Influence of surface energy anisotropy on morphological changes occurring by surface diffusion

Abstract

The influence of surface energy anisotropy on morphological changes occurring by surface diffusion, on simply shaped bodies, is investigated. A preliminary analysis of the equilibrium shape of a two-dimensional body for arbitrary anisotropy is given, the primary aim being to determine the range of validity of the perturbation scheme used in the subsequent time-dependent analysis. It is shown that such a scheme is valid for the entire range of shapes later considered if γ (ϑ)+d2γ (ϑ)/dϑ2≳0, where γ (ϑ) is the specific surface free energy of a surface whose normal is oriented at an angle ϑ to the reference crystallographic axes. Under this condition the complete relaxation, from an assumed initial circle to the final equilibrium shape, is derived, providing the surface diffusivity is isotropic. When γ (ϑ)+d2γ/dϑ2 is negative, the perturbation scheme furnishes proof of an initial unstable growth away from the circle, although it cannot be used to derive the complete relaxation behavior. Nevertheless, thereby a proof is provided of the existence of such an instability, which was derived earlier by Mullins for only a semi-infinite body, in a finite body (in two dimensions). For completeness, a brief discussion is given of the influence of small surface energy anisotropy in three dimensions for surface-diffusion-controlled shape changes from an initial sphere. Application of these results to the kinetics of particle shaping during the early stages of thin-film growth is also presented.