The crystal structure of Cu₂GeSe₃ and the structure-types of the I₂-IV-VI₃ family of semiconducting compounds

Almost 50 years after the initial report, the crystal structure of Cu₂GeSe₃, a I₂-IV-VI₃ semiconductor, has been revised using modern single-crystal X-ray diffraction data. The structure of this material can be properly described in the monoclinic space group Cc (No. 9) with unit-cell parameters a = 6.7703 (4) Å, b = 11.8624 (5) Å, c = 6.7705 (4) Å, β = 108.512 (6)°, V = 515.62 (5) ų, Z = 4, rather than in the orthorhombic space group Imm2 (No. 44) with unit-cell parameters a = 11.860 (3), b = 3.960 (1), c = 5.485 (2) Å, V = 257.61 ų, Z = 2, as originally proposed [Parthé & Garín (1971). Monatsh. Chem. 102, 1197–1208]. Contrary to what was observed in the orthorhombic structure, the distortions of the tetrahedra in the monoclinic structure are consistent with the distortions expected from considerations derived from the bond valence model. A brief revision of the structures reported for the I₂-IV-VI₃ family of semiconducting compounds (I: Cu, Ag; IV: Si, Ge, Sn; and VI: S, Se, Te) is also presented.

Computing details

Data collection: CrysAlis PRO 1.171.39.28e (Rigaku OD, 2015); cell refinement: CrysAlis PRO 1.171.39.28e (Rigaku OD, 2015); data reduction: CrysAlis PRO 1.171.39.28e (Rigaku OD, 2015); program(s) used to solve structure: ShelXT (Sheldrick, 2015); program(s) used to refine structure: SHELXL (Sheldrick, 2015); molecular graphics: DIAMOND (Brandenburg, 1999); software used to prepare material for publication: Olex2 (Dolomanov et al., 2009) and enCIFer (Allen et al., 2004).

(I)

Crystal data

Cu2GeSe3	F(000) = 768
Mr = 436.55	Dx = 5.624 Mg m^−3
Monoclinic, Cc	Mo Kα radiation, λ = 0.71075 Å
a = 6.7703 (4) Å	Cell parameters from 2471 reflections
b = 11.8624 (5) Å	θ = 3.1–34.8°
c = 6.7705 (4) Å	µ = 34.96 mm^−1
β = 108.512 (6)°	T = 293 K
V = 515.62 (5) Å^3	Irregular fragment, grey
Z = 4	0.24 × 0.23 × 0.22 mm

Data collection

Rigaku XtaLab Pro diffractometer	1824 independent reflections
Radiation source: fine-focus sealed X-ray tube, Enhance (Mo) X-ray Source	1605 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.021
Detector resolution: 5.8140 pixels mm^-1	θmax = 34.6°, θmin = 3.4°
ω scans	h = −10→10
Absorption correction: multi-scan CrysAlisPro 1.171.39.28e (Rigaku Oxford Diffraction, 2015) Empirical absorption correction using spherical harmonics, implemented in SCALE3 ABSPACK scaling algorithm.	k = −18→18
Tmin = 0.505, Tmax = 1.000	l = −10→10
4227 measured reflections

Refinement

Refinement on F^2	w = 1/[σ^2(Fo^2) + (0.0266P)^2 + 0.1027P] where P = (Fo^2 + 2Fc^2)/3
Least-squares matrix: full	(Δ/σ)max < 0.001
R[F^2 > 2σ(F^2)] = 0.027	Δρmax = 1.53 e Å^−3
wR(F^2) = 0.077	Δρmin = −1.83 e Å^−3
S = 1.16	Extinction correction: SHELXL-2018/3 (Sheldrick 2018), Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
1824 reflections	Extinction coefficient: 0.0158 (8)
56 parameters	Absolute structure: Flack x determined using 626 quotients [(I+)-(I-)]/[(I+)+(I-)] (Parsons, Flack and Wagner, Acta Cryst. B69 (2013) 249-259).
2 restraints	Absolute structure parameter: 0.043 (18)
Primary atom site location: dual

Special details

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

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

	x	y	z	Uiso*/Ueq
Cu1	−0.0001 (2)	−0.08657 (5)	0.49994 (18)	0.0163 (3)
Cu2	0.51489 (16)	−0.24677 (5)	0.50463 (15)	0.0152 (3)
Ge	0.52816 (19)	0.08587 (3)	0.52302 (18)	0.00457 (14)
Se1	0.38650 (10)	−0.08110 (3)	0.64001 (9)	0.00524 (19)
Se2	0.38880 (11)	0.24558 (4)	0.63172 (10)	0.00721 (16)
Se3	0.89215 (10)	0.08425 (3)	0.62468 (10)	0.0066 (2)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Cu1	0.0197 (9)	0.0157 (3)	0.0137 (6)	0.0019 (3)	0.0058 (6)	0.0006 (3)
Cu2	0.0146 (4)	0.0176 (3)	0.0126 (7)	−0.0014 (3)	0.0034 (4)	0.0013 (3)
Ge	0.0041 (3)	0.0067 (2)	0.0023 (3)	−0.0005 (3)	0.0001 (2)	−0.0003 (2)
Se1	0.0054 (3)	0.0071 (2)	0.0021 (3)	−0.00096 (16)	−0.0005 (2)	0.00054 (15)
Se2	0.0072 (3)	0.0082 (2)	0.0059 (3)	0.0019 (2)	0.00160 (19)	−0.0005 (2)
Se3	0.0041 (3)	0.0090 (2)	0.0061 (4)	0.00028 (14)	0.0006 (2)	0.00026 (15)

Geometric parameters (Å, º)

Cu1—Se1	2.4855 (18)	Cu2—Se2^v	2.3947 (15)
Cu1—Se2^i	2.3985 (10)	Cu2—Se3^i	2.4080 (10)
Cu1—Se3^ii	2.3964 (10)	Ge—Se1	2.4398 (9)
Cu1—Se3^iii	2.4106 (16)	Ge—Se1^v	2.4634 (15)
Cu2—Se1	2.4420 (10)	Ge—Se2	2.3371 (10)
Cu2—Se2^iv	2.4028 (16)	Ge—Se3	2.3388 (17)
Se2^i—Cu1—Se1	107.24 (5)	Cu2—Se1—Cu1	107.04 (4)
Se2^i—Cu1—Se3^iii	112.08 (5)	Cu2—Se1—Ge^vi	108.10 (4)
Se3^ii—Cu1—Se1	104.18 (5)	Ge^vi—Se1—Cu1	114.32 (5)
Se3^iii—Cu1—Se1	109.36 (6)	Ge—Se1—Cu1	111.85 (5)
Se3^ii—Cu1—Se2^i	113.85 (6)	Ge—Se1—Cu2	107.94 (5)
Se3^ii—Cu1—Se3^iii	109.73 (5)	Ge—Se1—Ge^vi	107.37 (5)
Se2^iv—Cu2—Se1	110.86 (5)	Cu1^vii—Se2—Cu2^viii	104.75 (5)
Se2^v—Cu2—Se1	109.92 (5)	Cu2^vi—Se2—Cu1^vii	109.78 (5)
Se2^v—Cu2—Se2^iv	111.11 (6)	Cu2^vi—Se2—Cu2^viii	111.08 (6)
Se2^iv—Cu2—Se3^i	106.56 (5)	Ge—Se2—Cu1^vii	110.50 (5)
Se2^v—Cu2—Se3^i	108.36 (4)	Ge—Se2—Cu2^viii	113.74 (6)
Se3^i—Cu2—Se1	109.94 (5)	Ge—Se2—Cu2^vi	107.00 (5)
Se1—Ge—Se1^v	105.15 (5)	Cu1^ix—Se3—Cu1^x	110.92 (5)
Se2—Ge—Se1	108.44 (6)	Cu1^ix—Se3—Cu2^vii	114.12 (6)
Se2—Ge—Se1^v	106.79 (5)	Cu2^vii—Se3—Cu1^x	108.96 (4)
Se2—Ge—Se3	114.02 (6)	Ge—Se3—Cu1^ix	108.27 (5)
Se3—Ge—Se1	112.57 (5)	Ge—Se3—Cu1^x	104.37 (6)
Se3—Ge—Se1^v	109.35 (5)	Ge—Se3—Cu2^vii	109.76 (4)

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