Low energy metastable states and immiscibility in (SiC)$_{1-X}$-(AlN)$_X$

A cluster expansion Hamiltonian was fit to VASP/PAW calculated supercell formation energies, $\Delta E_f$, and first principles based phase diagrams (miscibility gaps) were calculated for the wurtzite-structure pseudobinary system SiC$_{1-X}$AlN$_X$. An unusually wide range of $3 \alt \Delta E_f~ \alt 125$ kJ/mole MX (M= Al, Si; X= N, C) was calculated and all supercells with $\Delta E_f~ \alt 8$ kJ/mole exhibited characteristic (SiC)$_m$(AlN)$n$ crystallography, in which (SiC)$_m$ indicates m SiC-double layers $\bot$ to the hexagonal c-axis, and similarly for (AlN)$n$. The prediction of (SiC)$_m$(AlN)$n$ low-energy metastable states, may explain why one can synthesize SiC$_{1-X}$AlN$_X$ films, or single crystals of arbitrary bulk composition, in spite of the very strong tendency toward immiscibility. Specifically, one expects that metastable films or single crystals will be dominated by a disordered stacking of SiC- and AlN-double layers.