Crystal structure revision and identification of Li⁺-ion migration pathways in the garnet-like Li₅La₃M ₂O₁₂ (M = Nb, Ta) oxides

Bond valence sums for the ion positions in single-crystal structure data of the garnet-like fast lithium ion conductors Li₅La₃M ₂O₁₂ (M = Nb, Ta) exhibit unusually large deviations from the ideal valences. The root-mean-square bond valence mismatch (commonly termed "global instability index" GII) and the chemical plausibility of the structure model can be significantly improved by optimizing the light atoms (oxygen and lithium) positions using a bond valence mismatch minimization procedure in the previously suggested space group I2₁3 or its centrosymmetric counterpart Ia3. Possible pathways for lithium ion migration in Li₅La₃M₂O₁₂ are identified by a bond valence analysis. Li-bond valence mismatch isosurface models for Li ⁺-ion transport pathways are found to be nearly the same in both compounds Li₅La₃Nb₂O₁₂ and Li ₅La₃Ta₂O₁₂, The characteristic feature of the three-dimensional Li₊-ion pathway network is a nonplanar square of partially occupied Li sites.