The calculation of the electrostatic lattice energy of polar crystals by slice-wise summation, with an application to BeO

In the calculation of the electrostatic part of the lattice energy of polar crystals by slice-wise summation, as occurs in the Madelung method, an extra energy term, £„,„, is needed. This term is due to a double limit to infinity, one parallel to the slices, the other perpendicular to them. It was found that ECOTT = — 2 πμ/ V, where μ is the dipole moment of the slice and V the unit cell volume. The method is applied to BeO. Theory When the Madelung method (1918) is applied to polar crystals to calculate electrostatic lattice energies, some difficulties are encountered. As described before (Hartman, 1978) the crystal structure is divided into slices of thickness dm. The lattice energy E„ is calculated as E„ = Esl + £,„ (1) where Esl is the slice energy and £aU is the attachment energy defined as