Melting properties from ab initio free energy calculations: Iron at the Earth's inner-core boundary

We present a general scheme to accurately determine melting properties of materials from ab initio free energies. This scheme does not require prior fitting of system-specific interatomic potentials and is straightforward to implement. For the solid phase, ionic entropies are determined from the phonon quasiparticle spectra (PQS), which fully account for lattice anharmonicity in the thermodynamic limit. The resulting free energies are nearly identical (within 10 meV/atom) to those from the computationally more demanding thermodynamic integration (TI) approach. For the liquid phase, PQS are not directly applicable and free energies are determined via TI using the Weeks-Chandler-Andersen (WCA) gas as the reference system. The WCA is a simple, short-range, purely repulsive potential with established equation of states. As such, it is an ideal reference for ab initio TI of liquids. We apply this scheme to determine melting properties of hexagonal close-packed (hcp) iron at the Earth's inner core boundary (P = 330 GPa), a subject of great significance in Earth sciences. The important influences of system size and pseudopotentials are carefully analyzed. The results (melting temperature equals 6170 +/- 200 K, latent heat 56 +/- 2 kJ/mol, Clapeyron slope 8.1 +/- 0.2 K/GPa) are consistent with experiments as well as previous calculations.