Nprocesses, the relaxation-time approximation, and lattice thermal conductivity

Abstract

The two-fluid theory of phonon transport and thermal conductivity recently proposed by the author is refined, with the major source of error identified as the previous neglect of the subset of normal processes called NN processes. A correction is provided for these processes, which are mainly those of phonon splitting. This correction, based on the Callaway approximation, utilizes two shift parameters in the displaced Planck distribution, one for low-frequency modes and one for high-frequency modes. Comparison with experiment is performed on a group of LiF specimens of varying isotopic purity. The results demonstrate that the refined theory explains the behavior of the thermal conductivity across the region of peak value with high accuracy for the purer specimens. The role of the single-mode relaxation-time approximation is clarified as well as the significance of the linearly-frequency-dependent Landau-Rumer transition rate which tends to dominate the thermal-conductivity calculation. As in the earlier treatment, no explicit account of U processes is required. They are included implicitly in the Landau-Rumer rate along with NR processes, which are N processes ending in reservoir modes. The new formulation, dependent only on known transition-rate expressions, appears to provide a framework for systematic approximation to the Peierls-Boltzmann integral equation.