Uniform Motion of a Screw Dislocation in a Lattice

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 (\(v{}c/3\)), σ( v ) has many singular points reflecting the van Hove singularities.