Effective Line Tension of a Dislocation

Abstract

The change in energy of a dislocation in an elastically isotropic continuous medium, resulting from small deviations from its equilibrium position, is derived from a knowledge of the kink-kink interaction. The energy-minimization problem which arises when the dislocation is subject to an external stress is solved by a variational method, the displacement associated with an extensible string being taken as a trial function. The best value for the line tension so derived is significantly smaller (by roughly an order of magnitude in an extreme case) than the earlier estimates of Mott and Nabarro or Cottrell and agrees most closely with a later estimate by Nabarro. The extension of this method to dislocations in discrete lattices is discussed briefly and the use of the string model to analyze nonlinear effects is also considered.