Importance of Four-Phonon Scattering at High Temperatures or for Strongly Anharmonic Materials

Tianli Feng, Xiulin Ruan

Published 2015-10-02Version 1

Despite its great success, the recent first principle-based prediction of lattice thermal conductivity $\kappa$ typically only includes three-phonon scattering due to the challenge of evaluating the scattering rates of higher-order processes, and hence its accuracy is limited to relatively low temperatures. In this work, however, we have developed a formalism to explicitly determine quantum mechanical scattering probability matrices for the full Brillouin Zone, and by mitigating the computational cost we have directly calculated four-phonon scattering rates. We find that four-phonon scattering rates are comparable to three-phonon scattering rates at medium and high temperatures, and they increase quadratically with temperature. As a consequence, $\kappa$ of Lennard-Jones argon is reduced by more than 60\% at 80 K when four-phonon scattering is included. Also, in less anharmonic materials -- diamond, silicon, and germanium, $\kappa$ is still reduced considerably at high temperature.