Physical cluster theory of point defect interactions. I. General formalism

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Abstract
The configurations of point defects in a solid can be uniquely classified in terms of interacting physical clusters. Two point defects are counted as in the same physical cluster if their separation is less than or equal to some characteristic distance. The methods of Mayer cluster theory are used to derive a general formal exact law of mass action which relates concentrations and activity coefficients of physical clusters to concentration-independent equilibrium constants. The activity coefficients and distribution functions for physical clusters are obtained as series expansions in powers of physical cluster concentrations. From these results further expansions, individual terms of which converge even for ionic crystals, are obtained by the methods of the Mayer ionic solution theory. The relationship of these results to the Frenkel-Band theory of association in imperfect gases and to the Lidiard-Teltow theory of defect interactions in ionic crystals is briefly indicated and possible applications of the formalism suggested. A detailed application is given in the accompanying paper.

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