Iron under Earth’s core conditions: Liquid-state thermodynamics and high-pressure melting curve from ab initio calculations

Ab initio techniques based on density functional theory in the projector-augmented-wave implementation are used to calculate the free energy and a range of other thermodynamic properties of liquid iron at high pressures and temperatures relevant to the Earth’s core. The ab initio free energy is obtained by using thermodynamic integration to calculate the change of free energy on going from a simple reference system to the ab initio system, with thermal averages computed by ab initio molecular dynamics simulation. The reference system consists of the inverse-power pair-potential model used in previous work. The liquid-state free energy is combined with the free energy of hexagonal close packed Fe calculated earlier using identical ab initio techniques to obtain the melting curve and volume and entropy of melting. Comparisons of the calculated melting properties with experimental measurement and with other recent ab initio predictions are presented. Experiment-theory comparisons are also presented for the pressures at which the solid and liquid Hugoniot curves cross the melting line, and the sound speed and Grüneisen parameter along the Hugoniot. Additional comparisons are made with a commonly used equation of state for high-pressure–high-temperature Fe based on experimental data.