Accurate X-ray diffraction data required for proper evaluation of bond valence sums and global instability indexes: redetermination of the crystal structures of diamond-like Cu₂CdSiS₄ and Cu₂HgSnS₄ as a case study

Our calculations of the global instability index (G) values for some diamond-like materials with the general formula I₂–II–IV–VI₄ have indicated that the structures may be unstable or incorrectly determined. To com­pute the G value of a given com­pound, the bond valence sums (BVSs) must first be calculated using a crystal structure. Two examples of com­pounds with high G values, based on data from the literature, are the wurtz–stannite-type dicopper cadmium silicon tetra­sulfide (Cu₂CdSiS₄) and the stannite-type dicopper mercury tin tetra­sulfide (Cu₂HgSnS₄), which were first reported in 1967 and 1965, respectively. In the present study, Cu₂CdSiS₄ and Cu₂HgSnS₄ were prepared by solid-state synthesis at 1000 and 900 °C, respectively. The phase purity was assessed by powder X-ray diffraction. Optical diffuse reflectance UV/Vis/NIR spectroscopy was used to estimate the optical bandgaps of 2.52 and 0.83 eV for Cu₂CdSiS₄ and Cu₂HgSnS₄, respectively. The structures were solved and refined using single-crystal X-ray diffraction data. The structure type of Cu₂CdSiS₄ was confirmed, where Cd²⁺, Si⁴⁺ and two of the three crystallographically unique S²⁻ ions lie on a mirror plane. The structure type of Cu₂HgSnS₄ was also verified, where all ions lie on special positions. The S²⁻ ion resides on a mirror plane, the Cu⁺ ion is situated on a fourfold rotary inversion axis and both the Hg²⁺ and the Sn⁴⁺ ions are located on the inter­section of a fourfold rotary inversion axis, a mirror plane and a twofold rotation axis. Using the crystal structures solved and refined here, the G values were reassessed and found to be in the range that indicates reasonable strain for a stable crystal structure. This work, together with some examples gathered from the literature, shows that accurate data collected on modern instrumentation should be used to reliably calculate BVSs and G values.

Computing details

For both structures, data collection: SMART (Bruker, 2001); cell refinement: SAINT (Bruker, 2018); data reduction: SAINT (Bruker, 2018). Program(s) used to solve structure: SHELXT2018 (Sheldrick, 2015a) for Cu2CdSiS4; SHELXL2014 (Sheldrick, 2015a) for Cu2HgSnS4. For both structures, program(s) used to refine structure: SHELXL2018 (Sheldrick, 2015b); molecular graphics: ShelXle (Hübschle et al., 2011); software used to prepare material for publication: SHELXL2018 (Sheldrick, 2015b).

Copper cadmium silicon sulfide (Cu2CdSiS4)

Crystal data

Cu2CdSiS4	Dx = 4.266 Mg m^−3
Mr = 395.81	Mo Kα radiation, λ = 0.71073 Å
Orthorhombic, Pmn21	Cell parameters from 5413 reflections
a = 7.60853 (11) Å	θ = 3.1–32.8°
b = 6.48071 (9) Å	µ = 11.67 mm^−1
c = 6.24923 (10) Å	T = 296 K
V = 308.14 (1) Å^3	Polyhedra, green-yellow
Z = 2	0.25 × 0.14 × 0.09 mm
F(000) = 368

Data collection

Bruker SMART APEXII diffractometer	719 reflections with I > 2σ(I)
Radiation source: fine focus sealed tube X-ray source	Rint = 0.033
φ and ω Scans scans	θmax = 27.5°, θmin = 3.1°
Absorption correction: multi-scan (SADABS; Sheldrick, 2002)	h = −9→9
Tmin = 0.357, Tmax = 0.747	k = −8→8
3842 measured reflections	l = −8→8
723 independent reflections

Refinement

Refinement on F^2	w = 1/[σ^2(Fo^2) + (0.0249P)^2 + 0.0278P] where P = (Fo^2 + 2Fc^2)/3
Least-squares matrix: full	(Δ/σ)max = 0.001
R[F^2 > 2σ(F^2)] = 0.022	Δρmax = 1.33 e Å^−3
wR(F^2) = 0.047	Δρmin = −2.26 e Å^−3
S = 1.27	Extinction correction: SHELXL2018 (Sheldrick, 2015<>i>b), Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
723 reflections	Extinction coefficient: 0.446 (15)
44 parameters	Absolute structure: Flack x determined using 305 quotients [(I+)-(I-)]/[(I+)+(I-)] (Parsons et al., 2013)
1 restraint	Absolute structure parameter: 0.006 (10)
Primary atom site location: structure-invariant direct methods

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
Cd1	0.000000	0.34757 (5)	0.87283 (5)	0.0154 (2)
Cu1	0.24779 (7)	0.17667 (7)	0.36705 (17)	0.0187 (2)
Si1	0.000000	0.68042 (19)	0.3742 (6)	0.0077 (3)
S1	0.000000	0.3642 (2)	0.4680 (3)	0.0107 (4)
S2	0.000000	0.7045 (2)	0.0337 (3)	0.0102 (3)
S3	0.27593 (17)	0.16155 (17)	0.9983 (2)	0.0100 (3)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Cd1	0.0156 (3)	0.0145 (3)	0.0162 (3)	0.000	0.000	−0.0003 (2)
Cu1	0.0194 (3)	0.0180 (3)	0.0188 (4)	−0.00103 (18)	−0.0009 (3)	−0.0003 (3)
Si1	0.0083 (7)	0.0059 (6)	0.0090 (9)	0.000	0.000	0.0002 (7)
S1	0.0128 (7)	0.0063 (6)	0.0130 (8)	0.000	0.000	0.0004 (5)
S2	0.0113 (6)	0.0110 (7)	0.0084 (7)	0.000	0.000	0.0013 (6)
S3	0.0106 (4)	0.0087 (5)	0.0107 (6)	−0.0019 (3)	0.0013 (4)	0.0005 (3)

Geometric parameters (Å, º)

Cd1—S2^i	2.5223 (18)	Cu1—S1	2.3301 (11)
Cd1—S1	2.5320 (18)	Cu1—S3^v	2.3473 (16)
Cd1—S3	2.5448 (13)	Si1—S1	2.132 (2)
Cd1—S3^ii	2.5448 (13)	Si1—S2	2.134 (5)
Cu1—S2^iii	2.3152 (13)	Si1—S3^vi	2.135 (2)
Cu1—S3^iv	2.316 (2)	Si1—S3^vii	2.135 (2)
S2^i—Cd1—S1	111.06 (5)	Si1—S1—Cu1	115.27 (9)
S2^i—Cd1—S3	108.16 (4)	Si1—S1—Cu1^ii	115.27 (9)
S1—Cd1—S3	109.15 (4)	Cu1—S1—Cu1^ii	108.02 (7)
S2^i—Cd1—S3^ii	108.16 (4)	Si1—S1—Cd1	108.39 (12)
S1—Cd1—S3^ii	109.15 (4)	Cu1—S1—Cd1	104.38 (6)
S3—Cd1—S3^ii	111.17 (5)	Cu1^ii—S1—Cd1	104.38 (6)
S2^iii—Cu1—S3^iv	112.65 (7)	Si1—S2—Cu1^vii	118.23 (8)
S2^iii—Cu1—S1	112.05 (6)	Si1—S2—Cu1^vi	118.23 (8)
S3^iv—Cu1—S1	111.49 (7)	Cu1^vii—S2—Cu1^vi	111.96 (10)
S2^iii—Cu1—S3^v	102.54 (8)	Si1—S2—Cd1^iv	109.30 (7)
S3^iv—Cu1—S3^v	108.38 (6)	Cu1^vii—S2—Cd1^iv	97.22 (7)
S1—Cu1—S3^v	109.27 (6)	Cu1^vi—S2—Cd1^iv	97.22 (7)
S1—Si1—S2	110.15 (15)	Si1^iii—S3—Cu1^i	114.51 (13)
S1—Si1—S3^vi	111.19 (13)	Si1^iii—S3—Cu1^viii	112.49 (11)
S2—Si1—S3^vi	109.10 (11)	Cu1^i—S3—Cu1^viii	112.34 (6)
S1—Si1—S3^vii	111.19 (13)	Si1^iii—S3—Cd1	108.64 (7)
S2—Si1—S3^vii	109.10 (11)	Cu1^i—S3—Cd1	102.14 (5)
S3^vi—Si1—S3^vii	106.00 (13)	Cu1^viii—S3—Cd1	105.74 (6)

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

Copper mercury tin sulfide (Cu2HgSnS4)

Crystal data

Cu2HgSnS4	Dx = 5.644 Mg m^−3
Mr = 574.60	Mo Kα radiation, λ = 0.71073 Å
Tetragonal, I42m	Cell parameters from 1625 reflections
a = 5.5798 (12) Å	θ = 3.8–27.3°
c = 10.860 (3) Å	µ = 33.60 mm^−1
V = 338.11 (17) Å^3	T = 296 K
Z = 2	Prism, black
F(000) = 504	0.14 × 0.13 × 0.08 mm

Data collection

Bruker SMART APEXII CCD diffractometer	218 reflections with I > 2σ(I)
Radiation source: fine focus sealed tube X-ray source	Rint = 0.040
φ and ω scans	θmax = 27.3°, θmin = 3.8°
Absorption correction: multi-scan (SADABS; Sheldrick, 2002)	h = −7→7
Tmin = 0.352, Tmax = 0.746	k = −7→7
2088 measured reflections	l = −13→14
218 independent reflections

Refinement

Refinement on F^2	Secondary atom site location: difference Fourier map
Least-squares matrix: full	w = 1/[σ^2(Fo^2) + (0.0124P)^2] where P = (Fo^2 + 2Fc^2)/3
R[F^2 > 2σ(F^2)] = 0.014	(Δ/σ)max < 0.001
wR(F^2) = 0.032	Δρmax = 0.53 e Å^−3
S = 1.08	Δρmin = −0.85 e Å^−3
218 reflections	Extinction correction: SHELXL2018 (Sheldrick, 2015b), Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
14 parameters	Extinction coefficient: 0.0232 (10)
0 restraints	Absolute structure: Flack x determined using 76 quotients [(I+)-(I-)]/[(I+)+(I-)] (Parsons et al., 2013)
Primary atom site location: structure-invariant direct methods	Absolute structure parameter: 0.021 (11)

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
Hg1	0.500000	0.500000	0.500000	0.0195 (2)
Sn1	0.000000	0.000000	0.500000	0.00651 (19)
Cu1	0.500000	0.000000	0.250000	0.0181 (3)
S1	0.24020 (16)	0.24020 (16)	0.36322 (16)	0.0093 (4)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Hg1	0.0186 (2)	0.0186 (2)	0.0214 (3)	0.000	0.000	0.000
Sn1	0.0064 (2)	0.0064 (2)	0.0067 (3)	0.000	0.000	0.000
Cu1	0.0172 (4)	0.0172 (4)	0.0200 (6)	0.000	0.000	0.000
S1	0.0094 (6)	0.0094 (6)	0.0092 (8)	−0.0003 (6)	0.0014 (3)	0.0014 (3)

Geometric parameters (Å, º)

Hg1—S1^i	2.5317 (17)	Sn1—S1^vi	2.4081 (14)
Hg1—S1^ii	2.5317 (17)	Sn1—S1	2.4081 (14)
Hg1—S1^iii	2.5317 (17)	Cu1—S1	2.3258 (10)
Hg1—S1	2.5317 (17)	Cu1—S1^vii	2.3258 (10)
Sn1—S1^iv	2.4081 (14)	Cu1—S1^viii	2.3258 (10)
Sn1—S1^v	2.4081 (14)	Cu1—S1^ix	2.3258 (10)
S1^i—Hg1—S1^ii	108.15 (7)	S1—Cu1—S1^vii	106.23 (4)
S1^i—Hg1—S1^iii	110.14 (4)	S1—Cu1—S1^viii	106.23 (4)
S1^ii—Hg1—S1^iii	110.14 (4)	S1^vii—Cu1—S1^viii	116.17 (8)
S1^i—Hg1—S1	110.14 (4)	S1—Cu1—S1^ix	116.17 (8)
S1^ii—Hg1—S1	110.14 (4)	S1^vii—Cu1—S1^ix	106.23 (4)
S1^iii—Hg1—S1	108.15 (7)	S1^viii—Cu1—S1^ix	106.23 (4)
S1^iv—Sn1—S1^v	112.36 (4)	Cu1—S1—Cu1^x	116.03 (8)
S1^iv—Sn1—S1^vi	112.36 (4)	Cu1—S1—Sn1	110.63 (3)
S1^v—Sn1—S1^vi	103.83 (8)	Cu1^x—S1—Sn1	110.63 (3)
S1^iv—Sn1—S1	103.83 (8)	Cu1—S1—Hg1	106.45 (4)
S1^v—Sn1—S1	112.36 (4)	Cu1^x—S1—Hg1	106.45 (4)
S1^vi—Sn1—S1	112.36 (4)	Sn1—S1—Hg1	105.99 (7)

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