Motion of dislocations through a random array of weak obstacles

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Abstract
A dislocation interacting with point obstacles assumes a zigzag configuration. The mean zigzag amplitude and mean loop length of the dislocations are calculated by minimizing the energy of the configuration. A procedure originally due to Mott is generalized in order to include repulsive as well as attractive interaction and the influence of an external stress. Qualitatively similar results obtain for repulsive, attractive and mixed obstacles, quantitatively the differences can be considerable. In the light of these results current statistical theories of solid solution hardening are discussed and criticized.