Concentration and mobility of charge carriers in the superionic conductor Ba$_{1-x}$La$_x$F$_{2+x}$ (0.05 $\le x\le$ 0.5)

The frequency-temperature dependences of alternating current conductivity $\sigma_{ac}(\nu,T)$ for concentration series of single crystals of nonstoichiometric superionic conductor Ba$_{1-x}$La$_x$F$_{2+x}$ (0.05 $\le x\le$ 0.5) with the fluorite structure (sp. gr. $Fm\bar3 m$) were investigated. The electrophysical measurements carried out in the frequency range 10$^{-1}$–10$^7$ Hz and temperature range 210–409 K. From the analysis of the curves $\sigma_{\mathrm{ac}}(\nu,T)$ we obtained the concentration dependences of conductivity $\sigma_{\mathrm{dc}}(x)$, average frequency of charge carrier jumps $\nu_{\mathrm{h}}(x)$, enthalpies of activation of conductivity $\Delta H_{\sigma}(x)$ and hopping frequency $\Delta H_{\mathrm{h}}(x)$. The mobility $\mu_{\mathrm{mob}}(x)$ and concentration $n_{\mathrm{mob}}(x)$ of charge carriers (mobile interstitial ions $F^-_{\mathrm{mob}}$) are calculated within the framework of crystallophysical model. The dependences $\sigma_{\mathrm{dc}}(x)$, $n_{\mathrm{mob}}(x)$ and $\mu_{\mathrm{mob}}(x)$ are symbatic. It was found that contributions of the mobility $\mu_{\mathrm{mob}}(x)$ and concentration $n_{\mathrm{mob}}(x)$ of charge carriers to the concentration dependence of the “room” conductivity $\sigma_{\mathrm{dc}}(x)$ of the Ba$_{1-x}$La$_x$F$_{2+x}$ superionic conductor were almost identical, when the composition changes from $x$ = 0.05 to $x$ = 0.5.