Both SiC and ZnS exist in the cubic diamond-like (zinc blende) structure. A polytype is derived from the cubic stacking of atomic double layers by having a regularly repeated pattern of stacking faults. Dozens of such polytypes are known for SiC and ZnS.
A study with several co-workers has been completed into the origin of this phenomenon. Are the polytypes genuine stable phases frozen in from some higher equilibrium temperature? Or are they inherently metastable structures born of some growth mechanism?
Quantum mechanical calculations have shown that SiC polytypes formed from bands of 2 and 3 cubically stacked layers have a lower energy than other structures, in particular lower than the cubic or wurtzite structures. That already suggests that the polytypes can be stable phases. Further calculations of the phonon free energy and relaxation of the bond lengths rounds out the phase diagram. In this connection it is somewhat surprising that the material normally grows initially in the metastable cubic modification, transforming subsequently to a mixture of polytypes, but the calculations also suggest why this is so.
The answers for ZnS turn out to be different from those for SiC.