Kink-pair formation on dislocations within the framework of the line-tension model

This article deals with the plastic deformation of crystals under an applied stress and summarizes various theoretical concepts within the framework of a model of dislocation migration in crystals. The migration of one type of dislocations in their glide plane is described within the framework of a continuum approximation. The dynamics of the physical system is treated by a Hamiltonian method describing solitonic vibrations of a one-dimensional field added by discussions of a special perturbation which models the applied stress in the glide plane of the dislocation. Dislocation migration is governed by nucleation processes. Therefore, one has to apply thermodynamical concepts in order to calculate the formation rate of the nucleation configuration of the dislocation. This is done here by mapping the solitonic field onto a Brownian particle and using Kramers' famous work on nucleation in chemical reactions. The last section is devoted to an approach involving quantum thermodynamical effects and relating them to tunnelling processes of kinks on dislocations. The method used for calculating tunnelling rates is based on Feynman's path integral method in imaginary time formulation. (author). 26 refs, 12 figs