Surface defect formation in nanosized film coatings due to diffusion

The aim of this study is to solve the problem of surface defect formation in nanosized film systems due to surface diffusion by considering the effects of both surface and interface stresses. Elastic stress field caused by surface undulation is defined by using the constitutive equations of linear elasticity for bulk and surface phases. Based on method of superposition, a boundary perturbation technique, Goursat-Kolosov complex potentials and Muskhelishvili representations, the original boundary value problem is reduced to the successive solution of a system of singular and hypersingular integral equations for any order of approximation. This perturbation solution and thermodynamic approach allows us to derive a governing equation which gives the time-dependence of surface roughness amplitude.