X-ray-scattering study of the fast-ion conductorβ′′-alumina

The ion-ion correlations and a new crystal-structure determination of ${\beta }_{\mathrm{Na}}^{\prime \prime }$- and ${\beta }_{\mathrm{K}}^{\prime \prime }$-alumina reveal that the conducting ions are distributed between two independent sites instead of one given by previous work: Beevers-Ross-anti-Beevers-Ross and mid-oxygen with an occupation ratio of 60% and 40%, respectively. The two-dimensional short-range order is found to correspond to a theoretical composition of 1.66 ions per unit plane cell. A relation is established between three parameters: the coherence length of the SRO model ($\xi$), the thickness of the conduction slab ($E$), and the resistivities ($\rho$). It is shown that ${(\xi , E, \rho )}_{\mathrm{Na}}>{(\xi , E, \rho )}_{\mathrm{K}}$. The gradual change in the activation energies, observed for ${\beta }_{\mathrm{Na}}^{\prime \prime }$ and ${\beta }_{\mathrm{K}}^{\prime \prime }$ when the temperature is increased, is interpreted in relation with the decrease of both $E$ and $\xi$ in the same temperature range. Finally, ${\beta }^{\prime \prime }$-alumina, when compared to $\beta$-rich alumina with the same compensation mechanism and composition, exhibit higher conductivities due to larger conduction channels.