Activation energy of ion motion in the nanodimensional lattice of LaF$_3$ superionic conductor

Quantum chemistry calculations of the intracrystalline potential relief in the nanolattice of LaF$_3$ superionic crystal that contains 1200 ions and measures 3.5 $\times$ 2.0 $\times$ 2.2 nm along the $x$, $y$, and $z$ axis, respectively, have been performed. Using the MOPAC 2012 program package, the potential relief profile has been simulated in the central part of the nanolattice for an elementary act of disordering in the lowest melting sublattice of F$_1$ ions. It has been found that the height $E_m$ of barriers that prevent the motion of F$_1$ in the dielectric phase of LaF$_3$ crystal equals 0.37 eV and decreases to 0.15 eV in the superionic state. In addition, activation energy $E_a$ of F$_1$ sublattice disordering in the dielectric and superionic states is equal to 0.16 and 0.04 eV, respectively. The profiles of the potential relief calculated on the $xy$ and $xz$ faces of the LaF$_3$ 3D nanolattice for the case when an F1 ion moves along the $x$ crystal axis in the dielectric state are presented. The corresponding energy barriers are 1.5–2.0 times lower than those at the center of the LaF$_3$ nanlattice.