ELASTIC ANALYSIS OF THE ENERGY AND RELAXATION OF STEPPED SURFACES

We present an analytical, elastic analysis for the energy and relaxation of stepped surfaces. The analysis is based upon the observation that the most prominent feature of the non-reconstructive surface relaxation consists of the atoms at the top of the ledges relaxing inwards toward the bulk. This is modeled by replacing the true atomic structure with a continuum elastic half space subjected to a periodic array of line forces (with the periodicity of the steps) directed normal to the free surface. This model is then employed to determine the stress, strain and displacement fields and elastic energy associated with the surface relaxation. We find that the stress and strain fields decay quickly into the bulk as Y e(-Y), where Y is the distance from the surface normalized by the interledge spacing. The surface energy is largely controlled by the terrace energy and the ledge energy, while the ledge interaction energy decays as the inverse square of the ledge spacing. The elastic model provides an accurate description of the wavelength, phase and decay rate of the surface relaxations compared with atomistic simulation results for metals.