Analytical Models of Phonon-Point Defect Scattering

TL;DR

This paper reviews and refines the Klemens model for phonon-point defect scattering, comparing it with first principles results and proposing improvements for materials design and defect treatment.

Contribution

It provides a comprehensive review of the Klemens model, introduces a new treatment for the scattering parameter in multiatomic lattices, and simplifies defect scattering modeling in alloys.

Findings

The Klemens model aligns well with first principles results for isotope and alloy scattering.

A new treatment of the scattering parameter improves model accuracy for multiatomic systems.

Simplified models effectively describe scattering from vacancies and interstitial defects.

Abstract

Point defects exist widely in engineering materials and are known to scatter vibrational modes to reduce 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 to first principles results for isotope and alloy scattering, demonstrating the model as a useful materials design metric. A treatment of the scattering parameter ($\Gamma$) for a multiatomic lattice is recommended and compared to other treatments presented in 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.