Uniform Motion of a Screw Dislocation in a Lattice

Abstract

Uniform motion of a screw dislocation is studied in a simple cubic lattice in which atoms interact piecewise harmonically with nearest neighbours. The stress σ required for keeping the motion with velocity v is given exactly. The dislocation excites lattice waves with k given by ω(k)=v·k, where ω(k) is the dispersion relation of waves and k is not restricted within the first Brillouin zone. In contrast to continuum approximation, there is no singularity at v=c; c is the sound velocity. At low velocities (v\lesssimc⁄3), σ(v) has many singular points reflecting the van Hove singularities.