Dislocation nucleation at a surface step was analyzed based upon a general variational boundary integral formulation of the Peierls-Nabarro dislocation model. By modelling the surface step as part of the surface of a 3-dimensional crack, the free surface effect was taken into account by transferring the half space problem into an equivalent one in the infinite medium. The profiles of embryonic dislocations, corresponding to the relative displacements between the two adjacent atomic layers along the slip planes, were then rigorously solved through the variational boundary integral method. The critical conditions for dislocation nucleation were determined by solving the stress-dependent activation energies required to activate the embryonic dislocations from their stable to unstable saddle-point configurations. In particular, the effect of the step geometry, such as the height of the step, the dip angle of the slip plane and the inclined angle of the step surface on dislocation nucleation, was quantitatively ascertained. The results showed that the atomic-scale surface step could rapidly reduce the critical stress required for dislocation nucleation from the surface by nearly an order of magnitude. The decrease in critical stress as a function of the height of the step was more significant for slip planes with smaller dip angles and surface steps with smaller inclined angles.

Critical Conditions for Dislocation Nucleation at Surface Steps. C.Li, G.Xu: Philosophical Magazine, 2006, 86[20], 2957-70