Modelling of dislocations intersecting a free surface

The influence of surface corrections on three-dimensional dislocation dynamics is investigated by considering a curved dislocation intersecting a plane free surface. The Boussinesq-Cerruti formalism is used to determine the image field for this problem to high accuracy. A heuristic method for simultaneously regularizing the self-interaction and the image-field singularity allows curvature and image effects to compete dynamically. Comparison of our implementation against analytical predictions for the critical strain in a strained layer with a free surface yields excellent agreement. We find that while the image corrections determine the angle at which the dislocation enters the boundary, their overall effect on a curved dislocation is surprisingly small, varying from a few per cent for a 1 mu m half-loop at the surface to at most 40% for a half-loop with a radius as small as 1 nm. We conclude that for many dislocation problems, especially those involving only a few dislocations in a confined geometry, it is a meaningful first approximation to neglect long-range image effects altogether, the errors becoming large only at scales comparable to the Burgers vector. A useful way of implementing this approximation in the case of a free surface is to estimate an image force using a formula given by Lothe, and apply it to the surface intercept point only.