Theory of Valency Effect of Impurity Atoms on Hardening of Alloys

A theory of the electronic interaction between an edge dislocation and an impurity atom in a free electron metal is developed along a line similar to that given by Cottrell. Hunter and Nabarro (Phil. Mag 44 (1953) 1064). On the basis of a simple deformation potential and of the linearized Thomas-Fermi model, a screened potential around the dislocation is expressed analytically by the use of Green's theorem, and the electronic interaction energy is calculated by taking account of changes in the total energy of a free electron gas. The electronic interaction energy is not so small as has been considered. For example, in copper alloys the electronic interaction is 1∼4 times as great as an elastic one, unlike the result of Cottrell et al. .

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