In this dissertation we consider various schemes for estimating the effective sink strength of arrays of extended defects, in particular edge dislocations, loop dislocations and voids. Various approximate methods have been proposed in the past to deal with such arrays. We examine the relation between them for an array of edge dislocations and apply them to an array of loop dislocations. A feature of these approximations is their lack of sensitivity to the geometry of the array. We examine their limitations in this respect by considering a simple model problem for a random array of voids. We obtain a lower bound for the sink strength of the array which is extremely sensitive to its statistics. We display a distribution for which a simple self-consistent approximation violates the bound. We give an alternative formulation of the model problem for a void array and generate a self-consistent scheme which allows for the distribution of voids. We demonstrate that a simple implementation of this scheme can also lead to results which still violate a lower bound but at a higher concentration than the simple self-consistent calculation. We conclude that approximate methods should be used with caution at high concentrations of sinks.
|Date of Award||1982|