Methods of Calculating the Crystalline Electric Field

Abstract

Two convenient methods are developed for calculating the coefficients of expansion of the crystalline potential in spherical harmonics. One consists in extending Evjen's elementary method of obtaining Madelung's constant, dividing the lattice into multipoles, and summing their contributions in an elementary way, and the other is an extension of Bertaut's Fourier method of obtaining the electrostatic lattice energy of a point-charge lattice and that of a point-dipole lattice. For the latter, two slightly different methods are proposed. Applications to NaCl-type and CsCl-type lattices and to FeF ₂ and CoF ₂ lattices are given, and the merits and dismerits of the methods are discussed.