Mobility of ion carriers in piezoelectric Li$_{2}$B$_{4}$O$_{7}$ crystals

Impedance measurements of a Li$_{2}$B$_{4}$O$_{7}$ single crystal with Ag electrodes have been performed in the frequency range of 1–3 $\times$ 10$^7$ Hz at room temperature. A Li$_{2}$B$_{4}$O$_{7}$ crystal (sp. gr. $I$4$_1cd$, $Z$ = 8) has been oriented along the c crystallographic axis. Contributions from the crystal bulk and the crystal/electrode interface are distinguished from the impedance hodograph of the Ag|Li$_{2}$B$_{4}$O$_{7}$ |Ag system. The structural mechanism of lithium-ion transport in Li$_{2}$B$_{4}$O$_{7}$ crystals is discussed. Through conduction $\sigma_{\operatorname{dc}}$ = 2.3 $\times$ 10$^{-9}$ S/cm, carrier (vacancy $V_{\operatorname{Li}}^-$) mobility $\mu_{\operatorname{mob}}$ = 6 $\times$ 10$^{-10}$ cm$^2$/(s V), and their concentration $n_{\operatorname{mob}}$ = 2.4 $\times$ 10$^{19}$ cm$^{-3}$ (0.14% on the amount of lithium in the lattice) are calculated based on the electrical and structural data.