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 of110 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.
Although the mechanical theory of Granato and LUcke for the strain-amplitude-dependent internal friction and modulus changes of solids containing dislocations gives a fair account of many of the observed effects, simple theoretical considerations show that the effect of thermal fluctuations should be very important. To extend the theory to finite temperatures, a detailed study of the possible static equilibrium configurations of a pinned dislocation line as a function of external stress is required. This is done here for the two specific examples of a dislocation with a single pinning point and a dislocation with a continuous pinning agent. It is shown in a general way how the damping and modulus change can be computed from these results, and a qualitative discussion of expected behavior is given. For high concentrations of pinning points, the theory is also applicable in the field of yield point phenomena, and the results found here are compare(1 with previous calculations.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.