Dipole-field sums and Lorentz factors for orthorhombic lattices, and implications for polarizable molecules

Abstract

The relationship between dipole-field sums and Lorentz tensor components in single crystals is described and used to develop a method for computing the tensor components via rapidly convergent sums of Bessel functions. The method is used to compute Lorentz factors for simple, body-centered, and base-centered orthorhombic lattices and derivatives Lorentz factors for simple orthorhombic lattices. Both the Lorentz factors and their derivatives are found to be very sensitive to lattice structure. The Lorentz-factor formalism is used to derive the equivalent of the Clausius-Mossotti relation for general orthorhombic lattices and to relate permanent molecular dipole moment to crystal polarization for the case of a ferroelectric of polarizable point dipoles. It is found that the polarization "enhancement" due to self-polarization familiar from classical theory may actually be a reduction (i.e., $P<{P}_{0}$) in consequence of negative Lorentz factors in one or two lattice directions for noncubic crystals.