Effective Ionic Charge in Alkali Halides

Abstract

An expression is derived for the effective charge in the Born-Szigeti equation for the dielectric constant of ionic crystals with the NaCl structure. The derivation is based on a coupled oscillator model in which the lattice vibrations are coupled to the electronic motions within the ions. The deviation of the ionic charge from its nominal value is found to be proportional to the difference in electronic polarizability between the positive and negative ions. Agreement between theory and experiment is satisfactory. Secondary effects on the index of refraction and the reststrahl frequency are calculated. The model is in semiquantitative agreement with the observed dipole moments of alkali halide molecules.