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Silicon carbide polytypes are equilibrium structures

The phonon free energy is calculated for several silicon carbide polytypes using a valence overlap shell model. The three most commonly observed polytypes, i.e. (2), (23) and (3), are shown to be thermodynamically stable, with (2) and (3) as the low- and high-temperature phases, respectively, and (23) in between. The long-ranged phonon effect splits the multiphase degeneracy between phases (2) and (3) to which SiC is extremely close at T=0 K, and its stabilises (23) with a significantly large stability region of 500 K. The calculations of the interatomic displacement-displacement correlations demonstrate how the long-ranged interatomic interactions arise from the phonons. The formation theory of longer-period polytypes is also discussed.