Theoretical study of defect-mediated ionic transport in Li, Na, and K β and β′′ aluminas

Alkali-metal $\ensuremath{\beta}/{\ensuremath{\beta}}^{\ensuremath{'}\ensuremath{'}}$ aluminas are among the fastest ionic conductors, yet little is understood about the role of defects in the ion transport mechanism. Here, we use density functional theory (DFT) to investigate the crystal structures of the $\ensuremath{\beta}$ and ${\ensuremath{\beta}}^{\ensuremath{'}\ensuremath{'}}$ phases and their vacancy and interstitial defects. We find that charge transport is likely to be dominated by alkali-metal interstitials in $\ensuremath{\beta}$ aluminas and by vacancies in ${\ensuremath{\beta}}^{\ensuremath{'}\ensuremath{'}}$ aluminas. Lower bounds for the activation energy for diffusion are found by determining the minimum-energy paths for defect migration. The resulting migration barriers are lower than the experimental activation energies for conduction in Na $\ensuremath{\beta}$ and ${\ensuremath{\beta}}^{\ensuremath{'}\ensuremath{'}}$ aluminas, suggesting a latent potential for optimization. The lowest activation energy of about 20 meV is predicted for correlated vacancy migration in K ${\ensuremath{\beta}}^{\ensuremath{'}\ensuremath{'}}$ alumina.