Structure refinement of Cu₈GeS₆ using X-ray diffraction data from a multiple-twinned crystal

The structure of the orthorhombic room-temperature phase of Cu₈GeS₆ (copper germanium sulfide), M_r = 773.27, has been refined on the basis of X-ray diffraction data from a 12-fold twinned crystal applying a six-dimensional twin refinement technique. For 1804 unique reflections measured using Mo Kα radiation, R_F was 0.083 with 77 structure parameters and 12 scale factors. The symmetry operations, the unit cell and other crystal data are (0, 0, 0; ½, ½, 0) + x, y, z; y, x, z; ¼ − x, ¾ − y, ½ + z; ¾ − y, ¼ − x, ½ + z; a = b = 9.9073 (3) Å, c = 9.8703 (4) Å, α = β = 90°, γ = 90.642 (4)°; V = 968.7 (1) ų, Z = 4, D_x = 5.358 Mg m⁻³, μ = 21.70 mm⁻¹. The standard setting of the space group and the reduced unit cell are Pmn2₁; a = 7.0445 (3), b = 6.9661 (3), c = 9.8699 (5) Å; Z = 2.

Computing details

Program(s) used to refine structure: FMLSM V.3.20 (Kato, 1998).

Figures

(Cu8GeS6-2)

Crystal data

Cu8GeS6	The structural model can be described based on Pmn21 with lattice constants A=7.0445(3), B=6.9661(3), C=9.8699(5). For the structure refinement, new basis a=A+B, b=B-A, c=C are selected. The new cell is C-centered, and cell constants are a=b=9.9073(3), c=9.8703(4), α=β=90, χ=90.624(4). Symmetry operations based on a, b, and c are listed as symmetry equiv pos as xyz.
Mr = 773.27	Dx = 5.358 Mg m^−3
Orthorhombic, Pmn21	Mo Kα radiation, λ = 0.70930 Å
Hall symbol: P 2ac -2	Cell parameters from 25 reflections
a = 9.9073 (3) Å	θ = 15–22.5°
b = 9.9073 Å	µ = 21.70 mm^−1
c = 9.8703 (4) Å	T = 293 K
V = 968.7 (1) Å^3	Plate-like, gray
Z = 4	0.18 × 0.12 × 0.08 mm

Data collection

Enraf-Nonius CAD4 diffractometer	1805 reflections with I > 2σ(I)
Radiation source: xray tube	Rint = 0.054
Graphite monochromator	θmax = 34.8°, θmin = 3.6°
ω–2θ scans	h = 0→19
Absorption correction: gaussian ?	k = 0→19
Tmin = 0.10, Tmax = 0.23	l = −27→27
9341 measured reflections	3 standard reflections every 200 reflections
9341 independent reflections	intensity decay: none

Refinement

Refinement on F	89 parameters
Least-squares matrix: full	0 restraints
R[F^2 > 2σ(F^2)] = 0.087	Calculated w = 1
wR(F^2) = .094	(Δ/σ)max = 0.001
1805 reflections

Special details

Refinement. Observed reflections seem to be caused by a twinned pseudo-cubic crystal, composing of the major group with hkl and the minor group with h'k'l'. The twin operations of the symmetry equivalent position as x,y,z for the major group are respectively x,y,z, y,z,x, z,x,y, x,-y,-z, -y,-z,x and -z,x,-y. To assign integral indexes to all of the major and minor groups, a six-dimensional formalism is applied. The major group is assigned hkl000, while the minor group is assigned by 000h'k'l'. Symmetry operations are also expressed in the (3 + 3)-dimensional formalism using the space-group operations, the twin operations for the six major domains and the six-dimensional twin operation·(Kato, K., Acta Cryst.(1994) A50, 351–357, Z. Krist. (1997) 212, 423–427) Refinement was performed through a version V3.20 of FMLSM (Kato). Besides structral parameters, 12 scale factors were considered as parameters, because the volumes of the six major and six minor domains are proportional to the square of the scale factors. Atomic coordinates X,Y,Z based on the orthorhombic cell with a space group Pmn21 and cell parameters A=7.0445 (3), B=6.9661 (3), C=9.8699 (5) can be calculated from the values of x,y,z using the relations X=x-y, Y=x + y and Z=z.

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

	x	y	z	Uiso*/Ueq
Ge	0.1246 (2)	0.1246	0.5072 (13)	0.009 (1)
Cu1	0.3677 (4)	0.1567 (4)	0.2566 (15)	0.025 (1)
Cu2	0.1533 (5)	−0.0457 (4)	0.8512 (14)	0.029 (1)
Cu3	0.1735 (7)	−0.0268 (5)	0.1494 (14)	0.049 (2)
Cu4	0.3005 (5)	0.3005	0.0173 (17)	0.033 (2)
Cu5	0.3646 (5)	0.3646	0.4759 (15)	0.024 (2)
S1	0.4991 (7)	0.2573 (6)	0.8864 (16)	0.012 (2)
S2	−0.0001 (7)	−0.0001	0.6440 (18)	0.009 (2)
S3	0.2488 (7)	0.2488	0.6402 (17)	0.008 (2)
S4	0.3875 (6)	0.3875	0.251 (2)	0.019 (3)
S5	0.1357 (6)	0.1357	0.0	0.011 (2)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ge	0.005 (1)	0.005	0.018 (3)	0.003 (1)	0.001 (1)	0.001
Cu1	0.027 (2)	0.015 (1)	0.033 (3)	0.002 (2)	0.011 (2)	−0.001 (2)
Cu2	0.034 (2)	0.022 (2)	0.030 (3)	0.003 (2)	−0.003 (2)	−0.006 (2)
Cu3	0.091 (5)	0.024 (2)	0.032 (3)	0.019 (3)	−0.009 (3)	0.008 (2)
Cu4	0.023 (2)	0.023	0.054 (5)	0.009 (2)	0.012 (3)	0.012
Cu5	0.028 (2)	0.028	0.016 (4)	−0.012 (3)	0.005 (2)	0.005
S1	0.010 (3)	0.009 (3)	0.017 (5)	0.004 (3)	−0.002 (2)	−0.002 (2)
S2	0.008 (2)	0.008	0.013 (5)	−0.002 (3)	0.002 (3)	0.002
S3	0.006 (2)	0.006	0.013 (5)	0.002 (3)	−0.003 (3)	−0.003
S4	0.008 (2)	0.008	0.040 (8)	−0.002 (3)	−0.006 (3)	−0.006
S5	0.008 (2)	0.008	0.018 (6)	−0.007 (3)	0.000 (2)	0.000

Geometric parameters (Å, º)

Ge—S1^i	2.175 (7)	Cu3—S2^vi	2.345 (7)
Ge—S1^ii	2.175 (7)	Cu3—S5	2.219 (10)
Ge—S2	2.201 (11)	Cu4—S1^vii	2.396 (11)
Ge—S3	2.172 (10)	Cu4—S1^viii	2.396 (11)
S1^i—S1^ii	3.638 (12)	Cu4—S4	2.609 (19)
S2—S1^i	3.558 (12)	Cu4—S5	2.302 (11)
S2—S1^ii	3.558 (12)	Cu5—S2^ix	2.512 (15)
S3—S1^i	3.566 (12)	Cu5—S3	2.288 (15)
S3—S1^ii	3.566 (12)	Cu5—S4	2.238 (19)
S2—S3	3.468 (17)	Cu1—Cu2^ii	2.801 (7)
Cu1—S1^ii	2.363 (9)	Cu1—Cu3	2.837 (9)
Cu1—S3^ii	2.343 (8)	Cu1—Cu4	2.841 (9)
Cu1—S4	2.294 (8)	Cu2—Cu2^ix	2.804 (9)
Cu2—S1^iii	2.489 (9)	Cu2—Cu3^x	2.758 (7)
Cu2—S2	2.590 (13)	Cu2—Cu5^iv	2.702 (7)
Cu2—S4^iv	2.477 (9)	Cu3—Cu3^ix	2.823 (12)
Cu2—S5^v	2.329 (11)	Cu3—Cu5^ii	2.853 (9)
Cu3—S1^ii	2.469 (13)
S1—Ge—S1	113.5 (6)	S1—Ge—S3	108.8 (3)
S1—Ge—S3	110.2 (3)	S1—Ge—S1	105.0 (6)

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