Temperature dependence of dynamic dipole formation in PbTe

Abstract

PbTe-based thermoelectric materials remain of great interest due to their peculiar dynamic behavior and high thermoelectric performance. The true structure of pristine PbTe has been widely discussed, since the average rocksalt structure does not adequately account for the low lattice thermal conductivity. Single crystals of PbTe exhibit large amounts of x-ray diffuse scattering, which along with additional experimental observations has led to a series of structural models containing different types of disorder. Recently, analysis of the x-ray diffuse scattering from single-crystal PbTe confirmed the formation of local dynamic dipoles proposed earlier based on inelastic neutron scattering (INS) and one-dimensional pair distribution function (PDF) experiments. Here, we study the single-crystal diffuse x-ray scattering over a wider temperature range from 30 to 622 K in order to investigate the temperature dependence of the dynamic dipole formation. We observe that the longitudinal displacement correlations along the ⟨100⟩ directions form pairwise plateaus which results in a steplike decay of the correlations with increasing interatomic distance. This is consistent with previous observations from single-crystal diffuse scattering experiments on PbTe where the same steplike trend for the correlations was observed. However, upon lowering the temperature we observe a larger relative antiphase displacement contribution to the correlations proposed to originate from the softening of the transverse optical (TO) branch. As the local dipole formation depends on the absolute amplitude of antiphase displacements, and not the relative antiphase contribution to atomic displacements, it is found that the local dipole formation increases upon heating consistent with previous INS and PDF studies. The underlying mechanism responsible for the softening of the TO branch, and thereby the formation of dynamic dipoles, is investigated by comparison to the isostructural KCl system. The different dynamics in KCl and PbTe can be explained from the different bonding mechanism, where the metavalent bonding and ability to dynamically express a stereochemically active lone pair in PbTe gives rise to long-range interactions and TO phonon softening.