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, F vib , were evaluated. Miscibility gaps are predicted for all three quasibinaries, with consolute points, ͑X C , T C ͒, for AlN-GaN, GaN-InN, and AlN-InN equal to ͑0.50, 305 K͒, ͑0.50, 1850 K͒, and ͑0.50, 2830 K͒ without F vib , and ͑0.40, 247 K͒,

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... 0.50, 1620 K͒, and ͑0.50, 2600 K͒ with F vib , 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.