DFT Study of the Role of Al³⁺ in the Fast Ion-Conductor Li_{7–3<i>x</i>}Al³⁺_<i>x</i>La₃Zr₂O₁₂ Garnet

Abstract

We investigate theoretically the site occupancy of Al³⁺ in the fast-ion-conducting cubic-garnet Li_7-3<i>x</i> Al³⁺_<i>x</i> La₃Zr₂O₁₂ (<i>Ia</i>-3<i>d)</i> using density functional theory. By comparing calculated and measured ²⁷Al NMR chemical shifts an analysis shows that Al³⁺ prefers the tetrahedrally coordinated 24<i>d</i> site and a distorted 4-fold coordinated 96<i>h</i> site. The site energies for Al³⁺ ions, which are slightly displaced from the exact crystallographic sites (i.e., 24<i>d</i> and 96<i>h</i>), are similar leading to a distribution of slightly different local oxygen coordination environments. Thus, broad ²⁷Al NMR resonances result reflecting the distribution of different isotropic chemical shifts and quadrupole coupling constants. From an energetic point of view, there is evidence that Al³⁺ could also occupy the 48<i>g</i> site with its almost regular octahedral coordination sphere. Although this has been reported by neutron powder diffraction, the NMR chemical shift calculated for such an Al³⁺ site has not been observed experimentally.