A novel semi-discrete Peierls-Nabarro model was introduced which could be used to study dislocation spreading on more than one slip plane; such as dislocation cross-slip and junctions. Within this essentially continuum model, the non-linearity which arose from atomic interactions across the slip plane was dealt with by means of atomistic and/or ab initio calculations. As an example, a study was made of dislocation cross-slip and of the constriction process in these 2 contrasting face-centered cubic metals. It was found that screw dislocation in Al could cross-slip spontaneously; unlike the screw dislocation in Ag, which split into 2 partials and thus could not cross-slip without first constricting. The dislocation constriction energy and the critical stress for cross-slip were determined, and the cross-slip energy barrier to straight screw dislocations was estimated from the latter parameter.

A Non-Planar Peierls-Nabarro Model and its Application to Dislocation Cross-Slip. G.Lu, V.V.Bulatov, N.Kioussis: Philosophical Magazine, 2003, 83[31], 3539-48