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 diamo nd, 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 gr aphite melting suggest the presence of a first-order liquid-liquid phase tr ansition at roughly 6 GPa. We show that such a transition is consistent wit h shock compression data at higher pressures. We reanalyze experiments on t he diamond-liquid melting line with our equation of state. Our analysis sug gests that the diamond-liquid melting line may have a more positive slope a s a function of pressure than previously estimated. A maximum in the diamon d melting line is predicted by the model, in agreement with recent nb initi o simulations.