Lattice thermal conductivity: A comparison of molecular dynamics and anharmonic lattice dynamics

The thermal conductivity of a monatomic face-centered-cubic lattice has been calculated over a range of temperatures from one-twentieth to one-half the melting temperature. An inverse-twelfth-power ``soft-sphere'' potential was used to represent the interatomic forces. We have examined, quantitatively, the approximations involved in deriving the Peierls phonon-transport expression for the thermal conductivity and have determined the temperature range over which it is useful. This has involved extensive comparisons with the formally exact Green-Kubo method, using molecular dynamics to generate the phase-space trajectories. At low temperatures, the relaxation processes in a crystal can be described in terms of phonon lifetimes. We have calculated the lifetimes of all the phonon states of 108-, 256-, and 864-particle classical crystals, with periodic boundaries, by molecular dynamics and by anharmonic perturbation theory. These lifetimes were then used to estimate the thermal conductivity.