In β ′ -alumina, the dominant conduction mechanism involves the migration of oxygen ions (O 2-) through the crystal lattice, utilizing oxygen vacancies as diffusion paths. In β ′′ -alumina, the conduction mechanism revolves around the migration of sodium ions (Na + ) through the crystal lattice, facilitated by the presence of oxygen vacancies. In addition to the oxygen, repulsive forces between Na ions were found to play a crucial role in reducing the activation energy required for ion diffusion, as observed by Sato and Kikuchi and further emphasized by Wang and Pickett .