Interplay of surface misfit and monatomic steps on crystal surfaces. I. Basic theory

This paper is based on the phenomenon of surface misfit: the theoretical and empirical finding that the (free) equilibrium atomic spacings at and near a crystal surface are different from the interior spacings. Accordingly the formation of a monatomic step generates stresses which act at the crystal surface and pose a boundary-value problem. The stresses—tangential (τ and T) and normal (N)—have been modeled phenomenologically in terms of the crystal parameters: the surface misfit ($f_x$, $f_y$=$f_x$≡f, $f_z$), the shear modulus μ, Poisson’s ratio ν, the action region lengths L which are different for τ, T, and N, and the crystal lattice parameter a. Simplifying approximations, some of which are drastic, e.g., the limitation of misfit to the outer monolayer (ML) and the representation of a (single) stepped surface by an atomically smooth plane one, have been introduced.