A lattice-dynamics model of an oscillating screw dislocation

Abstract

The concept of the Boyer-Hardy source-force, or Kanzaki force, for a static screw dislocation is extended to describe a moving dislocation — in a simple cubic, nearest neighbour, harmonic lattice (snapping-bond model) — and together with the phonon Green's function is used to derive expressions for the atomic displacements and time-averaged energy disspation, viz. the rate of energy transfer from the moving dislocation to the lattice vibrations. For the case in which the dislocation oscillates harmonically in time, an expression for the energy dissipation is derived which, for megahertz frequencies and lower, is then reduced to a finite sum and finite integration, and is evaluated to lowest (zeroth) order in the frequency. The way in which the method may be extended to describe a lattice containing a low concentration c of point defects in a random array is then outlined, and it is shown how the change in energy dissipation, to lowest order, is proportional to c. The method developed here is such that it can, in principle, be further generalized in a completely unambiguous fashion, to allow for a non-linear or anharmonic atomic force-law in the dynamic source-force of the dislocation as well as a temperature dependent phonon damping in the Green's function.