Ab initio crystal structures and relative phase stabilities for the aleksite series, Pb _n Bi₄Te₄S _n+2

Density functional theory methods are applied to crystal structures and stabilities of phases from the aleksite homologous series, Pb n Bi 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 Pb 6 Bi 4 Te 4 S 8 ), 8 (unnamed Pb 8 Bi 4 Te 4 S 10 ), 10 (hitachiite) and 12 (unnamed Pb 12 Bi 4 Te 4 S 14 ). 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 ( M p X p +1 )· L ( M p +1 X p +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 = γ · c sub *, 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 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 (Pb 398 Bi 4 Te 4 S 400 ), a phase with d sub (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.