Ab initio crystal structures and relative phase stabilities for the aleksite series, Pb_nBi₄Te₄S_n+2

Density functional theory methods are applied to crystal structures and stabilities of phases from the aleksite homologous series, PbnBi(4)Te(4)S(n+2) (n = homologue number). The seven phases investigated correspond to n = 0 (tetradymite), 2 (aleksite-21R and -42R), 4 (saddlebackite-9H and -18H), 6 (unnamed Pb6Bi4Te4S8), 8 (unnamed Pb8Bi4Te4S10), 10 (hitachiite) and 12 (unnamed Pb12Bi4Te4S14). 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(MpXp+1).L(Mp+1Xp+2), 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(sub) 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(sub)*. Electron diffraction patterns show two brightest reflections at the centre of d(sub)*, described by the modulation vector q(F) = (i/N) . d(sub)*, i = S + L. A second modulation vector, q = gamma . c(sub)*, shows a decrease in gamma, from 1.8 to 1.588, across the n = 0 to n = 12 interval. The linear relationship between gamma and d(sub) 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 (Pb398Bi4Te4S400-), a phase with d(sub) (1.726 angstrom) 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.