The Interaction of Screw Dislocations and Sound Waves

In Part I, Peierls's model of a dislocation is adapted to dynamical problems by taking account of the inertia of the matter which in a continuum would lie between the two sheets of atoms defining the glide plane. The scattering of long shear waves by a screw dislocation is examined. The scattering cross-section is nearly proportional to the wave-length. The force acting on the dislocation in the direction of propagation of the wave depends on a specific interaction between a moving dislocation and a varying displacement field. This interaction is derived formally from an electromagnetic analogy, and its meaning is discussed. By its use, the momentum transfer cross-section is calculated, and shown to equal the scattering cross-section. In Part II, the results of Part I are applied to analyze Leibfried's estimate of the resistance to the motion of a dislocation caused by its interaction with lattice vibrations. The estimate depends on a confusion of two effects. It is shown for each effect that the contribution of long waves to the resistance is smaller than that calculated by Leibfried, but no quantitative estimate is given for the contribution of waves near the top of the Debye spectrum. It is concluded that Leibfried's result is correct in form and order of magnitude, but numerically too high.