Uniqueness and stability of activated dislocation shapes in crystals

Abstract

Simplified models of thermally activated dislocation glide constitute an important link between atomic-level studies of isolated dislocations and macroscopic thermodynamic properties of materials. These models rest upon the activation enthalpy, which is the energy to transform an initially straight dislocation into its activated state at finite applied stresses. Minimizing this activation enthalpy leads to a boundary value problem for the shape of the dislocation line. Besides two constant solutions corresponding to a straight dislocation in its stable and unstable states at the applied stress, there exist an infinite number of non-constant solutions. We investigate the characters of these solutions for dislocations anchored at their ends. Using the second variation of the activation enthalpy, we derive a set of conditions that define a unique activated state of the dislocation. The corresponding analysis demonstrates that the shape of the dislocation in this activated state must change with the applied stress to maintain the state of minimum activation enthalpy.