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

TL;DR

This paper introduces a first-principles method for constructing highly accurate equations of state for elemental solids and liquids, demonstrating its effectiveness through an aluminum Hugoniot comparison up to 5 Mbar.

Contribution

It presents a novel approach to derive equations of state from fundamental principles, incorporating a specific Hamiltonian decomposition and assessing high-pressure accuracy.

Findings

Errors less than 5% in thermal functions at low pressure

Constructed EOS for Aluminum matches experimental Hugoniot up to 5 Mbar

Method remains viable at high pressures

Abstract

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.