Dislocation nucleation at surface heterogeneities such as steps is analyzed based on the Peierls-Nabarro dislocation model. By modeling a surface step as part of a three-dimensional crack surface, the half space problem is transferred into an equivalent three dimensional crack problem in an infinite medium. The profiles of embryonic dislocations, corresponding to the relative displacements between the two adjacent atomic layers along the slip planes, are then rigorously solved through the variational boundary integral method. The critical conditions for dislocation nucleation are determined by solving the stress dependent activation energies required to activate embryonic dislocations from their stable to unstable saddle point configurations. The effects of step geometry are analyzed in detail. The results show that the atomic scale steps can significantly facilitates dislocation nucleation from stressed crystal surfaces. While the presented methodology of incorporating atomic information into continuum approach is noteworthy for providing insights of energetics of the atomic process involved in dislocation nucleation, further direct atomic simulation appears to be in need to correlate the effectiveness of this approach.

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