On the ionic conduction in β-alumina: Potential energy curves and conduction mechanism

Abstract

Potential energy curves for various carrier ions in β‐alumina have been calculated. All ions except the carrier ions (Li⁺, Na⁺, Ag⁺, K⁺, Rb⁺, Cs⁺) were assumed fixed in their equilibrium positions. These ionic positions were taken from Roth’s work. In our calculation the motion of carrier ions is restricted on lines of the two dimensional hexagonal network. We show that the site energy difference between the anti‐Beevers–Ross site and the Beevers–Ross site is approximately 2 eV in stoichiometric crystals. In nonstoichiometric crystals the extra carrier ions may be paired to form interstitialcy pairs. The potential energy barriers for the in‐phase motion of the interstitialcy pairs are found to be comparable to the experimental activation energies. Attempt frequencies have been calculated, and a simple random walk model is used for the electrical conductivities.