Vibrational Infrared and Raman Spectra of Non-Metals

Abstract

The vibrational properties of crystals determine the photon infrared absorption, inelastic neutron scattering and, to a large extent, inelastic photon scattering by phonons, i.e., Raman scattering. The interpretation of infrared and Raman spectra requires, therefore, an understanding of the basic features of lattice dynamics. The quantum theory of solids describes the crystal properties in terms of elementary excitations and their mutual interactions. Dynamic properties are represented by phonons (lattice vibrations) and their interactions mainly with other phonons (anharmonicity), electrons (electron-phonon coupling), and photons (interaction with radiation). This characterizes the scope of the article. Its emphasis is on the interrelation between theory and experiment, i.e., on the microscopic or model interpretation of experimental spectra.Work on infrared absorption and Raman scattering of non-metallic solids was summarized twenty years ago in two review articles in this Encyclopedia by LECOMTE (1958) and by MIZUSHIMA (1958). Since then, many important new experimental data have become available, thanks to very refined techniques for measuring spectra of pure and imperfect single crystals. Furthermore, the theory of the interactions of phonons and photons has been much improved, stimulated by the remarkable development of the theory of lattice vibrations and the mathematical techniques of many-body physics.In this article we describe the dispersion and absorption of infrared radiation and Raman scattering in non-metallic crystals, both perfect and containing point defects. At present, quantitative calculations are usually restricted to diatomic crystals, especially those with simple structures such as the alkali halides or germanium and its homologues, since our knowledge of lattice vibrations is still rather poor for polyatomic and low-symmetry crystals. The theory of lattice vibrations, as reviewed by COCHRAN and COWLEY (1967) in Vol. XXV /2a of this Encyclopedia, constitutes the background and the natural starting point for our investigations. There are other recent reviews by LUDWIG (1967), COCHRAN (1971), MARADUDIN et al. (1971), SINHA (1973), and several articles in: HORTON and MARADUDIN (eds., 1974). A summary of the developments during the last few years is given in Chap. B.An important part of the theory of lattice vibrations is the construction of models. A good example is the so-called shell model for phonons (see Sect. 4) which describes the adiabatic linear electron-ion interaction in terms of localized charges and coupling constants. This provides a natural explanation of some long-range ion-ion forces in insulators in terms of induced dipole forces. Anharmonic extensions of this shell model and its modifications seem very desirable, and first attempts in this direction are discussed.Models can often give a qualitatively and sometimes quantitatively correct description of certain processes in terms of a few parameters. They provide, therefore, an orientation for microscopic approaches. Furthermo...

Structural and Vibrational Properties of C60 and C70 Fullerenes Encapsulating Carbon Nanotubes

“…The Raman intensities can be calculated within the framework of the nonresonant bond polarizability model [27]. The basic assumption of the bond polarizability model is that the optical dielectric susceptibility of the material or molecule can be decomposed into individual contributions, arising only from the polarizability α ij b of bonds b between nearest neighbor atoms.…”

“…n , are linked to the Raman susceptibility of modes (see [27] for the detailed formalism) and are given by:…”

Anharmonic adlayer vibrations on the Si(111):H surface

“…Explicit expressions for the contributions of these diagrams are given in Ref. 76 ͓apart from ͑f͒ which may be easily evaluated following the rules given therein͔͒. In the temperature range where the infrared absorption experiments have been carried out, the thermal occupation number of the stretching mode is negligibly small.…”

Experimental and numerical exploration of intrinsic localized modes in an atomic lattice

“…Experiments on molecular overtone and combination bands by means of sensitive absorption, thermal lensing, and photoacoustic spectroscopy, particularly involving X-H vibrations, have been interpreted successfully in terms of normal modes for low-lying vibrational states and local modes for high-lying states. In condensed matter lattices, vibrational energy localization can be produced by lattice irregularities, and such defect-induced localized modes, which appear above the plane wave spectrum, in the frequency gaps between the plane wave branches, or in the acoustic spectrum, have been studied in great detail both theoretically [8][9][10][11][12] and experimentally [13][14][15]. For nonlinear atomic lattices, the study of localized vibrational energy has a much shorter history.…”