Lattice dynamics of thin ionic slabs. II. The long-range forces

The Coulomb interaction is calculated for thin ionic slabs of any structure and orientation. For ions lying on different planes, parallel to the plane of the slab, the direct-space double sum is transformed into a rapidly converging double sum in reciprocal space only, while for ions lying on the same plane, a two-dimensional version of Ewald's method is used. Finally we comment on the macroscopic field associated with long-wavelength vibrations of an infinite lattice on the basis of a two-dimensional summation method.