Lattice model calculations of elastic and thermodynamic properties at high pressure and temperature

Abstract

The elastic constants and the entire frequency spectrum have been calculated up to high pressure for the alkali halides in the NaCl lattice, based on an assumed functional form of the interatomic potential. The quasiharmonic approximation is used to calculate the vibrational contribution to the pressure and the elastic constants at arbitrary temperature. By explicitly accounting for the effect of thermal and zero point motion, the adjustable parameters in the potential are determined to a high degree of accuracy from the elastic constants and their pressure derivatives measured at zero pressure. The calculated Grüneisen parameter, the elastic constants and their pressure derivatives are in good agreement with experimental results up to about 600 K. The model predicts that for some alkali halides the Grüneisen parameter may decrease monotonically with pressure, while for others it may increase with pressure, after an initial decrease. In addition to giving good estimates of properties at high pressure and temperature, these calculations permit the estimation of the probable errors which arise from using less detailed theories. For pressures up to 0.5 K 0, which correspond to the lower mantle of the Earth and the deep interiors of the other terrestrial planets, simple linear extrapolation of the elastic constants with pressure leads to an error of less than 2% in the density and up to about 5% in the seismic velocities.