PHONON-PHONON INTERACTIONS IN MOLECULAR CRYSTALS STUDIED BY ULTRASONIC METHODS

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PHONON-PHONON INTERACTIONS IN MOLECULAR CRYSTALS STUDIED BY

ULTRASONIC METHODS

Bernard Perrin, F. Michard

To cite this version:

Bernard Perrin, F. Michard. PHONON-PHONON INTERACTIONS IN MOLECULAR CRYSTALS STUDIED BY ULTRASONIC METHODS. Journal de Physique Colloques, 1981, 42 (C6), pp.C6- 131-C6-133. �10.1051/jphyscol:1981639�. �jpa-00221575�

JOURNAL DE PHYSIQUE

CoZZoque C6, suppZ6ment au n012, Tome 42, de'cembre 1981 page C6- 131

PHONON-PHONON I N T E R A C T I O N S I N MOLECULAR CRYSTALS S T U D I E D BY ULTRASONIC METHODS

B. Perrin and F. Michard

Dgpartement de Recherches Physiques, Tour 22, Universite' P. e t M. Curie, 75230 Paris Cedex 05, France

Abstract.

-

In this work it is shown that this moZecuZar r e z a x a t i o n may be taken into account in the framework of Akhieser's theory and a relation between sound absorption and relaxation time is given.

Results obtained through acousto-optic interaction on ionic-mole- cular crystals are also mentioned.

1. Introduction. -Internal vibrations of molecules are quite unaffec- ted by lattice effects in molecular crystals so that there are only weak interactions between internal and external modes of vibrations of the molecules in these crystals. This weakness entails the existence of slow relaxation processes during the thermalization of the whole set of phonons after any perturbation of the thermal eauilibrium. The times involved in these processes lying in the ultrasonic frequency range, an ultrasonic relaxation may be expected in molecular crystals.

This 'rmolecular relaxation", due to a slow transfer of energy between the internal and external degrees of freedom of molecules, has been extensively studied in molecular gases and liquids and Liebermann ¹ was the first to suggest the extension of this phenomenon to the solid state. Since his pioneering work, some experimental studies led on organic molecular compounds have clearly shown the existence of a relaxation process which underliesa special ultrasonic behavior of mo- lecular crystals among dielectric ones. We present in this work recent theoretical and experimental developments concerning this field.

2. Theoretical aspect. - The present status of the theory in this field is unsatisfying in several points. For example, ~ i c h a r d s ~ ~ r e l a t i o n

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981639

JOURNAL DE PHYSIQUE C6- 132

given by

is used to relate the sound absorption a and the relaxation time r ; here 61 and s are respectively the angular frequency and the velocity of the sound beam, C and Cv are the specific heats at constantpressu-

P

re and constant volume and CI is the specific heat associated with the internal degrees of freedom of molecules. This expression has been derived considering specific properties of gas and liquid phases and its use in the solid state seems questionable. Yoreover no mention has never been made of the fact that, although molecular crystals belong to the family of dielectric crystals, the molecular relaxation does not seem predicted by the classical theories of ultrasonic attenuation in dielectric crystals. The answer to these two points may be found by considering a solid state point of view (in contrast to Liebermann's approach). The molecular relaxation times being greater than the mean lifetime of thermal phonons,this phenomenon occurs in a hydrodynamical regime of ultrasonic propagation and may be studied with the Boltzmann equation approach. The phonon collision operator involved in this approach is usually simplified by the collision time approximation which means that all 'the phonons have the same status during the ther- malization and which leads to the classical expression of the Akhieser loss 3

.

aR is a relaxation term given by

Here 'ijk~ are the elastic constants, PkL the thermal expan- sion tensor, e and K components of the polarization e and norma- +

i + j

lized wave vector K of the sound beam, T the temperature and p the density. For isotropic and cubic symmetries this expression may be reduced to

which differs from Richards' expression by the existence of the

structure factor resulting from the accounting for the properties of the solid state. Moreover for symmetries lower than cubic it is impossible to introduce in a natural way the quantity

(' ^iPCV)

in the expression of aR

.

3. Experimental aspect.-Most of the ultrasonic studies on molecular compounds which have been reported up to now have been led with the classical pulse echo method. In fact, this method does not seemadapted to this problem because a careful analysis of the frequency dependence of the absorption needs to use high frequencies (> 100 MHz) and more- over the attenuation is expected to be very large. On the other hand the light diffraction by elastic waves seems a suitable tool for this study whether ultrasonic waves are used (Bragg diffraction) or thermal waves (Brillouin scattering). The interest of light diffraction by elastic waves has been emphasized by an ultrasonic study 5-6 on the isomorphous cubic crystals Sr(N03)2 , Ba(NO3I2 and Pb(N03)2 (which may be termed ionic-molecular crystals) for which the ultrasonic absorp- tion has been measured for a large range of frequency and temperature.

In these compounds, a relaxation process has been identified which can be viewed as a molecular relaxation; thus this study seems to be the first experimental evidence of the molecular relaxation in ionic- molecular compounds and proves that this phenomenon is closely connec- ted with the "molecular character" of a crystal. An other consequence of this study is that the analysis of experimental results has shown that relation (3) offers a better fit than Richards'expression for ultrasonic measurements in molecular compounds.

IXFERENCES

.

1. -L.N. Liebermann, Phys. Rev.

113,

11,

5.-F. Michard and B. Perrin, Phonon Scattering in Condensed Matter, edited by H.J. Maris (Plenum Publishing Corporation, 1980)p. 141 6. -F. Plichard, to be published