First Principles Phase Diagram Calculation For Al$_{x}$Ga$_{1-x}$N

First principles phase diagram calculations were performed for the wurtzite and zincblende structures of the quasibinary system AlN-GaN. The cluster expansion method using the code ATAT was performed without and with excess vibrational contributions to the free energy, $F_{vib}$. The ab initio calculations were performed with VASP using the PAW pseudopotentials with PBE for the exchange and correlation energies. Preliminary results show miscibility gaps for both structures with a decrease in the consolute points, ($X_{C}$,$T_ {C}$), when including $F_{vib}$. The wurtzite structure is predicted to be approximately symmetric while the zincblende is predicted to be quite assymetric.