A lattice-dynamics model of the interaction of a dislocation with point defects

We consider a lattice dynamics model of a straight screw dislocation moving in a simple cubic lattice with nearest-neighbour « snapping bonds ». The effect on the lattice of the dislocation motion is described by a dynamic source-force, or Kanzaki-force, and the lattice response by the phonon Green's function. A random array of isotopic substitutional point defects is introduced, and the average-t-matrix approximation of the configurational averaged Green's function is employed to describe the defect-lattice response. By using these quantities to calculate the energy radiated, as phonons, from the moving dislocation, and equating this energy to the work done by the applied stress, we obtain numerically the relation between the applied stress and dislocation velocity as a function of defect concentration. This stress-velocity relation shows that the site mass-change, through their global effect upon the lattice dynamics can introduce a dynamic lattice softening contribution to the usual solute hardening effect of the interaction between dislocation and point defects.