Free energy model for solid high-pressure phases of carbon

Analytic free energy models for three solid high-pressure phases-diamond, body centered cubic phase with eight atoms in the unit cell (BC8), and simple cubic (SC)-are developed using density functional theory. We explicitly include anharmonic effects by performing molecular dynamics simulations and investigate their density and temperature dependence in detail. Anharmonicity in the nuclear motion shifts the phase transitions significantly compared to the harmonic approximation. Furthermore, we apply a thermodynamically constrained correction that brings the equation of state in accordance with diamond anvil cell experiments. The performance of our thermodynamic functions is validated against Hugoniot experiments.