Abstract
The probability distribution of the dilational strain is calculated for the idealized situation of a random array of straight edge dislocations in a finite spherical piece of material. The result is exactly separable into two contributions, one of which corresponds to the distribution in a region close to a single dislocation, and the other is a gaussian distribution. A physical understanding of these two distributions is presented, which makes it possible to extend the results semiquantitatively to the strain probability distributions in real situations, and to conclude from energy considerations that dislocations grown into crystals may often be effectively random.
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