The surface morphological stability of stressed crystalline solids underlies various materials processing and reliability problems in numerous technological applications ranging from aerospace to microelectronics and nanotechnology. Surfaces of stressed elastic solids have been shown to undergo morphological instabilities. Specifically, linear stability analyses have demonstrated that the competition between elastic strain energy and surface energy can cause the growth of perturbations from a planar surface morphology and specified the conditions for the onset of the so-called Asaro-Tiller or Grinfeld instability. In addition, numerical simulations accounting for all the important nonlinearities have addressed the surface dynamics beyond the instability onset and revealed instability mechanisms. In particular, it has been demonstrated that a planar surface of a stressed elastic solid can evolve rapidly into a cusped surface, with smooth tops and deep crack-like grooves by surface diffusion, in agreement with experimental observations. These theoretical predictions are consistent with experimental findings over a broad class of materials. However, the effects of the simultaneous action of an electric field on the morphological response of a conducting stressed solid surface have not been explored systematically.

In this presentation, we report results of linear stability analysis for the morphological response of a planar solid surface to the combined action of an applied electric field and mechanical stress, assuming that the solid responds elastically to stress. We derive a dispersion relation, which describes the growth or decay rate of a perturbation from the planar surface morphology of the stressed solid under the simultaneous action of the electric field. The analysis is based on a surface transport model that accounts for curvature-driven surface diffusion, surface electromigration, and stress-driven surface diffusion along with surface diffusional anisotropy. We find that the application of an electric field can have an important effect on the dynamical response of a planar stressed solid surface that is otherwise unstable with respect to long-wavelength perturbations. Specifically, application of a sufficiently strong electric field can stabilize the surface of the stressed electrically conducting solid material that would be otherwise vulnerable to surface cracking under certain thermomechanical conditions; therefore, the electric current protects the material against cracking and inhibits its damage. Furthermore, we report the effects on the surface morphological stability of key material properties, such as the strength of surface diffusional anisotropy and the material's texture that is set by the grain crystallographic orientation. We find that the morphological response of surfaces with <111> crystallographic orientation is easier to stabilize than that of surfaces with <100> or <110> crystallographic orientation.

In addition to the linear stability analysis, we report computational results for the morphological evolution of a solid surface perturbed from an initially planar morphology under the simultaneous action of an electric field and mechanical stress. The computational predictions for the morphological evolution are based on self-consistent dynamical numerical simulations according to the surface mass transport model that was employed in the stability analysis; in the simulations, the fully nonlinear model is solved self-consistently with the electric field and stress field distributions on the solid surface computed through a Galerkin boundary integral method. The numerical results confirm the main conclusions of the linear stability analysis. Our findings can be used toward development of systematic surface engineering strategies for improved materials reliability over a broad range of electromechanical conditions.

Extended Abstract Status: Not Uploaded