Abstract Electrostatic calculations are performed in idealized β-Al 2O 3, containing domains with displaced sodium ions. The average additional energy per sodium ion is calculated for several sizes and shapes of the domains. The movement of the domain walls is considered to be essential in the process of anomalously fast conduction. The electrostatic energy contribution to the activation energy for wall movement is calculated. Some rules are formulated which might permit the selection of possible super ionic conductors by electrostatic calculations in ionic compounds.