Analytic equation of state for solids with multi-exponential potential based on analytic mean field potential approach and applied to the epsilon phase of solid oxygen

The thermodynamic properties of the $\varepsilon $ phase of solid oxygen are studied by using the analytic mean field approach (AMFP). Analytic expressions for the Helmholtz free energy, internal energy and equation of state of solid oxygen have been derived based on the multi-exponential potential. The formulism for the case of double-exponential (DE) model is applied to the $\varepsilon $ phase of solid oxygen. Its four potential parameters are determined through fitting the experimental compression data of the $\varepsilon $ phase of solid oxygen. Numerical results of the pressure dependence of the volume calculated by using the AMFP are in good agreement with the original experimental data. This suggests that the AMFP is a useful approach to study the thermodynamic properties of the $\varepsilon $ phase of solid oxygen. Furthermore, we predict the variation of the volume, lattice parameters and intermolecular distances with pressure, and some thermodynamic quantities versus volume, at several higher temperatures.