Characteristics of the Li$^+$-ion conductivity of Li$_{3}R_{2}$(PO$_{4}$)$_{3}$ crystals ($R$ = Fe, Sc) in the superionic state

The characteristics of Li$^+$-ion conductivity $\sigma_{dc}$ of structural $\gamma$ modifications of Li$_{3}R_{2}$(PO$_{4}$)$_{3}$ compounds ($R$ = Fe, Sc) existing in the superionic state have been investigated by impedance spectroscopy. The type of structural framework [R$_{2}$P$_{3}$O$_{12}$]$_\infty^{3-}$ affects the $\sigma_{dc}$ value and the $\sigma_{dc}$ activation enthalpy in these compounds. The ion transport activation enthalpy in $\gamma$-Li$_{3}$Fe$_{2}$(PO$_{4}$)$_{3}(\Delta H_{\sigma}$ = 0.31 $\pm$ 0.03 eV) is lower than in $\gamma$-Li$_{3}$Fe$_{2}$(PO$_{4}$)$_{3}(\Delta H_{\sigma}$ = 0.36 $\pm$ 0.03 eV). The conductivity of $\gamma$-Li$_{3}$Fe$_{2}$(PO$_{4}$)$_{3}(\sigma_{dc}$ = 0.02 S/cm at 573 K) is twice as high as that of $\gamma$-Li$_{3}$Sc$_{2}$(PO$_{4}$)$_{3}$. A decrease in temperature causes a structural transformation of Li$_{3}R_{2}$(PO$_{4})_{3}$ from the superionic $\gamma$ modification (space group $Pcan$) through the intermediate metastable $\beta$ modification (space group $P 2_1/n$) into the “dielectric” $\alpha$ modification (space group $P 2_1/n$). Upon cooling, $\sigma_{dc}$ for both phosphates decreases by a factor of about 100 at the superionic $T_{\operatorname{SIC}}$ transition. In Li$_{3}$Fe$_{2}$(PO$_{4})_{3}$ $\sigma_{dc}$ gradually decreases in the temperature range $T_{\operatorname{SIC}}$ = 430–540 K, whereas in Li$_{3}$Sc$_{2}$(PO$_{4}$)$_{3}$ $\sigma_{dc}$ undergoes a jump at $T_{\operatorname{SIC}}$ = 540 $\pm$ 25 K. Possible crystallochemical factors responsible for the difference in the $\sigma_{dc}$ and $\Delta H_\sigma$ values and the thermodynamics and kinetics of the superionic transition for Li$_{3}R_{2}$(PO$_{4}$)$_{3}$ are discussed.