MEASUREMENTS OF THE ATTENUATION OF FOURTH SOUND IN HELIUM II

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MEASUREMENTS OF THE ATTENUATION OF

FOURTH SOUND IN HELIUM II

H. Lauter, H. Wiechert

To cite this version:

H. Lauter,

H. Wiechert.

MEASUREMENTS OF THE ATTENUATION OF FOURTH

JOURNAL DE PHYSIQUE Colloque C6, suppIPment au no 8, Tome 39, aozit 1978, page C6-321

MEASUREMENTS O F T H E ATTENUATION OF FOURTH SOUND I N H E L I U M

I 1

H.J. ~auter+ and H. Wiechert

I n s t i t u t filr Physik, Johcmnes Gutenberg-UniversitZit, 0-6500 Mainz, Gemcmy

Rdsumd.-'L'attsnuation du quatrisme son a dt6 mesurd dans la gamme de temperature allant de 0,s

K

Ti SOUS pression de vapeur saturante dans une cavitd torique remplie de poudre. Entre 1,3 K et Ti

l'attdnuation est due au mouvement de la composante normale de l'hdlium 11. Au dessous de 1,s K la

limitation du libre parcours des phonons par les parois des capillaires joue un r6le prddominant. Abstract.- The attenuation of fourth sound in He I1 has been measured in the temperature region 0.8 < T < T under saturated vapor pressure in an annular cavity filled with powder. In the tempera-

ture range ketween 1.3 and TA the attenuation is mainly caused by the slipping of the normal fluid

component of He 11. For T 5 1.8 K the limitation of the free paths of the phonons by the walls of the

capillaries plays the dominant role.

Fourth sound is a wave mode in narrow capilla- ries in which the normal fluid component of He I1 is almost completely clamped as a result of the friction with the walls and the oscillations are propagated only in the superfluid component/l,2/. Whereas the velocity of fourth sound has been stu- died quite thoroughly, only some measurements were reported on the attenuation of fourth sound/3,4/. In this short communication we supplement these stu- dies and present systematic absolute measurements on the damping of the fourth sound under saturated va- por pressure.

The attenuation of fourth sound has been deter- mined in the frequency range 1 -20 kHz by using a resonance technique. Standing azimuthal waves have been excited and detected in an annular cavity by means of condenser transducers. The half-width of a resonance peak gives directly the attenuation (per unit of time). In order to clamp the normal fluid component, the cavity was filled with fine-grained

powder (Linde 5 p e A and Type B aluminum oxide with

grain size of 0.3 pm and 0.05 um, re.spectively). The sizes of the pores formed between the powder grains were reduced progressively from run to run by pac- king the powder more tightly under mechanical pres- sure. The mean effective pore diameters were esti- mated by means of the BET method with nitrogen as adsorbate (see e.g./5/) and the pore size distribu- tion was determined by desorption measurements/6/.

According to thennohydrodynamic theories/l,7-

9/, the attenuation of fourth sound ab consists of '

two parts and can be written in the following func-

+

X, 38042 Grenoble, France

tional form : a4 = A(~~,~,c~,K...)w~ + ~ ~ ~ 1 2 , ( 1 )

where w is the angular frequency. The first part may be called the intrinsic attenuation. It depends on the square of the pore diameter d and is due to dis- sipative processes associated with the coefficients

of first and second viscosity 17 and and the ther-

mal conductivity K /7,8/. The second part is refer-

red to as external absorption and arises because of heat exchange from the helium to the surrounding walls of the porous specimen/l,7,9/. A least square fit to the experimental data was employed to extract

the coefficients A and B of the relation ( 1 ) . It

turned out that the external absorption amounts to

about 15 % of the total damping and shall not be

considered here furthermore.

The intrinsic attenuation of fourth sound (related to w2)is shown as a function of temperatu-

re for the samples 1-4 in figure 1. It is apparent

that the absorption is reduced continuously with decreasing pore diameter. In the temperature range

between 1.5 and TA the solid lines represent the

results of the theory/7,8/ by using unspecified po-

re diameters as fit parameters t~ the experimental

data. Obviously, the theoretical curves provide a good description of the temperature dependence of the fourth sound damping, which in this temperature range is mainly caused by the incompletely locked normal fluid component. However, at temperatures be-

low 1:5 K deviations from the theory occur, which

will be discussed in connection with figure 2.

In figure 2 the absorption of fourth sound is plotted versus temperature for the samples 5-7. The agreement between the experimental data and the theoretical curves (solid lines) in the upver temr

1 f . I

I

1.0 12 1 16 18 2.0 T C K I

Fig. 1 : The attenuation of fourth sound as a func- tion af temperature for the sample 1-4. The mean effective pore diameters of the samples are : (1) 0.185 ym, (2) 0.162 pm, (3) 0.155 um and (4J 0.143

pm. For temperatures above 1.5 K the solid lines

represent the results of the theory /7,8/, whereas at lower temperautres they only serve as guides for the eyes.

rature range is again very satisfactory, whereas at lower temperatures discrepancies appear. The rea- son for the deviations may be mean free-path effects. The mean free paths of the phonons increase rapidly as the temperature falls and become comparable to the pore diameters of the samples at those tempera- tures, where the data begin to deviate from the the theoretical curves. Thermohydrodynamic theories cannot explain these discrepancies. In order to elu- cidate this point, the theoretical curve calculated for the ideal case of a helium-filled lamina with a width of 0.1 pm is likewise represented in this fi- gure. The solid line indicates the contribution of

the first viscesity coefficient q to the fourth

sound damping and the dashed line the upper limit of the contribution of the second viscosity coeffi- cient

c 3

Fig. 2 : The attenuation of fourth sound in depen-

dence on temperature for the samples 5-7. The mean effective diameters of the samples are (5) 0.131pm,

(6) 0.118 ym and (7) 0.062 pm.

king the limitation of the free paths of the pho- nons into account which results in a reduced visco-

sity coefficient q according to Ill/. Since such a

calculation tends to describe the experimental data qualitatively correctly, we may conclude that mean free-path effects play the dominant role at low temperature.

the pore size djstrihution is taken into account. References

/ 3 / Dyumin,N.E. and Rudavskii,E.Ya., F i z . Nizk. Temp. _L (1975) 521

/ 4 / Hartoog,A., Van Beelen,H., De Bruyn Ouboter,R.

and Taconis,K.W., Proc. 14th Intern. Conf. on

Low Temp. Phys. (1975) 241

/ 5 / GSttert,H.. Lauter,H.J. and Wiechert,H., J.

Phys.C : Solid State Phys.

10

/ 6 / Kriss,M. and Rudnick,I., J. Low Temp. Phys.

3

(1970) 339

/ 7 / Sanikidze,D.G., Adamnk0,I.N. and Kaganov,M.I.,

Sov. Phys. JETP

2

1 1 1 1 I I / I / Atkins,K.R., Phys. Rev.

113

181 Wiechert,H. and Meinhold-Heerlein,L., J. Low

Temp. Phys. (1971) 273

Fig. 3 : The absorption of fourth sound as a func-

tion of the mean effective pore diameter of the / 9 / Achiam,Y. and Bergman,D.J., J. Low Temp. Phys.

samples at 1.9 K. For the nearer details see text.

-

/ l o / Putterman,S.J., Superfluid Hydrodynamics, North

Holland Publ. Comp. (1974) 139

/ I 1 1 Atkins,K.R., Phys. Rev.

108

137

(1965) A 1383

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