge1—O1	108.4 (8)	O2—Ge3—O2^xiii	30.6 (12)
O8—Ge1—O1^xiii	116.7 (5)	O7—Ge3—O2	114.6 (6)
O5—Ge1—O3	100.9 (6)	O7—Ge3—O2^xiii	85.4 (5)
O5—Ge1—O1	122.9 (8)	O7—Ge3—O10	118.8 (5)
O5—Ge1—O1^xiii	98.9 (6)	O7—Ge3—O4	120.7 (7)
O3—Ge1—O1	91.4 (8)	O2—Ge3—O10	98.5 (7)
O3—Ge1—O1^xiii	111.7 (8)	O2^xiii—Ge3—O10	106.8 (5)
O9—Ge2—O6^xv	123.2 (6)	O2—Ge3—O4	95.1 (8)
O9—Ge2—O3	101.3 (7)	O2^xiii—Ge3—O4	119.7 (6)
O9—Ge2—O4	100.6 (5)	O4—Ge3—O10	104.5 (5)

Symmetry codes: (i) x−y, −y, −z+2/3; (ii) −x+1, y−x, −z+4/3; (iii) y−x, −x, z−1/3; (iv) y−x+1, −x+1, z−1/3; (v) −x+1, y−x+1, −z+4/3; (vi) y−x+1, −x+1, z+2/3; (vii) −y+1, x−y, z+1/3; (viii) −x+1, y−x, −z+1/3; (ix) −y+1, x−y, z−2/3; (x) y, x, −z+1; (xi) x+1, y, z; (xii) x−y+1, −y, −z+5/3; (xiii) x−y, −y, −z+5/3; (xiv) y, x−1, −z+1; (xv) x, y, z+1.