Evaluation of computational techniques for solving the Boltzmann transport equation for lattice thermal conductivity calculations

Abstract

Three methods for computing thermal conductivity from lattice dynamics (the iterative method, the variational method, and the relaxation-time approximation) are compared for the prototypical case of solid argon. The iterative method is found to produce results in close agreement with Green-Kubo molecular-dynamics simulations, a formally correct method for computing thermal conductivity. The variational method and relaxation-time approximation are found to underestimate the thermal conductivity. The relationship among the methods is established; a combination of the iterative and variational methods is found to have a fastest convergence. Formal convergence of the iterative method is demonstrated and a simple mixing rule is shown to provide stability in practice. The ability to use these methods to provide detailed insight into the relationship between phonon properties and thermal conductivity is demonstrated.