Improved Callaway model for Lattice Thermal Conductivity

TL;DR

This paper refines the Callaway model for lattice thermal conductivity, addressing its limitations in accounting for Normal processes, thereby enhancing the accuracy of thermal conductivity calculations in perfect crystals.

Contribution

It clarifies and improves the Callaway model, specifically correcting the underestimation of Normal process suppression in thermal current relaxation.

Findings

Callaway model underestimates N-process suppression

Improved model enhances thermal conductivity predictions

Provides better framework for relaxation-time studies

Abstract

In developing the phonon quasiparticle picture, Peierls discovered that, in a perfect crystal, without Umklapp (U) events, a current-carrying distribution can never relax to a zero-current distribution. Callaway introduced a simplified approximate model version of the Peierls-Boltzmann equation, retaining its the ability to deal separately with Normal (N) and U events. This paper clarifies and improves the Callaway model, and shows that Callaway underestimated the suppression of N-processes in relaxing thermal current. The new result should improve computations of thermal conductivity from relaxation-time studies.