The thermal conductivity of the Lennard-Jones argon crystal is predicted using the Boltzmann transport equation under the single mode relaxation time approximation. The temperature and frequency dependence 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 thermal conductivity results are in agreement with predictions from the simulations using the Green-Kubo method. Assuming that the dispersion is linear or temperature independent, as is often done in analytical calculations, leads to large errors in the predictions. This result suggests that the fitting parameters required in such calculations offset significant errors introduced by these simplifying assumptions.

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