Determination of the Madelung potential of ionic crystals with a polar surface by the Ewald method

Application of the Ewald method to the evaluation of the Madelung potential of a crystal slab possessing two-dimensional periodicity has been studied. The method involves a simple differential equation to be solved. When each crystallographic plane parallel to the surface contains equal amounts of opposite charges, the unique boundary condition leads to a unique solution and the correct Madelung potential in the surface region and the bulk. If the planes are not charge neutral, the boundary condition is ambiguous. A slab consisting of a dipoleless repeating unit layer satisfies a unique boundary condition. The method is applied to NaCl, CsCl, and β-alumina. A simple surface modification is shown to produce the slab bulk self-potential equal to the infinite crystal bulk self-potential.