An analytical model was presented, for several of the quantities which characterized the mobility of a dislocation line within the framework of the Peierls-Nabarro model, which covered the entire range of possible values of dislocation width. These quantities included the first-order Peierls stress (minimum stress required to move a straight segment of dislocation), the kink profile, the kink-pair activation energy and the second-order Peierls stress (minimum stress required to move a kink in the dislocation line). These quantities were expressed in terms of fundamental properties of the material; especially the relevant generalized stacking-fault surface segment.

The Peierls-Nabarro Model and the Mobility of the Dislocation Line. B.Joós, J.Zhou: Philosophical Magazine A, 2001, 81[5], 1329-40