Mobility of charge carriers in a single crystal and nanoceramic of the superionic Pb$_{1-x}$Sn$_{x}$F$_{2}$ conductor ($x$ = 0.2)

A crystallophysical model of ion transfer in the superionic Pb$_{1-x}$Sn$_{x}$F$_{2}$ conductor with a fluorite (CaF$_2$) structure is proposed. The concentration dependence of the ionic conductivity of Pb$_{1-x}$Sn$_{x}$F$_{2}$ single crystals and poly- and nanocrystals is analyzed. The single-crystal form of the superionic conductor is characterized by the highest conductivity. The mobility and concentration of anionic charge carriers in a single crystal and ceramics of Pb$_{1-x}$Sn$_{x}$F$_{2}$ ($x$ = 0.2) is calculated on the basis of structural and electrophysical data. The mobility of carriers $\mu_{\operatorname{mob}}$ = 2.5 $\times$ 10$^{-6}$ cm$^2$/s V (at 293 K) in a single crystal is seven times higher than in nanoceramic. The concentration of carriers $n_{\operatorname{mob}}$ = 1.7 $\times$ 10$^{21}$ and 3.6 $\times$ 10$^{21}$ cm$^3$ (4.5 and 9.5% of the total number of anions) for a single crystal and nanoceramic, respectively. The comparison of isostructural Pb$_{0.67}$Cd$_{0.33}$F$_{2}$, and Pb$_{0.9}$Sc$_{0.1}$F$_{2.1}$ single crystals shows that anionic carriers have a maximum mobility in the $\beta$-PbF$_2$ and SnF$_2$ based solid solution.