Fig. 5: Correlated sodium motions within Na slabs.

a Arrhenius plot of Na+ diffusivity in P2 and P3-Na2/3Ni1/3Mn2/3O2 (chain ordering) from AIMD simulations. The error bars are the standard deviation of linear fit of MSD–Δt curves. The intralayer Na+ diffusion pathway in b P3-Na2/3Ni1/3Mn2/3O2 from AIMD at 800 K. The self-part of the van Hove correlation function (Gs) for sodium in c P2- and d P3-Na2/3Ni1/3Mn2/3O2. The distinct part of the van Hove correlation function (Gd) for sodium ions in e P2- and f P3-Na2/3Ni1/3Mn2/3O2. Both Gd and Gs are functions of the average Na–Na pair distance (r) and time step after thermal equilibration at 800 K. The isosurface level of both is set to 0.001.