Test of a theoretical equation of state for elemental solids and liquids

We propose a means for constructing highly accurate equations of state (EOS) for elemental solids and liquids essentially from first principles, based upon a particular decomposition of the underlying condensed matter Hamiltonian for the nuclei and electrons. We also point out that at low pressures the neglect of anharmonic and electron-phonon terms, both contained in this formalism, results in errors of less than 5% in the thermal parts of the thermodynamic functions. Then we explicitly display the forms of the remaining terms in the EOS, commenting on the use of experiment and electronic structure theory to evaluate them. We also construct an EOS for Aluminum and compare the resulting Hugoniot with data up to 5 Mbar, both to illustrate our method and to see whether the approximation of neglecting anharmonicity et al. remains viable to such high pressures. We find a level of agreement with experiment that is consistent with the low-pressure results.Comment: Minor revisions for consistency with published versio

Lattice Dynamics and the High Pressure Equation of State of Au

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 Gruneisen 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 ~200 GPa. Our result for the room temperature isotherm is in very good agreement with an earlier standard of Heinz and Jeanloz.Comment: 13 pages, 8 figures. Accepted by Phys. Rev.