Distribution of solute atoms round a slow dislocation

Abstract

The factors determining the average velocities of solute atoms attracted to a dislocation are discussed, and an equation is set up for the concentration of solute round the dislocation. This leads to a symmetrical distribution of a Maxwell-Boltzmann type round a stationary dislocation. In the case of a slowly moving dislocation the distribution is given as a series solution in Mathieu functions, and the non-symmetry of this distribution causes a force on the dislocation, opposing its motion. This force is calculated and shown to increase linearly with the speed of the dislocation, at low speeds, and a critical range exists above which the motion is unstable and the dislocation accelerates. The characteristics of the plastic flow below this critical range are compared with those of micro-creep in tin crystals and are shown to be similar. Quantitative agreement can be obtained by assuming plausible values for the density of dislocations and the rate of diffusion of solute atoms in tin, but the need for further experiments on micro-creep is emphasized.