Ab initio crystal structures and relative phase stabilities for the aleksite series, PbBiTeS.

Density functional theory methods are applied to crystal structures and stabilities of phases from the aleksite homologous series, PbBiTeS (n = homologue number). The seven phases investigated correspond to n = 0 (tetradymite), 2 (aleksite-21R and -42R), 4 (saddlebackite-9H and -18H), 6 (unnamed PbBiTeS), 8 (unnamed PbBiTeS), 10 (hitachiite) and 12 (unnamed PbBiTeS). These seven phases correspond to nine single- or double-module structures, each comprising an odd number of atom layers, 5, 7, (5.9), 9, (7.11), 11, 13, 15 and 17, expressed by the formula: S(MX)·L(MX), where M = Pb, Bi and X = Te, S, p ≥ 2, and S and L = number of short and long modules, respectively. Relaxed structures show a and c values within 1.5% of experimental data; a and the interlayer distance d decrease with increasing PbS content. Variable Pb-S bond lengths contrast with constant Pb-S bond lengths in galena. All phases are n-fold superstructures of a rhombohedral subcell with c/3 = d*. Electron diffraction patterns show two brightest reflections at the centre of d*, described by the modulation vector q = (i/N) · d*, i = S + L. A second modulation vector, q = γ · c*, shows a decrease in γ, from 1.8 to 1.588, across the n = 0 to n = 12 interval. The linear relationship between γ and d allows the prediction of any theoretical phases beyond the studied compositional range. The upper PbS-rich limit of the series is postulated as n = 398 (PbBiTeS), a phase with d (1.726 Å) identical to that of trigonal PbS within experimental error. The aleksite series is a prime example of mixed layer compounds built with accretional homology principles.