Anharmonicity and correlated dynamics of PbTe and PbS studied by single crystal x-ray scattering

The lead chalcogenides with rocksalt structure, $\mathrm{Pb}X$ ($X$ = S, Se, Te), show great promise for thermoelectric applications in various doped and alloyed forms. Part of the explanation for this is their favorable low lattice thermal conductivities whose origin has been heavily debated. Powder x-ray diffraction experiments suggested Pb to be off-centered particularly in PbS. However, as shown here, single crystal x-ray diffraction shows the anharmonicity to be insignificant in PbS from 20 to 300 K, while it is significant from 100 to 622 K in PbTe although without leading to any Pb off-centering. Inelastic neutron scattering and anharmonic ab initio studies previously suggested the soft transverse optical mode to play an important role with respect to lowering the thermal conductivities of the lead chalcogenides. Here, the diffuse x-ray scattering of single crystal PbS is modeled from 20 to 300 K by correlated atomic displacements. The results indicate softening of the zone center transverse optical mode with decreasing temperature. From a chemical bonding perspective, the soft transverse optical mode can be rationalized by invoking the concepts of stereoactive lone pair formation and metavalent/resonant bonding.