Crystal structure, cation ordering, and polytypic character of diaphorite, Pb₂Ag₃Sb₃S₈, a PbS-based structure

The crystal structure of diaphorite, Pb₂Ag₃Sb₃S₈, from hydrothermal veins at Příbram in central Bohemia (Czech Republic) was solved and refined from X-ray data of a crystal twinned by pseudo-merohedry. Diaphorite is monoclinic, space group P2₁/c, a = 17.852(4), b = 5.887(1), c = 15.809(3) Å and β = 116.17(3)°, Z = 4, ϱ = 6.06 g/cm³. The structure can be derived from the one of galena, PbS, by the substitution Ag⁺ + Sb³⁺ ↔ 2 Pb²⁺. In addition to eight S, three Sb, two Ag, and one Pb positions, the average structure exhibits also two mixed (Pb²⁺, Ag⁺) sites (M1, M2). The different coordination requirements for Pb²⁺ and Ag⁺ make a complete miscibility between these ions rather unlikely. The observed structure is a family or superposition structure and four possible, maximally Pb²⁺, Ag⁺ ordered structures can be derived with space-group symmetries (la): P1̄, (1b) and (2a): P2₁/n, and (2b): P2₁. The structures (1a) and (2b) have the same cell dimensions as the family structure whereas structures (1b) and (2a) have a doubled a periodicity compared to the family structure. In addition, each of the above space groups gives rise to two different configurational variants depending on the spatial relation of homoionic occupied M1 and M2 sites.