Extended Data Fig. 4: Ion diffusion in Ag β-alumina.
From: Defect-driven anomalous transport in fast-ion conducting solid electrolytes
a, tMSD of mobile ions. b, exponent of tMSD vs. time lag, plotted against the time-averaged displacement. As for Na β-alumina, the exponent does not reach unity until displacements are ≥ distances between defects. In b, the horizontal guide is the Fickian limit t1, and the vertical line is one unit cell (5.6 Å, 2 hops). c, Time slices of the distribution of ion displacements Δx along [100] at 300 K. d, Distributions of ion displacements Δx along [100], each rescaled by its variance σΔx. Laplace and Gaussian distributions are shown as black and grey dotted lines, respectively. e, The probability of an ion remaining within 1.7 Å (<1 hop, dashed) or 4.6 Å (<2 hops, solid) of an initial position. The relative change in the timescale due to varying the distance cutoff by 0.1 Å is ≤10%. f, Diffusion kernel correlation CD. As for Na β-alumina, CD peaks between one-hop and two-hop relaxation times at all simulated temperatures. In b and f, short-time checks of the ballistic limits (dashed), tMSD ∝ t2 and CD → 2, respectively, used 100-ps trajectories recorded every 1 fs.
