Charge carrier mobility in crystals of the Pb$_{0.67}$Cd$_{0.33}$F$_2$ superionic conductor

The frequency ($\nu$ = 10$^{-1}$–10$^7$ Hz) dependences $\sigma(\nu)$ of the conductivity of single crystals of the Pb$_{0.67}$Cd$_{0.33}$F$_2$ superionic conductor with the fluorite-type structure (CaF$_2$) in the temperature range of 132–395 K have been studied. The dependences $\sigma(\nu)$ have been discussed in the framework of the hopping relaxation of ionic carriers, which are mobile anions F$^{-}$. From experimental curves $\sigma(\nu)$, the direct-current (dc) conductivity $\sigma_{\mathrm{dc}}$ and the average charge carrier hopping frequency $\nu_h$ have been determined. This has made it possible to calculate the charge carrier mobility $\mu_{\mathrm{mob}}$ and charge carrier concentration $n_{\mathrm{mob}}$ in these crystals. At room temperature (293 K), the electrical parameters are $\sigma_{\mathrm{dc}}$ = 1.6 $\cdot$ 10$^{-4}$ S/cm, $\nu_h$ = 2.7 $\cdot$ 10$^7$ Hz, $\mu_{\mathrm{mob}}$ = 2.0 $\cdot$ 10$^{-7}$ cm$^2$/(s $\cdot$ V), and $n_{\mathrm{mob}}$ = 5.1 $\cdot$ 10$^{21}$ cm$^{-3}$.