Thermodynamic properties of ε-Fe with thermal electronic excitation effects on vibrational spectra

Abstract: The thermodynamic properties of hcp-iron ({\epsilon}-Fe) are essential for investigating planetary cores' internal structure and dynamic properties. Despite their importance to planetary sciences, experimental investigations of {\epsilon}-Fe at relevant conditions are still challenging. Therefore, ab initio calculations are crucial to elucidating the thermodynamic properties of this system. Here we use a free energy calculation scheme based on the phonon gas model compatible with temperature-dependent phonon frequencies. We investigate the effects of electronic thermal excitations, which introduces a temperature dependence on phonon frequencies, and the implication for the thermodynamic properties of {\epsilon}-Fe at extreme pressure (P) and temperature (T) conditions. We disregard phonon-phonon interactions, i.e., anharmonicity and their effect on phonon frequencies. Nevertheless, the current scheme is also applicable to T-dependent anharmonic frequencies. We conclude that the impact of thermal electronic excitations on vibrational properties is not significant up to ~ 4,000 K at 200 GPa but should not be ignored at higher temperatures or pressures. However, the static free energy, Fst, must always include the effect of thermal excitation fully in a continuum of Ts. Our results for isentropic equations of state show good agreement with data from recent ramp compression experiments up to 1,400 GPa conducted at the National Ignition Facility (NIF).