Firstly, and perhaps most importantly, we are simulating an infinite, pristine, single crystal, by imposing periodic boundary conditions over the unit cell of -LPS. Because SAE can only distinguish between sites with an inequivalent average local EFG , if Li hopping events only occur between sites with equivalent average EFGs (! Q (t 1 ) = !Q (t 2 )), the hACF ! Q i will not exhibit the characteristic exponential decay. While this would usually be associated with vanishing mobility (which is not the case in -LPS as shown in Figure ), it can also be due to insensitivity of SAE with respect to motion between equivalent !Q . Thus, if there are a few sets of mutually inequivalent sites with similar !Q one would obtain a partially averaged !Q , which is the weighted average between the !Q for each of these sites. A single crystal, therefore, will always be such a case, because all of the sites have the same predominant orientation throughout the simulation. A slow decay, beyond the microsecond timescale, would be dominated in a polycrystalline material by Li motion across grain boundaries of differently oriented crystalline grains. In this case, the ⌧ SAE decay could be modeled as a function of the Li diffusion coefficient and grain size distribution.