Within the conduction layer, three different cationic sites exist: anti-Beevers-Ross (aBR), Beevers-Ross (BR), and mid-Oxygen (mO) (Fig. )) . The sites are different based on the local oxygen environment, such as BR is formed by three top and three bottom oxygens, and aBR is formed by two oxygens (one top and one bottom). These sites are crucial in facilitating cationic diffusion and ion hopping within the material, as presented in Fig. ). Occupancy at these sites and the diffusion mechanism have been subjects of intense debate and investigation . Kummer conducted systematic experimental studies on various monovalent counterparts (Li + , Na + , Ag + , K + , Rb + ) of β-alumina. The studies revealed that the ionic radius, particularly between Na + and Ag + , was suitable for ion diffusion within the β-alumina framework (Fig. )) . This observation suggests the existence of an optimal cation size that maximizes diffusion within the material.