Direct evidence of cation disorder in thermoelectric lead chalcogenides PbTe and PbS

The extraordinary thermoelectric properties of lead chalcogenides have attracted huge interest in part due to their unexpected low thermal conductivity. Here, it is shown that anharmonicity and large cation disorder are present in both PbTe and PbS, based on elaborate charge density visualization using synchrotron powder X-ray diffraction (SPXRD) data analyzed with the maximum entropy method (MEM). In both systems, the cation disorder increases with increasing temperature, whereas the Te/S anions appear to be centered on the expected lattice positions. Even at the lowest temperatures of 105 K, the lead ion is on average displaced by ≈0.2 Å from the rock-salt lattice position, creating a strong phonon scattering mechanism. These findings provide a clue to understanding the excellent thermoelectric performance of crystals with atomic disorder. The SPXRD-MEM approach can be applied in general opening up for widespread characterization of subtle structural features in crystals with unusual properties.