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The structure of synthetic levyclaudite-(Sb), approximately (Pb1 − ySbyS)1.357[Sn1 − 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, ∼(Pb0.70Sb0.30S), derived from the NaCl archetype, is positively charged; the H pseudo-hexagonal layer, ∼(Sn0.85Cu0.30S2), 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 (14cQ ≅ 13cH), which would correspond to an energy minimization through a charge transfer density modulation wave, common to all two-dimensional misfit-layer inorganic compounds.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S010876810602547X/ck5020sup1.cif
Contains datablocks global, I

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S010876810602547X/ck5020sup2.hkl
Supplementary material

Computing details top

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

Figures top
[Figure 1]
[Figure 2]
[Figure 3]
[Figure 4]
[Figure 5]
[Figure 6]
[Figure 7]
[Figure 8]
[Figure 9]
(I) top
Crystal data top
Cu0.299Pb0.951S3.357Sb0.406Sn0.851V = 275.72 (5) Å3
Mr = 474.1Z = 2
Triclinic, C1F(000) = 407
q1 = 0.00350a* + 0.15180b* + -0.01560c*; q2 = 0.63250a* + 1.07450b* + -0.44740c*‡Dx = 5.709 Mg m3
a = 3.6733 (4) ÅMo Kα radiation, λ = 0.71069 Å
b = 6.3120 (5) ŵ = 37.04 mm1
c = 11.9039 (12) ÅT = 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.

texobject1427796013.png; texobject1427796014.png

Data collection top
Absorption correction: gaussian
(Jana2006; Petricek, Dusek & Palatinus, 2006)
Rint = 0.100
Tmin = 0.039, Tmax = 0.912θmax = 35.0°, θmin = 6.4°
99197 measured reflectionsh = 55
29574 independent reflectionsk = 1212
0 reflections with I > 2.5σ(I)l = 1719
Refinement top
Refinement on F186 parameters
R[F2 > 2σ(F2)] = 0.074Weighting scheme based on measured s.u.'s w = 1/(σ2(F) + 0.0004F2)
wR(F2) = 0.090(Δ/σ)max = 0.001
S = 2.65Δρmax = 3.34 e Å3
12026 reflectionsΔρmin = 3.21 e Å3
Crystal data top
Cu0.299Pb0.951S3.357Sb0.406Sn0.851β = 90.687 (9)°
Mr = 474.1γ = 89.941 (8)°
Triclinic, C1V = 275.72 (5) Å3
q1 = 0.00350a* + 0.15180b* + -0.01560c*; q2 = 0.63250a* + 1.07450b* + -0.44740c*‡Z = 2
a = 3.6733 (4) ÅMo Kα radiation
b = 6.3120 (5) ŵ = 37.04 mm1
c = 11.9039 (12) ÅT = 293 K
α = 92.484 (8)°0.3 × 0.2 × 0.0024 mm
† 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.

texobject1427796015.png; texobject1427796016.png

Data collection top
Absorption correction: gaussian
(Jana2006; Petricek, Dusek & Palatinus, 2006)
29574 independent reflections
Tmin = 0.039, Tmax = 0.9120 reflections with I > 2.5σ(I)
99197 measured reflectionsRint = 0.100
Refinement top
R[F2 > 2σ(F2)] = 0.074186 parameters
wR(F2) = 0.090Δρmax = 3.34 e Å3
S = 2.65Δρmin = 3.21 e Å3
12026 reflections
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/UeqOcc. (<1)
Sn0000.01480 (12)0.851 (2)
Cu0.0029 (9)0.0057 (5)0.1147 (3)0.0229 (11)0.149 (2)
S10.5033 (2)0.84278 (12)0.12342 (7)0.0177 (3)
Pb0.05541 (5)0.24113 (4)0.36783 (2)0.03573 (12)0.701 (10)
Sb0.0554080.2411320.3678320.03573 (12)0.299 (10)
S20.0402 (3)0.2583 (2)0.59639 (13)0.0310 (4)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Sn0.0137 (2)0.00983 (16)0.0208 (3)0.00043 (12)0.00029 (14)0.00055 (12)
Cu0.0180 (16)0.0138 (13)0.037 (2)0.0009 (10)0.0004 (12)0.0021 (11)
S10.0193 (4)0.0133 (3)0.0205 (5)0.0005 (3)0.0005 (3)0.0008 (3)
Pb0.0382 (2)0.03020 (16)0.0390 (2)0.00096 (11)0.00807 (14)0.00192 (11)
Sb0.0382 (2)0.03020 (16)0.0390 (2)0.00096 (11)0.00807 (14)0.00192 (11)
S20.0395 (8)0.0295 (6)0.0237 (7)0.0002 (5)0.0052 (6)0.0019 (5)

Experimental details

Crystal data
Chemical formulaCu0.299Pb0.951S3.357Sb0.406Sn0.851
Mr474.1
Crystal system, space groupTriclinic, C1
Temperature (K)293
Wave vectorsq1 = 0.00350a* + 0.15180b* + -0.01560c*; q2 = 0.63250a* + 1.07450b* + -0.44740c*‡
a, b, c (Å)3.6733 (4), 6.3120 (5), 11.9039 (12)
α, β, γ (°)92.484 (8), 90.687 (9), 89.941 (8)
V3)275.72 (5)
Z2
Radiation typeMo Kα
µ (mm1)37.04
Crystal size (mm)0.3 × 0.2 × 0.0024
Data collection
Diffractometer?
Absorption correctionGaussian
(Jana2006; Petricek, Dusek & Palatinus, 2006)
Tmin, Tmax0.039, 0.912
No. of measured, independent and
observed [I > 2.5σ(I)] reflections
99197, 29574, 0
Rint0.100
(sin θ/λ)max1)0.807
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.074, 0.090, 2.65
No. of reflections12026
No. of parameters186
No. of restraints?
Δρmax, Δρmin (e Å3)3.34, 3.21

† 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.

texobject1427796017.png; texobject1427796018.png

Computer programs: (Jana2006; Petricek and Dusek, 2000).

 

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