  Solid-state ionic conduction is a key enabler of electrochemical energy
storage and conversion. The mechanistic connections between material
processing, defect chemistry, transport dynamics, and practical performance are
of considerable importance, but remain incomplete. Here, inspired by studies of
fluids and biophysical systems, we re-examine anomalous diffusion in the iconic
two-dimensional fast-ion conductors, the $\beta$- and
$\beta^{\prime\prime}$-aluminas. Using large-scale simulations, we reproduce
the frequency dependence of alternating-current ionic conductivity data. We
show how the distribution of charge-compensating defects, modulated by
processing, drives static and dynamic disorder, which lead to persistent
sub-diffusive ion transport at macroscopic timescales. We deconvolute the
effects of repulsions between mobile ions, the attraction between the mobile
ions and charge-compensating defects, and geometric crowding on ionic
conductivity. Our quantitative framework based on these model solid
electrolytes connects their atomistic defect chemistry to macroscopic
performance with minimal assumptions and enables mechanism-driven
'atoms-to-device' optimization of fast-ion conductors.
