The Theory of the Dielectric Constant of Ionic Crystals, I

We worked out the dielectric constants of "0 and " of the alkali-halide crysral on the basis of the quantum theory of solids. We have used the variational method of Slater and Kirkwood in our energy-calculations and adopted Landshoff's method for evaluating the exchange integrals among the non-orthogonal wave functions. The relation among the vatious theories, due to Shockley, Mott and Frohlich, of the dielectric constant of ionic crystal have been clarified from the viewpoint of our theory. The numerical results for LiF are in good accordance with the experiment. § 1. Introductionl ) Many of the characteristic properties of polar crystals, i.e., the behaviour of the conduction electrons or the existence of defects in the lattice will, after all, sensitively depend on the dielectric properties of the crystal. So we see it is essentially required to elucidate the dielectric properties of the mentioned crystals in detail on the basis of the quantum theory of solids, since the available theories of dielectric properties are usually based on the rather phenomenological considerations. As a preliminary to the general formulation of the theory we shall here work quantum-mechanically the simplest case of the dielectric constant of ionic crystals in the homogeneous external fields of both high frequency and static natures. As is well-known in the classical theory, the relation between the polarizability (a) of an ion pair and the dielectric constant (xo) for high frequency field is represented by one or the other of the following two formulae according to the assumptions of the effective field I!',tI' around each ion of the crystal. Namely, we have