Computer Simulation of the Lattice Dynamics of Solids

Neutron-diffraction data on dispersion curves for the rare-gas solids has emphasized the need for an anharmonic treatment of lattice dynamics. The molecular-dynamic technique is a powerful way of examining the temperature and volume dependence of phonon properties, since anharmonicity is treated without approximation. Using a Lennard-Jones potential, classical calculations have been made, at different temperatures and volumes, of average phonon properties such as pressure and energy, correlations in velocity and position, frequency distribution of normal modes, and phonon-dispersion curves. The volume dependence of the frequency was used to test the Gruneisen approximation. The magnitude of fluctuations in temperature and in the various correlations were compared with theory. These calculations predict relatively large shifts in frequency at constant volume as the temperature is raised in the regime where the classical approximation is valid.