First-principles modeling of lithium ordering in the LLTO (LixLa2/3-x/3TiO3) superionic conductor

Ab initio periodic quantum-mechanical calculations were performed on selected ordered schemes of the La-Li-square (vacancy) distribution in the Li0.5La0.5TiO3 and Li0.3125La0.5625 square 0.125TiO3 phases. Perovskite superstructures were built on the basis of Z (formula units/primitive cell) = 4 and 8 in the first case (symmetries C2me to Im), and Z = 16 in the second one (Pm), with initial configurations from the experimental P4/nbm tetragonal structure of Li0.3La0.567TiO3. The B3LYP functional (hybrid DFT/Hartree-Fock) was used, with an all-electron basis set of atomic orbitals (CRYSTAL06 code). For each ordered model, maps of the electrostatic potential were computed in the ionized unrelaxed superstructure, in order to study the field acting on Li+ ions. The complete structure was then fully relaxed by energy minimization with respect to all atomic positions (78 atoms/cell in the Z = 16 case). The anti-phase octahedral tilt was reproduced for A-type cages with mixed La-Li composition in the same (001) layer, but not for full La-Li ordering in different layers. The optimized Li positions were found to lie in different sites within the A-cavities and depend significantly on the local environment. Experimental results of the average tetragonal LLTO structure could thus be explained, by finding correspondences between the observed Li sites and specific low-energy lithium ordered configurations.