Incommensurate structures on the surface of an elastic half space

Abstract

A static incommensurate structure on the surface of an elastic half space covered by a monolayer of another substance with different stiffness and a different equilibrium interatomic spacing is considered, and a system of one-dimensional nonlinear integro-differential equations describing such a structure is derived. In the case of an absolutely rigid monolayer (the opposite case from that usually considered in the Frenkel–Kontorova model: the limit of a soft monolayer on an absolutely rigid substrate) some new classes of periodic solutions of the Peierls equation for incommensurate surface structures are found which differ substantially from those known previously. An approximate description of the structure of nonuniform surface states is obtained for a stiff monolayer with a low compliance on a soft half space and for a soft monolayer on a stiff half space with a low compliance, i.e., the approximate dependence of the period of these structures on the incommensurability parameter (the difference of the lattice periods of the half space and monolayer) and their stiffnesses is found. The results obtained permit a qualitative description of the transformation of incommensurate surface structures in the whole range of the aforementioned parameters.