Optical phonons of small crystals
- 1 January 1970
- journal article
- Published by IOP Publishing in Reports on Progress in Physics
- Vol. 33 (1), 149-196
- https://doi.org/10.1088/0034-4885/33/1/304
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.Keywords
This publication has 101 references indexed in Scilit:
- Infrared Absorption in Small KCl CrystalsPhysical Review B, 1969
- Optical Modes of Vibration in an Ionic Crystal Sphere*Journal of the Optical Society of America, 1968
- Retardation Effects on the Limiting Phonon Frequencies of Finite-Size Ionic CrystalsPhysical Review B, 1967
- Magnetostatic Modes in the Canted Antiferromagnet MnCO3Physical Review B, 1966
- Optical Phonons in Finite CrystalsPhysical Review Letters, 1966
- Lattice Vibrations in Ionic Crystals of Finite SizePhysical Review Letters, 1964
- Zur Ultrarotdispersion der Alkali-HalogenideThe European Physical Journal A, 1960
- The Infrared and Ultraviolet Absorption Spectra of Cytosine and Isocytosine in the Solid State1,2Journal of the American Chemical Society, 1952
- Das ultrarote Spektrum von MagnesiumoxydThe European Physical Journal A, 1934
- Messungen am NaCl und KCl im Spektralbereich ihrer ultraroten EigenschwingungenThe European Physical Journal A, 1931