Annealing kinetics of vacancies to dislocations

Several investigators have found annealing kinetics in systems containing excess vacancies and dislocations which are described approximately by a relation of the form exp (–kt^m), where k is a constant, t is time and m is a number < 1. They have interpreted this result on the basis of a model in which the vacancies annihilate at dislocations and the vacancy–dislocation interaction determines the value of m. This annealing law is considered in detail in the present note, and it is concluded that: (1) there is no theoretical basis for expecting such a relation to describe the large scale annealing of vacancies to dislocations except under very unusual strong drift conditions. Instead, first-order decay should obtain under usual conditions in a simple system where a fixed number of randomly distributed dislocations operating with constant efficiency are the only sinks present; (2) it is impossible to explain the agreement of several previous sets of annealing data with the above equation with m∼1/2 on the basis of a 1/r² type vacancy-dislocation interaction as supposed previously. It is therefore meaningless to attempt to extract the volume of a vacancy from such data; (3) in actual experiments a range of annealing laws may be observed in systems undergoing apparent annealing to dislocations. Various causes include differences in the distribution, geometry, and efficiency of the dislocation sinks and the intrusion of other annealing mechanisms. A recent example for the case of quenched and deformed gold is given.