Effect of iso- and heterovalent cation substitutions on the superionic Faraday transition in fluorite-type modification $\beta$-PbF$_2$

The influence of isovalent substitutions of Pb$^{2+}$ $\to$ Cd$^{2+}$ and heterovalent substitutions of Pb$^{2+}$ $\to$ Sc$^{3+}$ on a superionic Faraday transition in Pb$_{1-x}$Cd$_x$F$_2$ ($x$ = 0.33) and Pb$_{1-x}$Sc$_x$F$_{2+x}$ ($x$ = 0.1) solid solutions based on the fluorite-type modification $\beta$-PbF$_2$ with sp. gr. $Fm\bar{3}m$ has been studied. The Faraday phase transition can be characterized by the temperature $T_{tr}^\lambda$ corresponding to maximum on the heat capacity curve and temperature $T_{tr}^\alpha$ corresponding to the beginning of the structural disorder anion sublattice. Both of these temperatures are found on the temperature conductivity dependence $\sigma_{dc}(T)$ of $\beta$-PbF$_2$, Pb$_{0.67}$Cd$_{0.33}$F$_2$ and Pb$_{0.9}$Sc$_{0.1}$F$_{2.1}$ crystals. The values of $T_{tr}^\lambda$ and $T_{tr}^\alpha$ in solid solutions compared with $\beta$-PbF$_2$ ($T_{tr}^\lambda$ = 715 $\pm$ 10 K, $T_{tr}^\alpha$ = 597 $\pm$ 12 K) decrease by 100–110 and 30–45 K for Pb$_{0.67}$Cd$_{0.33}$F$_2$ and Pb$_{0.9}$Sc$_{0.1}$F$_{2.1}$, respectively. Decreasing of temperature $T_{tr}^\lambda$ leads to an increase in temperature interval of existence of the superionic state. For $T>T_{tr}^\lambda$ the anionic conductivity of fluorite-type Pb$_{0.67}$Cd$_{0.33}$F$_2$, Pb$_{0.9}$Sc$_{0.1}$F$_{2.1}$, and $\beta$-PbF$_2$ crystals reaches anomalously high values of $\sigma_{dc}$ = 1–2 S/cm (873 K) at an ion transfer activation enthalpy equals to $H_\sigma\approx$ 0.3 eV.