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FREQUENCY DEPENDENCE OF SOUND
ABSORPTION OF VITREOUS SILICA BETWEEN 10
MHz AND 35 GHz
R. Vacher, J. Pelous, F. Plicque, A. Zarembowitch
To cite this version:
JOURNAL DE PHYSIQUE
CoZZoque CS, suppZlment au nO1O, Tome 42, octobre 1982 page CS-553
FREQUENCY DEPENDENCE OF SOUND ABSORPTION OF VITREOUS SILICA BETWEEN
10 MHz AND 35 GHz
R. Vacher, J . Pelous, F. ~ l i c ~ u e * and A . ~arembowitch*
Laboratoire de Spectromdtrie RayZeigh BriZZouin (ERA 460), Universitd des Sciences et Techniques du Languedoc, Place E. BataiZZon, 34060 MontpeZZier Cedex, France
* ~ l ~ u r t e m e n t de Recherches Fhysiques (LA 71), Universitl Pierre et Marie Curie 75230 Paris Cedex 05, F r a m e
Abstract.- We present new measurements of the attenuation of ul- tranonic and hypersonic waves for temperatures ranging from 10 to 300 K in silica glass. The results show that the relaxation process which is predominant for the absorption of ultrasonic waves is not sufficient for describing hypersonic attenuation. Anharmonic three-phonon interactions are proposed to explain the excess damping, and are seen to be in qualitative agreement with the observed temperature dependence above 300 K.
The acoustic attenuation of vitreous silica below room tempera- ture is dominated by a strong broad peak which is observed at about 50 K for ultrasonic f r e q ~ e n c i e s . ~ This maximum can be explained by assuming a coupling of elastic waves with a thermally activated rela- xation process having a broad spectrum of relaxation times. Structural defects involving oxygen a t ~ m s l - ~ or Si04 tetrahedrons3 have been proposed as a microscopic description of relaxing systems. On the other hand, Pine4 claimed that anharmonic three-phonon interactions were the most likely explanation for the peak observed in his Bril- louin scattering results. However, several authors (see e.g. Ref.5) have demonstrated that these two points of view were incompatible.
Our purpose is to find a description of the elastic properties of vitreous silica, which agrees with both ultrasonic and hypersonic re- sults. This analysis must be based on experiments performed on the sa- me sample, as the elastic properties of glasses are known to be sensi- tive to the impurity content and thermal history of the ample.^
Therefore, we have measured the velocity and attenuation of longitudi- nal and transverse elastic waves, for temperatures ranging from 10 to 300 K at ultrasonic (5
-
200 EHz) and hypersonic (16-
35 GHz)frequencies. The experimental set-up as well as the whole set of re- sults are given in Ref.7. Here, we present only the results concerning the attenuation of longitudinal waves and discuss their frequency dependence.
207 MHz
T E M P E R A T U R E
(
K )1 : Attenuation of longitudinal ultrasonic waves. Dashed line : calculation
-
of relaxational attenuation (see text).
Fig. 1 shows the absorption of 200 VHz
-
longitudinal waves. In order to describe these results we have used the following expres- sion for the attenuation via thermally activation o f two-level sys- tems : *m
a(db.cm-l) = 4.34 D'/~~V'~T
I
P(v)~'T(V) ( 1 + w2r2(~))-'d~ 0where p is the mass density, v the sound velocity, w the angular frequency, D is the deformation potential determined by the change of energy of two-level systems under a unit strain, P(V) is the dis- tribution o f activation energies and T(V) is the relaxation time, assumed to obey the Arrhenius law : r(V) = T O exp(V/kT)
.
3 5
G H z
Fig. 2 : Attenuation of longitudinal hypersonic waves. Dashed line : calculation of relaxational attenuation (see text).
(the results above 300 K are taken from 9ef. 9). This value has to be compared to the attenuation due to aaharmonic phonon-phonon inter- actions in quartz which is about 2000 db.cm-' at 40 GHz
.
We there-fore think that this process contributes appreciably to hypersonic at- tenuation in vitreous silica.
The theoretical calculation of the attenuation due to phonon- phonon interaction in the Akhieser regime (UT < 1) in crystals is gi- ven by : l 0
a
(db
.
cm- l ) = 4.34 y 2 ~ ~ ~ 2 ~ / p v 3where C is the specific heat per unit volume and T the lifetime of thermal phonon. This expression, valid for crystals in the Akhieser regime, assumes that the sound waves is a driving field which destroys the equilibrium of thermal phonons, considered as localized wave packets. This picture seems to apply to glasses, at least in first approximation.
C5-556 JOURNAL DE PHYSIQUE
From the experimental values for K and C
,
a nearly constant valueT
-
10-l3 S,
corresponding to a mean free path of about 10,
.is found between 300 and 1000 K.
This constant value of the mean free path of high frequency pho- nons responsible for a large part of heat transport has been assumedll to be due to the disorder. It would lead to an attenuation a
*
T,
in disagreement with the experiment. It seems most likely that the at- tenuation is due to lower frequency phonons which are able to propa- gate on larger distancies in the amorphous network and therefore to undergo three-
phonon processes. The lifetime of such phonons is known to vary as T T at high temperatures and would lead to theright temperature dependence for the attenuation.
References. -
O.L. Anderson and H.E. Bommel, J. Am. Ceram. Soc.
2
(1955) 125. R.E. Strakna and H.T. Savage, J. Appl. Phys.35
(1964) 1445.M.R. Vukcevich, J. Non-Crystalline Solids _?_1 (1972) 25. A.S. Pine, Phys. Rev.
123
(1961) 2020.C.A. Ffaynell and G.A. Saunders, Solid State Comm.
11
(1971) 1345. J.T. Krause, J. Appl. Phys.42
(1971) 3035.R. Vacher, J. Pelous, F. Plicque and A. Zarembowitch, to be published.
*
J. Jackle,L.
Pichc, W. Arnold and S. Hunklinger, J. Non-Crystalline solids2
(1976) 365.J. Pelous and R. Vacher, Solid State Commun.
18
(19761 657.l 0 H.J. Maris in "Physical Acoustics", edited by W.P. Mason and R.N. Thurston (Academic, New York, 1971) Vol. 8, p . 279.
