A crystal-physical model of electrotransfer in the superionic conductor Pb$_{1-x}$Sc$_{x}$F$_{2+x}$ ($x$ = 0.1)

The frequency ($\nu$ = 10$^{-1}$ – 10$^{7}$ Hz) dependences of electrical conductivity $\sigma(\nu)$ of single crystals of superionic conductor Pb$_{0.9}$Sc$_{0.1}$F$_{2.1}$ (10 mol % ScF$_3$) with fluorite type structure (CaF$_2$) in the temperature range 153–410 K have been investigated. The static bulk conductivity $\sigma_{dc}$ =1.5 $\times$ 10$^{-4}$ S/cm and average hopping frequency $\nu_h$ = 1.5 $\times$ 10$^7$ Hz of charge carriers (mobile ions F$^-$) at room temperature (293 K) have been defined from the $\sigma_{dc}(\nu)$ experimental curves. Enthalpies of thermoactivated processes of ionic conductivity $\sigma_{dc}(T)$ ($\Delta H_{\sigma}$ = 0.393 $\pm$ 0.005 eV) and dielectric relaxation $\nu_h(T)$ ($\Delta H_h$ = 0.37 $\pm$ 0.03 eV) coincide within their errors. A crystal-physical model of fluorine-ion transport in a Pb$_{0.9}$Sc$_{0.1}$F$_{2.1}$ crystal lattice has been proposed. The characteristic parameters of charge carriers have been calculated: concentration $n_{mob}$ = 2.0 $\times$ 10$^{21}$ cm$^{-3}$, the distance of the hopping $d\approx$ 0.5 nm and mobility $\mu_{mob}$ = 4.5 $\times$ 10$^{-7}$ cm$^2$/s V (293 K).