These MD simulations revealed the importance of non-stoichiometric composition in enhancing cationic diffusion and observed a transition from low-temperature hopping transport to a higher-temperature liquid-like transport . Further MD studies by Thomas and Zendejas focused on Na-β ′′ -alumina and provided additional atomistic insights into the diffusion of Na + ions, including correlation effects and the presence of mobile and immobile Na + ions in the diffusion mechanism.