Abrupt-Kink Model of Dislocation Motion

Abstract

A new model of dislocation motion is presented. The behavior of a dislocation in the presence of an applied stress is described in terms of a redistribution of kinks along its length. In contrast with previous models, in which a kink is envisaged as a smooth step extending over many lattice constants, we suppose a kink to be abrupt. Consequently, kink diffusion is considered to be a thermally activated process. Transport equations are formulated which include the effects of generation, diffusion, and collision of kinks. General results obtained from these equations show that a dislocation does not behave like an extensible string in this model. Particular application to small harmonically-time-dependent stresses leads naturally to a new theory of the Bordoni anelastic peak. The characteristic relaxation time depends on line length as well as the attempt frequency and activation energy for diffusion. As a result the decrease in the peak height and slight lowering of the peak temperature upon alloying or neutron irradiation are explained. Assuming an exponential distribution of line lengths, the results of the theory are used to evaluate the merit of different published values of the activation energy. Calculated attenuation peaks for different frequencies are shown to account for the experimentally observed large half-widths in pure cold-worked metals. The absence of a peak in well-annealed metals is explained if dislocations are then arranged parallel to the close-packed directions, thereby eliminating the kink density. The process by which cold-working annealed materials can give rise to kinks is discussed. Experiments are suggested which might further test the theory.