Non-Uniform Strain in Epitaxial Surface Gratings: Beyond the Ordinary Elastic Description

A generalized elastic description of non-uniform strain in layered epitaxial surface gratings is presented. The proposed total free energy of the system contains a surface term responsible for the interaction energy between different media, beside the ordinary bulk elastic energy density contribution.The equilibrium equations and the related boundary conditions corresponding to the actual deformed state are obtained. The presence of surface crystalline order induced on amorphous material by a crystalline substrate is also discussed.