PHONON DAMPING IN CRYSTALLINE AND AMORPHOUS SOLIDS AT HYPERSONIC FREQUENCIES

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PHONON DAMPING IN CRYSTALLINE AND AMORPHOUS SOLIDS AT HYPERSONIC

FREQUENCIES

R. Vacher, J. Pelous

To cite this version:

R. Vacher, J. Pelous. PHONON DAMPING IN CRYSTALLINE AND AMORPHOUS SOLIDS AT HYPERSONIC FREQUENCIES. Journal de Physique Colloques, 1981, 42 (C6), pp.C6-125-C6-127.

�10.1051/jphyscol:1981637�. �jpa-00221573�

JOURNAL DE PHYSIQUE

CoZZoque C6, suppZ6ment au n ^'12, Tome 42, d6eembre 1981 page ^C6-125

PHONON DAMPING I N C R Y S T A L L I N E AND AMORPHOUS S O L I D S A T HYPERSONIC FREQUENCIES

R. Vacher and J. Pelous

Labomtoire de SpectromQtrie RayZeigh BriZZouin (ERA 460), Universitg des Sciences e t Techniques du Languedoc, PZace E. BataiZZon, 34060 MontpeZZier Cedex, France

Abstract.- We present new Brillouin scattering measurements, for temperature ranging from 1 K to room temperature in a broad range of insulating solids

(crystalline and amorphous solids). We analyse the temperature dependence of the attenuation of longitudinal phonons (frequency higher than 15 BIZ) on the basis of the physical processes responsible for the phonon damping.

Measurements of acoustic attenuation in solids for frequencies higher than 10 GHz are scarce, because the large attenuation at these frequencies makes the ul- trasonic experiments difficult, excepted at low temperatures. Brillouin scattering, which is the appropriate tool for such measurements, has been used in a broad range of insulating solids for temperatures ranging from 1 K to 300 K. We have studied io- nic and molecular crystals, inorganic glasses and amorphous polymers. Our purpose is to bring out the laws for the temperature variation of the damping, to compare them with those observed at lower frequencies, and to analyse these results on the basis of the theoretical models describing the physical processes responsible for the at- tenuation.

( i ) Ionic crystaZs. In such materials, the acoustic damping a is known to originate from anharmonic phonon-phonon interaction. Sodium Chloride is used here as an exam- ple. In this crystal, previous ultrasonic measurements1 have demonstrated the exis- tence of two well-defined limiting regimes. At low temperatures (below 20 K) the condition w~ >> 1 was fulfilled (w is the frequency of the acoustic wave and T the lifetime of thermal phonons). The experiment gave a ^Q, T" in agreement with the theo- ry in the Landau-Rmer regime.* At higher temperatures, the Akhieser regime (w-rel) was reached : the ultrasonic attenuation a was then found proportional to To which also agrees with theory. In contrast, Brillouin experiments around 30 GIz indicates a 2,

F ,

A satisfying explanation of this surprising behaviour can be found extending the current theories of the attenuation due to phonon-phonon interactions, to the unu- sual temperature-frequency regime reached in our experiments.

(ii) MoZecuZar crystals. Our experiments in succinonitrile4 and a-sulfur5 have de- monstrated that a dispersion and attenuation of elastic waves can be observed by Brillouin scattering in molecular crystals. Such experiments at hypersonic frequen- cies show that relaxation processes with characteristic times of the order of

lo-"

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981637

C6- 126 JOURNAL .DE PHYSIQUE

are present in these crystals, in addition to anharmonic phonon-phonon processes.

For more details on the molecular relaxation observed in a-sulfur, the reader is re- ferred to the paper presented separately at the same Conference.6

(iiil Inorganic glasses. Above 1 K, twostriking features are observed in most of the inorganic glasses. For temperatures around 1 K, the ultrasonic attenuation is pro- portional to T3 (frequencies lower than 1 M z ) . In this temperature range the domi- nant process is the relaxational absorption via phonon-assisted tunnelling. At hi- gher temperatures, a - m r e or less pronounced - absorption peak is often observed, which is assigned to thermally activated relaxation processes. Such a behaviour has been observed in glasses of very different chemical composition as, for instance, vitreous Si02 and LaSF,, a metallic oxyde glass, for frequencies of about 100 W z . Our Brillouin scattering experiments in LaSF7, plotted in Fig.1, exhibit a complete- ly different behaviour (the frequency is about 40 GHz) : a is found nearly propor- tional to T in the whole temperature raze studied.

I

0 100 200 300

T E M P E R A T U R E (K )

Fig. 1 - Hypersonic attenuation of longitudinal waves (42 GHz) in metallic oxyde glass LaSF7.

In vitreous S O 2 , we have already shown8 that the relaxation process which accounts for all of the ultrasonic attenuation can only explain one part of the hy- personic values. Phonon-phonon interactions have been suggested to explain this ex- cess. A shilar explanation can be proposed for LaSF7 results.

(ivl Amorphous polymers. At ultrasonic frequencies, the peak due to thermally acti- vated relaxations is also observed in polymers. However, at low temperatures, a ap- pears here proportional to wT. Our results in polystyrene (Fig.2-the frequency is about 18 GHz) exhibit a T-dependence in a large temperature range, and agree appro- ximately with an w-law where compared to the ultrasonic values below 10 K. The best candidate for explaining a wT law is a distribution of thermally activated relaxa- tion processes, with a nearly constant density of activation energies.

' I

5

However, as for inorganic glasses, the hypersonic results cannot be described as a whole on the basis of the ultrasonic values of the relaxation parameters.

The above results show that, for all of the insulating solids studied, the temperature dependence of acoustic damping is very different for ultrasonic and hy- personic frequencies. In amorphous materials, the thermally activated relaxations appear to be insufficient for explaining the hypersonic results above 20 K. Phonon- phonon interactions seem to contribute appreciable to the acoustic damping.

=

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a

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I L. G. MerkuZov. R. V . kbvatenok and E. V. Konovodchenko, Sou. Phus. Solid S t a t e

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TEMPERATURE ( K ) A A A d

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J.P. Bonnet, M. Boissier, R. Vaeher, (to be published):

H . Fontaine, R. Fouret, L. Boyer and R. Vacher, J . Physique, 33 (1972) 1115.

R. Vaeher, J . SaprieZ and M. Boissier, J . AppZ. Phys. 45 (19741 2855.

M. Boissier, R. Vaeher and B. Perrin, t h i s conference.

A. Raychaudhuri, private cormtunication.

R. Vacher, J . PeZous, F. PZicque and A. Zarembowitch, J . Non-Cryst. Solids, t o be published.

J.Y. Duquesne and G. BeZZessa, J . Physique (France), t o be pubZished.

Fig. 2 - Hypersonic attenuation of longitudinal waves (18 GIz) in amorphous polystyrene.