PHONONS IN AMORPHOUS MATERIALS

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Abstract
The study of the propagation of phonons is an important tool to investigate the sometimes unexpected and puzzling dynamic properties of amorphous solids. At first, as a typical- example, we shall discuss the acoustic Properties of vitreous silica. In the second part of the review emphasis will be given to the anomalous low temperature properties of amorphous materials. A. Introduction. - The vibrational excitations in crystals are generally well under­ stood. In perfect crystals the vibrational motion of undamped atoms is easily decom­ posed into independent normal modes. These modes are plane-wave excitations, called phonons, and are characterized by a frequency, wavevector and polarization vector. Anharmonic effects lead to a coupling between these modes resulting in a finite life­ time. In general crystal imperfections give rise to localized excitations which can also limit the phonon lifetime through elastic or inelastic scattering. In contrast,the situation is much more complex and much less understood in non-cry­ stalline solids. The enormous simplification engendered by the periodicity of the crystalline structure is lacking. The proper normal modes are no longer plane-waves. One immediate consequence is that phonons are damped as in anharmonic crystals. This effect becomes more and more important as the phonon wavelength approaches the inter­ atomic spacing. Therefore, the dispersion curve is smeared out more and more with increasing wavevector and phonons in the original sense do not exist any more. At low frequencies, i.e. in the long wavelength limit, however, glasses, like crystals, behave as elastic continua. A well defined dispersion relation exists, and both longitudinal and transverse sound waves have been directly observed in glasses up to frequencies of about 1+0 GHz by Brillouin scattering experiments. Most of the information on the vibrational properties of amorphous solids has been obtained at wavevectors close to the origin of the "Brillouin zone". There the main difference between the properties of crystals and disordered solids lies in the fact that in the latter, selection rules which are based on the long range order are violated. As a consequence many effects which show sharp features in crystals, are considerably broadened in the amorphous solid. In this review we restrict ourselves mainly to the propagation of long wavelength phonons. In the first part of this paper we will describe the propagation of phonons in vitreous silica. In the second part of the review emphasis will be placed on the anomalous low temperature properties of glasses in general. B. Phonon Scattering in Solids. - Like the atoms of an ideal gas, the phonons in a perfect harmonic dielectric crystal are free of interaction. Thus in such a sample a sound wave would not be attenuated. In fact at low temperatures high quality die­ lectric crystals approach this ideal behaviour. Similar properties are expected for amorphous dielectrics because long wave-length phonons are not sensitive to the underlying structure. However, we will see, that amorphous networks exhibit internal degrees of freedom which give rise to absorption processes much stronger than those observed in their crystalline counterparts. Neglecting a few exceptions, the mechanisms of phonon scattering may be divided into three categories: elastic scattering, resonant absorption,and relaxation absorption.

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