Dipole fields and electric-field gradients in their dependence on the macroscopic and microscopic crystal parameters for orthorhombic and hexagonal lattices. I

Abstract

The theory of depolarization and Lorentz tensors is presented from a unified point of view; the formalism can be applied to the calculation of dipole fields in homogeneously polarized crystals as well as electric-field gradients. The connection between depolarization tensors and the non-absolute convergence of the dipole series is pointed out and related to the problem of the convergence of the Madelung series. This way of thinking leads to a method of obtaining the Lorentz tensor by direct summation without being disturbed by the oscillations associated with the summation over spheres. Asymptotic expressions for the Lorentz factors and related quantities are derived for layer and chain structures for the case of orthorhombic and hexagonal lattices. A two-dimensional analogue of the Lorentz factor, called the Lorentz coefficient, is introduced, which describes dipole sums in two-dimensional lattices. It is shown that the difference of two lattice-point Lorentz factors of a simple orthorhombic lattice tends to a limit if the basic lattice vector in the third direction tends to zero.