First (3 + 2)-dimensional superspace approach to the structure of levyclaudite-(Sb), a member of the cylindrite-type minerals

The structure of synthetic levyclaudite-(Sb), approximately (Pb_{1 − y}Sb_yS)_1.357[Sn_{1 − x}(Cu₂)_xS₂], has been determined by single-crystal X-ray diffraction on the basis of the (3 + 2)-dimensional superspace approach. This misfit-layer compound, of the cylindrite type, results from the combination of two heavily modulated triclinic Q and H subsystems with a common q wavevector and only one shared reciprocal axis (stacking direction). The Q pseudo-tetragonal layer, ∼(Pb_0.70Sb_0.30S), derived from the NaCl archetype, is positively charged; the H pseudo-hexagonal layer, ∼(Sn_0.85Cu_0.30S₂), derived from the CdI₂ archetype, is negatively charged, owing to the replacement of Sn⁴⁺ in an octahedral coordination by Cu⁺ pairs in an opposite triangular coordination. The analysis shows a strong transverse displacive modulation of the two layers, referred to as a `mondulation', correlated to a maximal Sb site occupation factor in the concavity of the Q layer undulation. The wavelength control of the `mondulation' obeys the vernier principle (14c_Q ≅ 13c_H), which would correspond to an energy minimization through a charge transfer density modulation wave, common to all two-dimensional misfit-layer inorganic compounds.

Computing details

Program(s) used to refine structure: (Jana2006; Petricek and Dusek, 2000); software used to prepare material for publication: (Jana2006; Petricek and Dusek, 2000).

Figures

(I)

Crystal data

Cu0.299Pb0.951S3.357Sb0.406Sn0.851	V = 275.72 (5) Å^3
Mr = 474.1	Z = 2
Triclinic, C1†	F(000) = 407
q1 = 0.00350a* + 0.15180b* + -0.01560c*; q2 = 0.63250a* + 1.07450b* + -0.44740c*‡	Dx = 5.709 Mg m^−3
a = 3.6733 (4) Å	Mo Kα radiation, λ = 0.71069 Å
b = 6.3120 (5) Å	µ = 37.04 mm^−1
c = 11.9039 (12) Å	T = 293 K
α = 92.484 (8)°	Platelet, black
β = 90.687 (9)°	0.3 × 0.2 × 0.0024 mm
γ = 89.941 (8)°

† Symmetry operations: (1) x₁, x₂, x₃, x₄, x₅; (2) −x₁, −x₂, −x₃, −x₄, −x₅; (3) 1/2+x₁, 1/2+x₂, x₃, x₄, x₅; (4) 1/2−x₁, 1/2−x₂, −x₃, −x₄, −x₅.

‡ ;

Data collection

Absorption correction: gaussian (Jana2006; Petricek, Dusek & Palatinus, 2006)	Rint = 0.100
Tmin = 0.039, Tmax = 0.912	θmax = 35.0°, θmin = 6.4°
99197 measured reflections	h = −5→5
29574 independent reflections	k = −12→12
0 reflections with I > 2.5σ(I)	l = −17→19

Refinement

Refinement on F	186 parameters
R[F^2 > 2σ(F^2)] = 0.074	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0004F^2)
wR(F^2) = 0.090	(Δ/σ)max = 0.001
S = 2.65	Δρmax = 3.34 e Å^−3
12026 reflections	Δρmin = −3.21 e Å^−3

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
Sn	0	0	0	0.01480 (12)	0.851 (2)
Cu	0.0029 (9)	0.0057 (5)	0.1147 (3)	0.0229 (11)	0.149 (2)
S1	0.5033 (2)	0.84278 (12)	0.12342 (7)	0.0177 (3)
Pb	0.05541 (5)	0.24113 (4)	0.36783 (2)	0.03573 (12)	0.701 (10)
Sb	0.055408	0.241132	0.367832	0.03573 (12)	0.299 (10)
S2	−0.0402 (3)	0.2583 (2)	0.59639 (13)	0.0310 (4)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Sn	0.0137 (2)	0.00983 (16)	0.0208 (3)	−0.00043 (12)	−0.00029 (14)	0.00055 (12)
Cu	0.0180 (16)	0.0138 (13)	0.037 (2)	−0.0009 (10)	−0.0004 (12)	0.0021 (11)
S1	0.0193 (4)	0.0133 (3)	0.0205 (5)	−0.0005 (3)	−0.0005 (3)	0.0008 (3)
Pb	0.0382 (2)	0.03020 (16)	0.0390 (2)	−0.00096 (11)	−0.00807 (14)	0.00192 (11)
Sb	0.0382 (2)	0.03020 (16)	0.0390 (2)	−0.00096 (11)	−0.00807 (14)	0.00192 (11)
S2	0.0395 (8)	0.0295 (6)	0.0237 (7)	−0.0002 (5)	−0.0052 (6)	0.0019 (5)