Lattice dynamics and the high-pressure equation of state of Au

Abstract

Elastic constants and zone-boundary phonon frequencies of gold are calculated by total energy electronic structure methods to twofold compression. A generalized force constant model is used to interpolate throughout the Brillouin zone and evaluate moments of the phonon distribution. The moments are used to calculate the volume dependence of the Gr\"uneisen parameter in the fcc solid. Using these results with ultrasonic and shock data, we formulate the complete free energy for solid Au. This free energy is given as a set of closed-form expressions, which are valid to compressions of at least ${V/V}_{0}=0.65$ and temperatures up to melting. Beyond this density, the Hugoniot enters the solid-liquid mixed phase region. Effects of shock melting on the Hugoniot are discussed within an approximate model. We compare with proposed standards for the equation of state to pressures of $\ensuremath{\sim}200\mathrm{GPa}.$ Our result for the room-temperature isotherm is in very good agreement with an earlier standard of Heinz and Jeanloz.