We investigate the harmonic and anharmonic contributions to the phonon spectrum of lead telluride, and perform a complete characterization of how the anharmonic effects dominate the phonons in PbTe as temperature increases. This effect is the strongest factor in the favorable thermoelectric properties of PbTe: an optical-acoustic phonon band crossing reduces the speed of sound and the intrinsic thermal conductivity. We present the detailed temperature dependence of the dispersion relation and compare our calculated neutron scattering cross section with recent experimental measurements. We analyze the thermal resistivitys variation with temperature and clarify misconceptions about existing experimental literature. This quantitative prediction opens the way to phonon phase space engineering, to tailor the lifetimes of crucial heat carrying phonons.
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