Explicit Gibbs free energy equation of state applied to the carbon phase diagram

We provide a simple explicit form for the Gibbs free energy G (P, T) of diamond, graphite, and liquid carbon. The Gibbs free energy function is shown to reproduce the known equation of state properties of carbon up to pressures of 600 GPa (6 MBar) and temperatures of 15 000 K. Recent experiments on graphite melting suggest the presence of a first-order liquid-liquid phase transition at roughly 6 GPa. We show that such a transition is consistent with shock compression data at higher pressures. We reanalyze experiments on the diamond-liquid melting line with our equation of state. Our analysis suggests that the diamond-liquid melting line may have a more positive slope as a function of pressure than previously estimated. A maximum in the diamond melting line is predicted by the model, in agreement with recent ab initio simulations.