Empirical relationship between effective ionic charges and optical dielectric constants in binary and ternary cubic compounds

Abstract

The effective ionic charge ${Z}^{*}e$ of each ion is determined within a narrow variable range for cubic and near-cubic ternary compounds. The Szigeti effective charge ${e}_{s}^{*}[=\frac{{3\sqrt{\ensuremath{\epsilon}}}_{\ensuremath{\propto}}{Z}^{*}e}{({\ensuremath{\epsilon}}_{\ensuremath{\propto}}+2)}]$ is also evaluated for the anion from the value ${Z}^{*}e$ by using the observed optical dielectric constant ${\ensuremath{\epsilon}}_{\ensuremath{\infty}}$. The correlation between ${e}_{s}^{*}$ and the dielectric constant ${\ensuremath{\epsilon}}_{\ensuremath{\infty}}$ is empirically found for many kinds of binary and ternary compounds as ${\ensuremath{\epsilon}}_{\ensuremath{\infty}}\ensuremath{-}1=\frac{2.0}{[(\frac{{e}_{s}^{*}}{{Z}_{\mathrm{eff}}e})+{(\frac{{e}_{s}^{*}}{{Z}_{\mathrm{eff}}e})}^{2}]}$. The value ${Z}_{\mathrm{eff}}$ indicates the effective chemical valency. In the correlation, the relatively large scatter for some compounds is explained by the $d$- or $f$-electron effect on the dielectric constant ${\ensuremath{\epsilon}}_{\ensuremath{\infty}}$, and by the screening and the anisotropic effects on the effective charge. From these results, the applicable ranges of the equation used and of the localized effective charge are discussed.