Entropy Factors for Thermally Activated Unpinning of Dislocations

Abstract

The entropy factor and effective jump frequency for the thermally activated unpinning of dislocations are computed by use of the statistical mechanics treatment of absolute rate theory. Three problems are considered in detail: The first is a model problem of three mass points, the second a dislocation line of length 2l pinned by an impurity at its center, and third a dislocation line pinned uniformly over its length. The unique feature about the theoretical treatment of the diffusion of dislocations in crystals, as contrasted with the diffusion of point defects, is that good quantitative approximations for the frequencies of the system in both the ground state and the activated state can be obtained from the vibrating string model. The approximations of this model are good for the lowest frequencies, which turn out to be the important ones for the processes considered. The entropy factor is very large for long loop lengths. For a typical case of a binding energy of$\frac{1}{10}$ eV, the frequency factor for a dislocation pinned at its center is the order of 5×10¹⁰ cps, independent of the loop length or of the attack frequency. For a continuously pinned dislocation, the effective frequency is greater than the Debye frequency.