The charge carriers mobility in single crystal and nanoceramics of ionic conductor Sr$_{1-x}$Y$_x$F$_{2+x}$ ($x$ = 0.3)

The heterovalent solid solution Sr$_{1-x}$Y$_x$F$_{2+x}$ with fluorite structure (sp. gr. $Fm\bar3m$) can be synthesized in single-crystal and nanoceramic forms. Comparison of their electrical properties shows that nanoceramics have a higher ionic conductivity than single crystals the same composition. In the single-crystal state of the solid solution, the migration mechanism dominates interstitial ions F'$_i$ in the bulk of the sample, in the nanoceramic state ther is the vacancy migration mechanism $V^\bullet_{\mathrm{F}}$ along the grain boundaries of the sample. Using electrophysical and structural data, we calculated mobility $\mu_{\mathrm{mob}}$ and concentration $n_{\mathrm{mob}}$ of ionic charge carriers in a single crystal ($a$ = 0.5722 nm) and ceramics ($a$ = 0.57442 nm) of composition Sr$_{0.7}$Y$_{0.3}$F$_{2.3}$. The defect mobility F'$_i$ ($\mu_{\mathrm{mob}}$ = 4.5 $\cdot$ 10$^{-10}$ cm$^2$/(V $\cdot$ s) at 500 K) in a single crystal is less than the mobility of vacancies $V^\bullet_{\mathrm{F}}$ in nanoceramics by 140 times. The concentration charge carriers is $n_{\mathrm{mob}}$ = 1.1 $\cdot$ 10$^{21}$ and 6.9 $\cdot$ 10$^{21}$ cm$^{-3}$ (2.2 and 14.2% of the total number of anions) for single crystal and nanoceramics, respectively.