Fig. 2 : The Li–O polyhedra, topological pathways and comparison of C_Li, C_e and experimental ionic conductivity (σ_exp) in cubic garnet structure.

a Li–O polyhedra in the crystal structure. b Different types of ions and pathways identified through percolation analysis. c The comparison of the varying trends of \({C}_{{\rm{Li}}}\), \({C}_{{\rm{e}}}\) and the experimental ionic conductivity (\({\sigma }_{\exp }\)) relative to Li content (\({x}_{{\rm{Li}}}\)) in garnet structures. The simulation conditions are \({E}_{{\rm{nn}}}\) = 0.06 eV, \(\triangle {E}_{{\rm{site}}}\) = 0.12 eV and T = 300 K. The insert plot provides a more direct comparison of \({C}_{{\rm{e}}}\) and \({\sigma }_{\exp }\) after normalization, demonstrating a high R² value of 0.901. The values of \({\sigma }_{\exp }\) are adapted from the following compositions: Li₃Er₃Te₂O₁₂, Li₅La₃Bi₂O₁₂, Li₆La₃Zr_1.5W_0.5O₁₂, Li_6.2La₃Zr_1.2Sb_0.8O₁₂, Li_6.4La₃Zr_1.4Ta_0.6O₁₂, Li_6.5La₃Zr_1.75Te_0.25O₁₂, Li_6.75La₃Zr_1.75Ta_0.25O₁₂, Li₇La₃Zr₂O₁₂ and Li_7.5La_2.5Sr_0.5Zr₂O₁₂, all of which are measured at room-temperature except for Li₃Er₃Te₂O₁₂ (measured at 450 °C) due to the measurement difficulty of its negligible room-temperature ionic conductivity^13,16,39.