Crystal-physical model of ion transport in nonlinear optical crystals of KTiOPO$_{4}$

The ionic conductivity along the principal axes $a$, $b$, and $c$ of the unit cell of the nonlinear-optical high-resistance KTiOPO$_{4}$ single crystals (rhombic syngony, space group $Pna 2_1$), which are as-grown and after thermal annealing in vacuum, has been investigated by the method of impedance spectroscopy. The crystals were grown from a solution-melt by the Czochralski method. The as-grown KTiOPO$_{4}$ crystals possess a quasi-one-dimensional conductivity along the crystallographic c axis, which is caused by the migration of K$^+$ cations: $\sigma_{\parallel c}$ = 1.0 $\times$ 10$^{-5}$ S/cm at 573 K. Wherein the characteristics of the anisotropy of ionic conductivity of the crystals is equal to $\sigma_{\parallel c}/\sigma_{\parallel a}$ = 3 and $\sigma_{\parallel c}/\sigma_{\parallel b}$ = 24. The thermal annealing at 1000 K for 10 h in vacuum increases the magnitude of $\sigma_{\parallel c}$ of KTiOPO$_4$ by a factor of 28 and leads to an increase in the ratio $\sigma_{\parallel c}/\sigma_{\parallel b}$ = 2.1 $\times$ 10$^{3}$ at 573 K. A crystal-physical model of ionic transport in KTiOPO$_{4}$ crystals has been proposed.