Calculation of electrostatic fields in ionic crystals based upon the Ewald method

Formulas for the electrostatic potential, field strength and field gradient due to monopoles, dipoles and quadrupoles are given, based upon the Ewald summation method. A convenient choice of the convergence parameter in the Ewald method is demonstrated in some actual calculations. A method to calculate self-consistent electrostatic fields due to self induced dipoles is evaluated. Monopole and self-consistent fields are calculated in Pb₂O₃, βMn₂O₃, FeTiO₃, MnF₃ and Pb₃O₄. The influence of the anion parameter on the electrostatic field is investigated for idealized CdCl₂ and TiO₂. Results of Madelung and induced dipole polarization energy for a series of arbitrary compounds are given. The effect of spontaneous polarization in polar crystals is discussed.