The cluster-expansion method was used to perform first principles phase diagram calculations for the wurtzite-structure quasibinary systems (SiC) 1ÀX (AlN) X , (SiC) 1ÀX (GaN) X and (SiC) 1ÀX (InN) X ; and to model variations of band gaps as functions of bulk compositions and temperature. In SiC-AlN, plane wave pseudopotential formation-energy calculations predict low-energy metastable states with formation energies, DE f . 0.004 eV/mole (mol ¼ one cation þ one anion). The crystal structures of

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... these states are all of the form (SiC) m (AlN) n (SiC) o (AlN) p ... (m,n,o,p integers), where (SiC) m indicates m SiC-diatomic-layers ? to the hexagonal c-axis (c Hex ) and similarly for (AlN) n , (SiC) o and (AlN) p . The presence of low-energy layer-structure metastable states helps to explain why one can synthesize (SiC) 1ÀX (AlN) X films, or single crystals with any value of X, in spite of the apparently strong tendency toward immiscibility. In SiC-GaN, ordered structures are predicted at X ¼ 1/4, 1/2, and 3/4 (Pm, Pmn2 1 and Pm, respectively). In SiC-InN, one Cmc2 1 ordered phase is predicted at X ¼ 1/2.