Thermodynamic properties of ε-iron with T-dependent phonons

The quasi-harmonic approximation (QHA) is an extremely powerful method for computing thermodynamic properties of materials at high pressures (P) and temperatures (T). However, anharmonicity, electronic excitations in metals, or both, introduce an intrinsic T-dependence on the phonon frequencies. Here, we investigate the effect of electronic excitations on the phonon frequencies and the implication for the thermodynamics properties of ε-Fe at extreme P, T conditions. Phonon-phonon interactions are disregarded here. Because phonon frequencies are T-dependent, we first obtain the entropy using the phonon gas model formula, still valid in the context of phonon-quasiparticles, and then the vibrational free energy by integrating the entropy. We demonstrate that inclusion of the electronic thermal excitation effect on phonon dispersions makes a significant difference in the thermodynamic properties of ε-Fe at Earth’s inner core conditions and beyond.