Optical phonons of small crystals

Abstract

The long wavelength optical phonons of ionic crystals give rise to dipole-dipole forces, whose long range nature causes the vibrations to depend on the size and shape of the crystal sample. This dependence affects significantly most spectral properties of all crystals whose dimensions are of the order of or shorter than the wavelength of reststrahlen (characteristically several tens of micrometres). In experimental work in which the infrared properties of ionic crystals were examined on small samples, in powder form or in colloidal suspension or in the shape of thin layers, the peculiarities due to size and shape were not always properly recognized. The infrared frequencies of the material which are derived with disregard to these peculiarities may be in error by some tens of wavenumbers. In the experimental section of the review we interpret the general characteristics of the experimental spectra and analyse in detail some representative infrared measurements in the light of the theory. The theory of optical vibrations which takes account of the finiteness of the specimen is formulated firstly in general terms and then by special reference to samples which have one, two or three dimensions short (slab, cylinder and sphere-like geometries). Synthetic spectra are drawn whose characteristic features are interpreted in terms of bulk and surface modes. In the theory retardation effects, i.e. the coupling between lattice and electromagnetic waves, are also included, and the quantized modes are combinations of these, i.e. polaritons. For tiny crystallites of such size that the characteristic infrared radiation wavelength is much larger than the sample size, retardation effects can be neglected. The theory becomes much simpler and the spectrum sharper. Some of the absorption peaks are due to optical surface modes, and their positions are simply related to the characteristic shapes of the crystallites. The theory is so presented as to provide a practical aid in the correlation of spectra with sample shape. The consequences on the spectra of other, less common variables of experiments, for example, the refractive index of the environments, are also calculated. The rôle of optical surface modes in Raman - and electron - scattering is then discussed. Simple geometrical arrangements of small sized crystals enable the spectra of surface modes to be scanned.