Cluster Formation of Ion-Defect Pairs in Compensated Lattices

Abstract

Expressions for the dimer and trimer formation of aliovalent cation—lattice‐defect pairs in crystalline compensated lattices have been derived from the minimization of free energy expressions which are given in terms of canonical partition functions. Numerical calculations have been made for the KCl:Sr²⁺ system by assuming the principle of linear superposition. It is shown that while extensive dimer formation occurs through wide ranges of temperatures and concentrations, trimer and higher cluster formations are of significance only at relatively high concentrations. Although the uncertainties of the interaction energies in many cases may weaken some quantitative aspects of the theoretical calculations, the general procedure given in the paper can be readily applied to other compensated lattices such as alkaline‐earth halides containing trivalent cations. The over‐all qualitative features of the theory serve to elucidate some of the more puzzling experimental observations reported recently in the literature.