Study of charge carrier mobility in superionic conductor La$_{0.95}$Sr$_{0.05}$F$_{2.95}$ by electric modulus spectroscopy

The spectra of the complex electric modulus $M^*(\nu)=M'+ iM''$ for a single crystal of the superionic conductor La$_{0.95}$Sr$_{0.05}$F$_{2.95}$ with the tysonite structure (space group $P\bar3c1$) were studied in the frequency ranges of 10$^{-1}$–10$^7$ Hz and temperatures of 133–273 K. The diagrams of the complex electric modulus $M^*(\nu)$ are characterized by a distribution of the dielectric relaxation time of charge carriers (fluorine vacancies). Relaxation peaks caused by the mobility of ion carriers are observed on the frequency dependences of the imaginary part of the electric modulus $M''(\nu)$. Based on the temperature change in the position of the relaxation maxima, the average hopping frequency, carrier mobility and activation enthalpy of ion transfer were calculated, which are $\nu_{\mathrm{h}}$ = 3.1 $\cdot$ 10$^7$ Hz, $\mu_{\mathrm{mob}}$ = 1.5 $\cdot$ 10$^{-7}$ cm$^2$/(sV) at room temperature (293 K, extrapolation) and $\Delta H_{\mathrm{h}}$ = 0.37 $\pm$ 0.02 eV, respectively.