The Frenkel-Kontorova approach to phase transition into an incommensurate phase, with the formation of a misfit dislocation superlattice on a surface, was extended to the case of alloys in which the lattice mismatch depended upon the local composition. A model was considered that took account of the possibility of atomic diffusion between the surface and the bulk. Special conditions at the surface were accounted for by introducing a chemical potential for that alloy atom which led to a difference in composition between the bulk and the surface. The average mismatch between the surface and the bulk lattices was calculated, as was the critical value of the chemical potential at which a phase transition into an incommensurate phase with misfit dislocations occurred.

Misfit Dislocations on the Surface of Alloys. N.V.Fomin, D.V.Shantsev: Semiconductor Science and Technology, 1996, 11[5], 717-21