Surface instability of an elastic conducting halfspace in an electric field: Lattice diffusion

The surface evolution of an elastic conducting material subject to an infinitesimal surface perturbation and uniform loading in an electric field was evaluated with respect to lattice diffusion. A dispersion relation describing morphological evolution of the elastic material as a function of the electric field intensity was derived, and the time evolution of the surface perturbation was obtained. The critical spatial frequency of the infinitesimal surface perturbation, at which the growth rate of the perturbation is zero, increases with the increase of the electric field intensity and is independent of Young's modulus of the elastic halfspace. An electrical field enhances the surface growth of elastic conducting solids for atomic migration controlled by lattice diffusion, while tensile stress tends to smooth surface perturbations.