Stress-driven morphological instability of axi-symmetrical surface coatings

The morphological evolution of an axi-symmetrical surface coating subjected to a uniform residual stress and a longitudinal surface-perturbation was analyzed when surface diffusion is the dominant mechanism for atomic migration. The surface stability of the surface coating was controlled by the gradient of chemical potential associated with surface energy and the elastic energy introduced by the residual stress and surface-perturbation. An explicit formula of the dispersion relation was obtained for determining the evolution of the surface-perturbation and critical frequency. The stability of several special geometries was discussed. It was observed that the critical frequency is a linear function of the film thickness for thin film coatings.