Ab initio calculations of the melting line of MgSiO₃ and Fe

The phase diagram silicates and iron at high pressure is of considerable interest for geophysics and planetary science. Understanding the process of crystallization of the mantle and core of rocky exoplanets largely depends on our ability to simulate the states of planetary materials at high pressure and high temperature that are considerably different from those at the Earth interior. Using density functional theory molecular dynamics, we investigate the melting curve of MgSiO₃ and iron at megabar pressures. We derived the melting temperature by equating the Gibbs free energies of solid and liquid phases that we derived through the thermodynamic integration method. The melting curve allows us to study the crystallization behavior under high compression, and the access to free energies allows us to obtain isentropes, which are the thermodynamic paths that represent the interior of convective planetary interiors. We compare the melting curves of these two materials and the adiabatic gradients to determine how the cores of super-Earth planets crystallize.