On the Linear Dielectric Properties of Finite Ionic Crystals

The basic equations for determining the linear dielectric constants of a finite ionic crystal with arbitrary basis are derived and shown to be equivalent to those obtained by Born and Huang for an infinite crystal. The derivation is based on the assumption that the relaxation of the interionic spacing at the surface of the crystal merely extends over a few layers of ions. The approach used in these calculations is extended to the description of certain long-wavelength oscillations with shape-dependent frequencies.