Monte Carlo simulation of phonon transport in UO2 single crystals

Abstract

The Monte Carlo (MC) method is applied to solve the Boltzmann transport equation for phonons in uranium dioxide single crystals, with the objective of understanding thermal transport in this material at the mesoscale. The overall solution scheme tracks the phonon density as it evolves in space and time due to phonon drift and phonon–phonon scattering by normal and Umklapp processes. Unlike most previous works on solving the Boltzmann transport equation for phonons by the MC technique, our scheme for calculating phonon lifetime, based on normal and Umklapp scattering, eliminates the need for using many fitting parameters. Instead, the Grüneisen parameter, which is a well-characterized material property, is the only parameter of the problem. The results elucidate the simulation domain size over which the computed conductivity is size dependent; this helps to determine the minimum domain size required to simulate bulk thermal transport and hence calculate the thermal conductivity. The latter is computed over the temperature range 300–1000 K. The computed conductivity values are in good agreement with the previously published experimental and molecular dynamics simulation results.