Physical cluster theory of point defect interactions. II. Application to AgCl doped with CdCl2

The Lidiard-Teltow approximation (L) describes a point defect system of cation vacancies and divalent impurity cations in AgCl doped with CdCl2 as a collection of nearest-neighbor impurity-vacancy pairs and unpaired impurities and vacancies. The concentrations of the latter and related by a law of mass action using Debye-Hückel activity coefficients for unpaired species. The formalism of the previous paper is applied to the same equilibrium. The leading terms of the exact cluster expansions for activity coefficients in the mass action law are reduced analytically and calculated numerically in two approximations, P and T. The approximations L, P, and T agree well for concentrations at which an extension of L indicates that larger defect clusters (triplets, etc.) can be neglected but they tend to diverge at higher concentrations than this, i.e., at impurity contents larger than 7 × 10−3 for temperatures greater than or equal to 250°C but at lower concentrations for lower temperatures. The agreement between P and T approximations confirms the adequate convergence of the new cluster expansions; the agreement of the L approximation with them indicates that it is an accurate approximation although it neglects the effects of paired defects and the discreteness of the lattice on the Debye-Hückel shielding as well as certain other Coulombic interactions retained in P and T.