Fig. 2: Atomistic simulations of grain and grain boundary diffusion.

a Comparison of La-La pair distribution function, g(r), for Li_6.25La₃Zr₂O₁₂ at 700 K between the crystalline cubic structure and a representative disordered model (ρ = 4.77 g cm⁻³), showing the breakdown of long-range order for the disordered representation of high-angle grain boundaries. b, c Normalized histograms of b E_a and c log (D₀) for individual Li⁺ comprised of all disordered models for Li_7−xLa₃Zr₂O₁₂ with x = 0.25, 0.50, and 0.75 (see Supplementary Note 3 for details). The computed E_a and D₀ for cubic Li_6.25La₃Zr₂O₁₂ are labeled as brown vertical lines in b, c. The mode of the E_a histogram is highlighted in b and corresponds to 0.52 eV, near the center of the lower-energy peak (blue). d Histogram of experimental LLZO E_a values reported in the literature, taken from the references in Supplementary Table 3 of Supplementary Note 4.