Analytical Models of Phonon–Point-Defect Scattering

Point defects exist widely in engineering materials and are known to scatter vibrational modes, resulting in reduction in thermal conductivity. The Klemens description of point-defect scattering is the most-prolific analytical model for this effect. This work reviews the essential physics of the model and compares its predictions with first-principles results for isotope and alloy scattering, demonstrating the model to be a useful metric of material design. A treatment of the scattering parameter ($\mathrm{\ensuremath{\Gamma}}$) for a multiatomic lattice is recommended and compared with other treatments presented in the literature, which have been at times misused to yield incomplete conclusions about the system's scattering mechanisms. Additionally, we demonstrate a reduced sensitivity of the model to the full phonon dispersion and discuss its origin. Finally, a simplified treatment of scattering in alloy systems with vacancies and interstitial defects is demonstrated to suitably describe the potent scattering strength of these off-stoichiometric defects.