Dielectric Properties of Interacting Ion-Impurity Systems in KCl

Abstract

The theory of the dielectric properties of assemblies of interacting impurity ions in solids at low temperatures is discussed, with particular reference to KCl:${\mathrm{OH}}^{-}$, KCl:${\mathrm{Li}}^{+}$, and KCl:${\mathrm{Li}}^{+}$. A quantum-mechanical approach in which the effects of zero-field splitting in the motional spectrum of the ions are included is maintained throughout. An analytical study of the properties of an especially simple model with features relevant to the problem of interacting impurity dipoles is presented. The dielectric virial-expansion formalism is introduced, and numerical results for the theoretical second dielectric virial coefficient $B\left(T\right)\mathrm{}$ for each of the three species are given. The question of convergence of the virial expansion is considered, and it is shown that convergence fails for the specific case of KCl:${\mathrm{OH}}^{-}$ at impurity densities so far studied. An alternative theory for this system is presented which gives numerical predictions in satisfactory agreement with experiment. The basic notion of this theory is that neighboring impurity ions are locked into coherent ferroelectric pairs. At sufficiently low temperatures, this pairing is partially disrupted by largely antiferro-electric interactions between distinct pairs.