Commensurate-incommensurate phase transition of a physisorbed layer on an elastic substrate

The effect of substrate distortion upon commensurate-incommensurate (C-I) transitions in physisorbed layers is considered. For appropriate values of the elastic constants, the misfit parameter becomes proportional to the square root of the chemical potential near the transition. For other values of the elastic constants, a first-order transition results. This effect is quite different from three-dimensional C-I transitions, where the interaction with (transverse) strains always produces a first-order transition.