First principles phase diagram calculations for the wurtzite-structure systems AlN–GaN, GaN–InN, and AlN–InN

First principles phase diagram calculations were performed for the wurtzite-structure quasibinary systems AlN–GaN, GaN–InN, and AlN–InN. Cluster expansion Hamiltonians that excluded, and included, excess vibrational contributions to the free energy, Fvib, were evaluated. Miscibility gaps are predicted for all three quasibinaries, with consolute points, (XC,TC), for AlN–GaN, GaN–InN, and AlN–InN equal to (0.50, 305K), (0.50, 1850K), and (0.50, 2830K) without Fvib, and (0.40, 247K), (0.50, 1620K), and (0.50, 2600K) with Fvib, respectively. In spite of the very different ionic radii of Al, Ga, and In, the GaN–InN and AlN–GaN diagrams are predicted to be approximately symmetric.