Lattice Vibrations and Optical Waves in Ionic Crystals

Abstract

LATTICE vibrations in ionic crystals are usually treated with the unretarded Coulomb forces. Despite some discussions in the existing literature^1,2, the precise nature of the effect due to retardation remains unknown. We have found that explicit solution of the problem is possible for diatomic crystals with optical isotropy, mainly because the lattice vibrations concerned are very long waves, for which the lattice behaviours can be described by the following equations³: where w is the displacement of the positive ions relative to the negative, multiplied by the square root of the ratio of the reduced mass of the ions to the lattice cell volume; P and E are the dielectric polarization and the electric field; ɛ₀, ɛ_∞ and ω₀ are the static and high-frequency dielectric constants and the infra-red dispersion frequency (circular).