Quantitative validation of the Boltzmann transport equation phonon thermal conductivity model under the single-mode relaxation time approximation

The phonon thermal conductivity of the Lennard-Jones argon face-centered cubic crystal is predicted between temperatures of 20 K and 80 K using the Boltzmann transport equation under the single-mode relaxation time approximation. The temperature and frequency dependencies of the phonon dispersion and phonon relaxation times are obtained from lattice-dynamics calculations based on the results of molecular-dynamics simulations. No fitting parameters are required. The predicted thermal conductivities are in reasonable agreement with independent predictions made from the simulations using the Green-Kubo method. The assumption of an isotropic medium, as used in the Boltzmann transport equation formulation, leads to an overprediction of the Green-Kubo results at low temperatures. At higher temperatures, where anharmonic effects become increasingly important, the harmonic nature of the relaxation time calculation method leads to an underprediction of the Green-Kubo results. Assuming that the low-frequency behavior of the relaxation times can be extended over the entire frequency range, that there is no dispersion, or that the dispersion is independent of temperature, leads to significant errors in the predictions. This finding indicates that in analytical calculations, where such assumptions are often made, these errors are offset by the use of fitting parameters.