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

Abstract

The structure of synthetic levyclaudite-(Sb), approximately (Pb1 − y Sb y S)1.357[Sn1 − x (Cu2) x S2], 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.