Structural disorder, anisotropic micro-strain and cation vacancies in thermo-electric lead chalcogenides

Thermoelectric materials can interconvert heat and electricity, and the extraordinary thermoelectric properties of lead chalcogenides (PbX, X = S, Se, Te) attract immense scientific interest. A key topic is the role of the cation in reaching a very low thermal conductivity necessary for efficient energy conversion. Here we present new structural insights about the deceptively simple rock-salt lead chalcogenides through a comparative multi-temperature synchrotron powder X-ray diffraction study. For the first time, the presence of anisotropic microstrain broadening as well as lead vacancies are quantified for all three compounds. The microstrain implies extended breakage of cubic symmetry as a sign of the incipient ferroelectric nature of PbX. The degree of microstrain is correlated to the transition pressure of a symmetry reducing phase transition, and this trend can be explained by anion mediated s-p hybridization on lead. The observed number of vacancies is greatest for PbS (4-8%), but two samples of PbS show different cation occupancy, and thus sample-dependent vacancies might be the property that unifies conflicting results reported for PbX. Gram-Charlier analysis identifies a local non-spherical distribution of Pb; however, model unbiased maximum entropy analysis indicates that any static displacement of Pb, if present, is less than 0.2 Å at 100 K.