Molecular dynamical calculations of energy transport in crystalline solids

Abstract

Thermal conductivity (diffusivity), heat pulse propagation, and shock wave propagation in one-, two, and three-dimensional lattices have been studied by the method of molecular dynamics, a method well suited to non-equilibrium and strongly anharmonic problems. In this review, particular attention has been paid to the approach to thermal equilibrium after a disturbance. In one dimension, it is shown that energy sharing between modes of vibration is difficult, therefore it is doubtful that the soliton concept is a useful one in non-linear problems where thermal relaxation is involved. In two and three dimensions, energy sharing occurs readily. Under appropriate conditions heat flow occurs by diffusion and a temperature gradient is set up. The computed value of lattice thermal conductivity is in agreement with experiment. In pulsed heating, the coupling between the thermal and elastic disturbances generates a composite second sound wave which leads to a simple explanation of the temperature dependent second sound velocity observed experimentally. In shock compression, the thermal relaxation behind the shock front causes the shock profile to be non-steady overall, in contradiction to the steady profile assumed in the usual Hugoniot relations for a continuum. The PVT relationship deduced from shock wave data are affected to a significant extent at high compressions.