Mixed Alkali Effect in Crystals of $\beta$- and ${\beta }^{\prime \prime }$-Alumina Structure

We develop a microscopic model for the mixed alkali effect in crystals of the $\beta$- and ${\beta }^{\prime \prime }$-alumina type, which is based on the formation of certain mobile defects and the fact that different types of mobile ions have a different preference to become part of these defects. Our computer simulations for the ionic conductivity are in excellent agreement with experimental data. Our model predicts a common shape of the rescaled conductivity isotherms independent of temperature and the specific type of probe, which is also in agreement with the available experimental results.