Electron theory of interaction between point defects in metals

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Abstract
By employing a simple model of point charges in a uniform electron gas, it is shown how interaction energies between imperfections (for example, impurity-vacancy or vacancy-vacancy interactions) may be evaluated within the framework of low-order perturbation theory. Close contact may be established throughout with the earlier investigation of Alfred and March (1957), in which, however, a restrictive assumption that the perturbing potential was slowly varying had to be made. Our work now removes this assumption completely and provides a firm basis for the so-called electrostatic model of the interaction between imperfections. In view of the long-range oscillations in the electrostatic potential around a defect, the interaction energy also has an oscillatory behaviour as a function of distance. The relevance of our work to the Lazarus theory of impurity diffusion in metals is discussed. In this caso, the numerical results are in fair agreement with those of the earlier treatment, and lend farther support to the Lazarus theory. Also the investigation of Seeger and Bross (1956) on the di-vacancy may be critically examined by comparison with the present findings. It then appears that the terms in the total interaction energy which these earlier workers have omitted may be large. Indeed, in our calculations they are sufficient to change the sign of the interaction. It is finally pointed out that the present theory may have relevance in the interpretation of the results of Biondi and Rayne (1959, Rayne 1961) on optical absorption in Cu-Zn and Cu-Ge alloys.