Supporting information
Crystallographic Information File (CIF) https://doi.org/10.1107/S0108270105021979/fa1148sup1.cif | |
Structure factor file (CIF format) https://doi.org/10.1107/S0108270105021979/fa1148Isup2.hkl |
Ge4Se9 was prepared by the reaction of elemental Ta, Ge and Se by use of the flux technique. A combination of the pure elements, Ta powder (CERAC, 99.999%), Ge powder (CERAC, 99.5%) and Se powder (CERAC, 99.95%), were mixed in silica tubes in an atomic ratio of Ta:Ge:Se = 1:2:10, and then RbCl was added in a weight ratio of TaGe2Se10:RbCl = 1:2. The tubes were evacuated to 10−2 Torr (1 Torr = 133.322 Pa), sealed, and heated gradually (50 K hr−1) to 1073 K in a box furnace, where they were kept for 96 h. The tubes were slowly cooled to 473 K at the rate of 4 K h−1 and quenched. The excess halide was removed with distilled water. Orange block crystals of up to 0.3 mm in length were obtained. The crystals are stable in air and water.
Systematic absences are consistent with the orthorhombic space groups Pbcm and Pca21. The initial positions for all atoms were determined by direct methods with the program SHELXS97 (Sheldrick, 1997). A solution with a low figure of merit could only be found in the non-centrosymmetric space group Pca21. No additional symmetry, as tested by PLATON (Spek, 2003), was detected in this structure. The absolute structure cannot be determined from powder data because Friedel pairs are overlapped. Refinement with the positional parameters from the previous report based on the powder study (Fjellvåg et al., 2001) gave a value of 0.86 (6) for the Flack parameter (Flack, 1983) (wR2 = 0.0804). Refinement of the inverse structure, which is the setting reported in this work, leads to a Flack parameter of 0.11 (6) and an improved reliability factor (wR2 = 0.0742). The highest residual electron density is 1.13 Å from the Ge1 site and the deepest hole is 1.65 Å from the Se5 site. The anisotropic displacement parameters of atoms Se1, Se2 and Se5 are larger than those of the other Se atoms and this is probably due to the ample free space around those atoms.
Data collection: RAPID-AUTO (Rigaku, 2005); cell refinement: RAPID-AUTO; data reduction: RAPID-AUTO; program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: locally modified version of ORTEP (Johnson, 1965); software used to prepare material for publication: WinGX (Farrugia, 1999).
Ge4Se9 | F(000) = 1736 |
Mr = 1001.08 | Dx = 4.419 Mg m−3 |
Orthorhombic, Pca21 | Mo Kα radiation, λ = 0.71073 Å |
Hall symbol: P 2C -2AC | Cell parameters from 11241 reflections |
a = 17.805 (6) Å | θ = 3.1–27.5° |
b = 7.002 (2) Å | µ = 29.64 mm−1 |
c = 12.071 (6) Å | T = 291 K |
V = 1504.8 (10) Å3 | Block, orange |
Z = 4 | 0.30 × 0.10 × 0.05 mm |
Rigaku R-AXIS RAPID-S diffractometer | 2837 reflections with I > 2σ(I) |
ω scans | Rint = 0.060 |
Absorption correction: numerical (NUMABS; Higashi, 2000) | θmax = 27.5°, θmin = 3.1° |
Tmin = 0.042, Tmax = 0.220 | h = −21→23 |
13705 measured reflections | k = −9→8 |
3410 independent reflections | l = −15→15 |
Refinement on F2 | 1 restraint |
Least-squares matrix: full | w = 1/[σ2(Fo2) + (0.0242P)2 + 4.9288P] where P = (Fo2 + 2Fc2)/3 |
R[F2 > 2σ(F2)] = 0.037 | (Δ/σ)max = 0.001 |
wR(F2) = 0.074 | Δρmax = 1.32 e Å−3 |
S = 1.06 | Δρmin = −0.93 e Å−3 |
3410 reflections | Absolute structure: Flack (1983), with 1615 Friedel pairs |
118 parameters | Absolute structure parameter: 0.11 (6) |
Ge4Se9 | V = 1504.8 (10) Å3 |
Mr = 1001.08 | Z = 4 |
Orthorhombic, Pca21 | Mo Kα radiation |
a = 17.805 (6) Å | µ = 29.64 mm−1 |
b = 7.002 (2) Å | T = 291 K |
c = 12.071 (6) Å | 0.30 × 0.10 × 0.05 mm |
Rigaku R-AXIS RAPID-S diffractometer | 3410 independent reflections |
Absorption correction: numerical (NUMABS; Higashi, 2000) | 2837 reflections with I > 2σ(I) |
Tmin = 0.042, Tmax = 0.220 | Rint = 0.060 |
13705 measured reflections |
R[F2 > 2σ(F2)] = 0.037 | 1 restraint |
wR(F2) = 0.074 | Δρmax = 1.32 e Å−3 |
S = 1.06 | Δρmin = −0.93 e Å−3 |
3410 reflections | Absolute structure: Flack (1983), with 1615 Friedel pairs |
118 parameters | Absolute structure parameter: 0.11 (6) |
x | y | z | Uiso*/Ueq | ||
Ge1 | 0.83078 (5) | 0.81452 (11) | 0.82476 (10) | 0.0161 (2) | |
Ge2 | 0.77487 (5) | 0.31194 (11) | 0.83619 (9) | 0.0158 (2) | |
Ge3 | 0.64516 (5) | 0.67879 (13) | 0.90030 (10) | 0.0195 (2) | |
Ge4 | 0.45911 (5) | 0.82432 (12) | 0.90229 (10) | 0.0178 (2) | |
Se1 | 0.95600 (5) | 0.83969 (12) | 0.88252 (12) | 0.0309 (3) | |
Se2 | 0.55310 (5) | 0.75528 (16) | 1.03362 (10) | 0.0298 (3) | |
Se3 | 0.82032 (5) | 0.54355 (11) | 0.71060 (10) | 0.0212 (2) | |
Se4 | 0.75587 (5) | 0.79487 (13) | 0.98270 (10) | 0.0251 (2) | |
Se5 | 0.64820 (5) | 0.34144 (13) | 0.88599 (13) | 0.0332 (3) | |
Se6 | 0.60988 (5) | 0.82677 (14) | 0.73224 (10) | 0.0277 (3) | |
Se7 | 0.49224 (5) | 0.67033 (13) | 0.73442 (10) | 0.0259 (2) | |
Se8 | 0.35219 (5) | 0.70145 (14) | 0.99326 (10) | 0.0234 (2) | |
Se9 | 0.78705 (5) | 1.05985 (11) | 0.70791 (10) | 0.0231 (2) |
U11 | U22 | U33 | U12 | U13 | U23 | |
Ge1 | 0.0158 (4) | 0.0120 (4) | 0.0205 (7) | −0.0007 (3) | 0.0013 (4) | −0.0011 (4) |
Ge2 | 0.0152 (4) | 0.0132 (4) | 0.0190 (7) | 0.0006 (3) | −0.0006 (4) | −0.0012 (4) |
Ge3 | 0.0141 (4) | 0.0220 (4) | 0.0223 (7) | 0.0024 (3) | 0.0005 (5) | −0.0008 (4) |
Ge4 | 0.0141 (4) | 0.0196 (4) | 0.0198 (7) | 0.0032 (3) | −0.0014 (5) | 0.0005 (4) |
Se1 | 0.0160 (4) | 0.0196 (4) | 0.0570 (10) | 0.0007 (3) | −0.0068 (5) | −0.0025 (5) |
Se2 | 0.0191 (4) | 0.0526 (6) | 0.0177 (7) | 0.0135 (4) | −0.0007 (5) | −0.0004 (5) |
Se3 | 0.0331 (4) | 0.0145 (4) | 0.0160 (6) | −0.0028 (3) | 0.0021 (5) | −0.0013 (4) |
Se4 | 0.0206 (4) | 0.0373 (5) | 0.0174 (7) | −0.0071 (4) | 0.0031 (5) | −0.0077 (5) |
Se5 | 0.0158 (4) | 0.0210 (4) | 0.0628 (11) | −0.0033 (3) | 0.0071 (6) | −0.0045 (5) |
Se6 | 0.0230 (5) | 0.0380 (5) | 0.0221 (7) | −0.0001 (4) | 0.0020 (5) | 0.0046 (5) |
Se7 | 0.0218 (4) | 0.0345 (5) | 0.0215 (7) | 0.0007 (4) | −0.0002 (5) | −0.0056 (5) |
Se8 | 0.0198 (4) | 0.0326 (5) | 0.0178 (7) | −0.0040 (4) | −0.0003 (5) | 0.0026 (4) |
Se9 | 0.0372 (5) | 0.0147 (4) | 0.0174 (6) | 0.0040 (3) | −0.0040 (5) | −0.0024 (4) |
Ge1—Se4 | 2.3307 (18) | Ge3—Se6 | 2.3630 (18) |
Ge1—Se1 | 2.3427 (14) | Ge3—Se5 | 2.3689 (14) |
Ge1—Se3 | 2.3523 (15) | Ge4—Se2 | 2.3553 (16) |
Ge1—Se9 | 2.3550 (15) | Ge4—Se8 | 2.3600 (15) |
Ge2—Se5 | 2.3431 (14) | Ge4—Se1iii | 2.3652 (14) |
Ge2—Se8i | 2.3450 (17) | Ge4—Se7 | 2.3699 (18) |
Ge2—Se9ii | 2.3580 (15) | Se1—Ge4iv | 2.3652 (14) |
Ge2—Se3 | 2.3628 (15) | Se6—Se7 | 2.3638 (14) |
Ge3—Se4 | 2.3528 (15) | Se8—Ge2v | 2.3450 (17) |
Ge3—Se2 | 2.3587 (17) | Se9—Ge2vi | 2.3580 (15) |
Se4—Ge1—Se1 | 107.79 (7) | Se6—Ge3—Se5 | 112.37 (6) |
Se4—Ge1—Se3 | 112.73 (5) | Se2—Ge4—Se8 | 100.67 (6) |
Se1—Ge1—Se3 | 108.08 (5) | Se2—Ge4—Se1iii | 106.78 (5) |
Se4—Ge1—Se9 | 110.11 (5) | Se8—Ge4—Se1iii | 113.00 (5) |
Se1—Ge1—Se9 | 115.98 (5) | Se2—Ge4—Se7 | 107.77 (6) |
Se3—Ge1—Se9 | 102.19 (6) | Se8—Ge4—Se7 | 115.65 (5) |
Se5—Ge2—Se8i | 111.17 (7) | Se1iii—Ge4—Se7 | 111.84 (6) |
Se5—Ge2—Se9ii | 108.85 (5) | Ge1—Se1—Ge4iv | 97.30 (4) |
Se8i—Ge2—Se9ii | 116.55 (5) | Ge4—Se2—Ge3 | 94.65 (7) |
Se5—Ge2—Se3 | 115.71 (5) | Ge1—Se3—Ge2 | 101.81 (6) |
Se8i—Ge2—Se3 | 110.19 (5) | Ge1—Se4—Ge3 | 98.86 (7) |
Se9ii—Ge2—Se3 | 93.49 (6) | Ge2—Se5—Ge3 | 97.39 (4) |
Se4—Ge3—Se2 | 102.44 (7) | Ge3—Se6—Se7 | 91.31 (5) |
Se4—Ge3—Se6 | 115.74 (6) | Se6—Se7—Ge4 | 91.11 (5) |
Se2—Ge3—Se6 | 107.54 (6) | Ge2v—Se8—Ge4 | 96.42 (6) |
Se4—Ge3—Se5 | 110.86 (5) | Ge1—Se9—Ge2vi | 100.55 (6) |
Se2—Ge3—Se5 | 106.98 (6) |
Symmetry codes: (i) x+1/2, −y+1, z; (ii) x, y−1, z; (iii) x−1/2, −y+2, z; (iv) x+1/2, −y+2, z; (v) x−1/2, −y+1, z; (vi) x, y+1, z. |
Experimental details
Crystal data | |
Chemical formula | Ge4Se9 |
Mr | 1001.08 |
Crystal system, space group | Orthorhombic, Pca21 |
Temperature (K) | 291 |
a, b, c (Å) | 17.805 (6), 7.002 (2), 12.071 (6) |
V (Å3) | 1504.8 (10) |
Z | 4 |
Radiation type | Mo Kα |
µ (mm−1) | 29.64 |
Crystal size (mm) | 0.30 × 0.10 × 0.05 |
Data collection | |
Diffractometer | Rigaku R-AXIS RAPID-S diffractometer |
Absorption correction | Numerical (NUMABS; Higashi, 2000) |
Tmin, Tmax | 0.042, 0.220 |
No. of measured, independent and observed [I > 2σ(I)] reflections | 13705, 3410, 2837 |
Rint | 0.060 |
(sin θ/λ)max (Å−1) | 0.649 |
Refinement | |
R[F2 > 2σ(F2)], wR(F2), S | 0.037, 0.074, 1.06 |
No. of reflections | 3410 |
No. of parameters | 118 |
No. of restraints | 1 |
Δρmax, Δρmin (e Å−3) | 1.32, −0.93 |
Absolute structure | Flack (1983), with 1615 Friedel pairs |
Absolute structure parameter | 0.11 (6) |
Computer programs: RAPID-AUTO (Rigaku, 2005), RAPID-AUTO, SHELXS97 (Sheldrick, 1997), SHELXL97 (Sheldrick, 1997), locally modified version of ORTEP (Johnson, 1965), WinGX (Farrugia, 1999).
Ge1—Se4 | 2.3307 (18) | Ge3—Se2 | 2.3587 (17) |
Ge1—Se1 | 2.3427 (14) | Ge3—Se6 | 2.3630 (18) |
Ge1—Se3 | 2.3523 (15) | Ge3—Se5 | 2.3689 (14) |
Ge1—Se9 | 2.3550 (15) | Ge4—Se2 | 2.3553 (16) |
Ge2—Se5 | 2.3431 (14) | Ge4—Se8 | 2.3600 (15) |
Ge2—Se8i | 2.3450 (17) | Ge4—Se1iii | 2.3652 (14) |
Ge2—Se9ii | 2.3580 (15) | Ge4—Se7 | 2.3699 (18) |
Ge2—Se3 | 2.3628 (15) | Se6—Se7 | 2.3638 (14) |
Ge3—Se4 | 2.3528 (15) | ||
Se4—Ge1—Se1 | 107.79 (7) | Se4—Ge3—Se2 | 102.44 (7) |
Se4—Ge1—Se3 | 112.73 (5) | Se4—Ge3—Se6 | 115.74 (6) |
Se1—Ge1—Se3 | 108.08 (5) | Se2—Ge3—Se6 | 107.54 (6) |
Se4—Ge1—Se9 | 110.11 (5) | Se4—Ge3—Se5 | 110.86 (5) |
Se1—Ge1—Se9 | 115.98 (5) | Se2—Ge3—Se5 | 106.98 (6) |
Se3—Ge1—Se9 | 102.19 (6) | Se6—Ge3—Se5 | 112.37 (6) |
Se5—Ge2—Se8i | 111.17 (7) | Se2—Ge4—Se8 | 100.67 (6) |
Se5—Ge2—Se9ii | 108.85 (5) | Se2—Ge4—Se1iii | 106.78 (5) |
Se8i—Ge2—Se9ii | 116.55 (5) | Se8—Ge4—Se1iii | 113.00 (5) |
Se5—Ge2—Se3 | 115.71 (5) | Se2—Ge4—Se7 | 107.77 (6) |
Se8i—Ge2—Se3 | 110.19 (5) | Se8—Ge4—Se7 | 115.65 (5) |
Se9ii—Ge2—Se3 | 93.49 (6) | Se1iii—Ge4—Se7 | 111.84 (6) |
Symmetry codes: (i) x+1/2, −y+1, z; (ii) x, y−1, z; (iii) x−1/2, −y+2, z. |
The synthesis of polycrystalline Ge4Se9 has been reported and its structure was previously determined ab initio from X-ray powder diffraction data using a combination of direct methods and the Rietveld technique (Fjellvåg et al., 2001). Single crystals of reasonable quality and size suitable for a single-crystal X-ray diffraction study have not been obtained with traditional solid-state synthetic techniques. We have used alkali metal halides as fluxes to prepare single crystals of metal chalcogenides, and this synthetic technique appears to be of general utility in preparing crystalline chalcogenides (Do & Yun, 1996; Kim et al., 1997). We describe here the synthesis and structural characterization of Ge4Se9 single crystals.
The general features of the structure of Ge4Se9 are the same as previously reported (Fjellvåg et al., 2001). A view down the b axis clearly shows the layered nature of the structure (Fig. 1). Fig. 2 shows that an individual layer is composed of infinite chains of corner-sharing Ge tetrahedra. The chains are connected via Ge2Se7 units parallel to the a axis to form a two-dimensional layer, and these layers are stacked to complete the three-dimensional structure with a van der Waals gap, as shown in Fig. 1. There is no bonding interaction, only van der Waals forces, between the layers.
The structure of Ge4Se9 is closely related to that of monoclinic α-GeSe2 (Dittmar & Schäfer, 1976). One-dimensional chains composed of corner-sharing tetrahedral GeSe4 units are found in both structures. While the edge-sharing Ge2Se6 unit (Fig. 3a) bridges the chains in GeSe2, the corner-sharing Ge2Se7 link (Fig. 3b) connects the chains in Ge4Se9.
The Ge—Se distances [2.331 (2)–2.370 (2) Å] are in good agreement with those calculated from the covalent radii of Ge and Se (1.22 and 1.16 Å, respectively; Webelements, 2005) and are comparable with those of other selenogermanates, such as SrCu2GeSe4 [2.345 (5)–2.370 (4) Å; Tampier & Johrendt, 2001]. As would be expected, the Ge—Se distances found here from single-crystal diffraction data are more regular than those reported previously with powder diffraction data [2.287 (8)–2.405 (6) Å]. The bond angles found in the GeSe4 tetrahedra do not deviate significantly from the ideal tetrahedral value, except the Se3—Ge2—Se9ii angle [93.49 (6)°; symmetry code: (ii) x, y − 1, z].
The short Se6—Se7 separation [2.3638 (14) Å] found in the Ge2Se7 unit is consistent with a typical (Se—Se)2− pair (Sunshine & Ibers, 1987). The electrostatic bond valence sums calculated for the present structure (Adams, 2001) are 4.1008–4.1748 for the Ge atoms, 1.1761 and 1.1651 for atoms Se6 and Se7, respectively, and 2.0281–2.1271 for the other Se atoms, which are in good agreement with the estimated oxidation states from classical charge balance, [Ge4+]4[Se2−]7[Se22−]. The global instability index GII = 0.1108 v.u. is a typical value for an unstrained structure (Adams, 2001).