Extension of the Madelung Method for the Evaluation of Lattice Sums

Abstract

The Madelung formulas for the electrostatic potential of a linear or planar Bravais lattice of ions, neutralized by a uniform distribution of charge, are extended to the lattice sums over a linear or planar Bravais lattice involving two-body interactions of the type $R^{-n}$ ($R$, interatomic distance; $n>\mathrm{}0\mathrm{}$), evaluated at points outside the lattice. The application of these generalized Madelung formulas in the evaluation of the specific face energy for neutral planes of an ionic solid of composition MX is briefly discussed.