NUCLEATION OF SOLID 4He IN VYCOR UNDER PRESSURE : SUPERFLUID OSCILLATIONS NEAR THE MELTING PRESSURE

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NUCLEATION OF SOLID 4He IN VYCOR UNDER

PRESSURE : SUPERFLUID OSCILLATIONS NEAR

THE MELTING PRESSURE

D. Brewer, A. Dahm, Hutchins, W. Truscott, D. Williams

To cite this version:

JOURNAL DE PHYSIQUE _{Colloque C6, supplPment au no 8, Tome 39, aofit 1978, page C6-351}

NUCLEATION OF S O L I D 4 ~ e I N VYCOR UNDER PRESSURE

:

D.F. Brewer, A.J. Dahm t, Hutchins, W.S. Truscott and D.N. Williams Physics Laboratory, University of busses, Brighton, EN1 9QH, England.

Rbsum6.- Des experiences antdrieures ont montrd qu'il est possible de nucleer des dtats localises de 3 ~ e prss d'une surface solide P pression infdrieure 1 la pression de solidification et P temperature infdrieure 2 100 mK. Nous avons fait d'autres experiences sur cette question dans le cas de "He su-

perfluide et d'une suface de verre poreux "Vycor", en observant les oscillations superfluides dans une superfuite de Vycor en fonction de la pression aux temperatures de plus de 1 K. Nous trouvons que contrairement aux calculs l'bcoulement superfluide continue jusqu'l la pression de solidifica- tion et qu'aucun bouchage deu capillaire par le solide n'est observd.

Abstract.- Previous experiments have shown that it is possible to nucleate localized states of 3 ~ e near a solid wall at pressures below the melting pressure and at temperatures below 100 mK. We have further investigated the question of solid nucleation of He by carrying ou superfluid '~e oscilla- tions experiments through a Vycor superleak as a function of pressure and of temperature above 1 K. We find that, contrary to calculation, superflow continues right up to the melting curve and no bloc- king of the capillary due to filling with solid is observed.

In a helium film adsorbed on glass the van der Waals force between the substrate and helium atoms compresses the first layer to solid density, even when the vapour pressure is very low, and the atoms in the first monolayer become localized. It is not unexpected that a similar effect should occur when the substrate is in contact with bulk fluid, and that on raising the pressure the second and hi- gher statistical layers should reach solid density before the fluid reaches the bulk solidification pres- sure. A simple calculation shows that in %e, a hy- drostatic pressure of only a few bar should be suf- ficient to raise the second layer to solid density if it were to behave like ordinary three-dimensional bulk liquid.

Whether or not the second statistical layer would "solidify" under such conditions below the bulk melting pressure depends on the detailed physi- cal processes of formation of solid (or localized) layers at a few atomic distances from a wall in a field of force, which are not well understood. Expe- riments with 'He in porous glass below 100 mK have shown that Pomei-anchuk cooling does take place in the pores, but at pressures which are only about 213 bar below bulk melting pressure, rather than twenty bar or so /I/. Assuming that the cooling occurs, as in bulk liquid, because of the entropy gain on trans- forming from mobile to localized states, this result

t

Western Reserve University, Cleveland, Ohio, U.S.A.

indicates that the localized states are rather dif- ferent from those in solid %e. In order to investi- gate the nucleation problem further we are carrying out a number of different experiments. One of these, which we describe here, is the observation of the frequency of pressure-induced superfluid oscillations of 'He through a superleak as a function of pressu- re and temperature. The frequency depends on the fractional density of superfluid p /p, and on the ratio of cross-sectional area to length of the su- perleak, a/Z : in sufficiently small pores, the lat- ter can change significantly by the addition of a few layers of solid at the wall. The apparatus (si- milar to the figure of reference 1 3 1 ) consists of two copper chambers (V1 and VZ) joined by a Vycor glass superleak, 9 mm long and about 1 mm in diame- ter which was glued into a copper tube with Stycast 2850 GT. Oscillations through the superleak could be induced by means of a vibrating diaphragm, D,

1.59 cm in diameter and 12.5 pm thick, made of ei- ther nylon or kapton. Both sides of the diaphragm

0

were coated with 1200 A layer of gold, and the dia- phragm was stretched to a suitable tension which de- termined its natural resonant frequency. Electrodes on each side of the diaphragm formed, with the gold films, two parallel plate capacitors, and a varia- ble frequency A.C. voltage then allowed the diaph- ragm to be displaced sinusoidally at frequencies of order 10Hz. Measurementswere mostly made by pluc- king the diaphragm and observing the frequency of

the decaying oscillations. The displacement ampli- tude was usually a few microns, sufficiently small at these frequencies that the flow through the su- perleak was kept subcritical.

The theory of such superfluid oscillations was originally worked out by Robinson / 2 / . In our experiments, the oscillation frequency is given by

ps a 8x5 (,,2 = --

- -

P2 11 ~2

(1 + small correction terms) (1) where o is the diaphragm tension and A its area. Fi- gure 1 shows the results obtained for the pressure variation of the frequency, at three different tem- peratures.

PRESSURE [BAR)

Fig. 1 : Change in superfluid oscillation frequen- cy through two superleaks as a function of pressure. Note the greatly expanded frequency scale for the large superleak (curve 1) : the fractional change for this superleak is considerably less than for Vycor.

Curve I gives results for a wide superleak of rec- tangular cross-section 50 pm by 3 mm and 9 mm long. This superleak was prepared for a similar experiment in superfluid 3 ~ e , and is described in another paper in this Conference / 3 / . The results shown are in excellent agreement with equation (I), in which all the quantities are accurately known. At point M the melting curve is reached, the superleak blocks, and the signal disappears. The remaining curves are for two other temperatures with the Vycor superleak, which unfortunately has a much more complex geometry. They gi.ve the variation of the product (p /p)a/R with pressure, in which, however, the superfluid

fraction (p /p) can itself be a significantly varying 0 function of a in these channels which are only $70 A in diameter. A conclusion that can be drawn unequivo- cally however, is that there is no indication that the Vycor pores have become blocked with solid befo-

re the bulk melting curve is reached. Using the Franchetti-type / 4 / calculation for the density as a function of distance from the wall as recently done by Landau and Saam /5/, we expect a considera- ble reduction in a at relatively low pressures and complete blockage of the pores.

These results for '~e in Vycor above I K dif- fer qualitatively from those with 3 ~ e in Vycor be- low 100 mK where nucleation of localized states 2/3 bar below seems most probable. They also disagree with results of experiments of ' ~ e on grafoil where it was inferred that solid is nucleated at quite low pressures 151. On the other hand, they agree quali- tatively with measurements of the dielectric cons- tant of 'He-vycor under pressure 161. (Note, however that neither of the 4 ~ e in Vycor experiments can discriminate between solid being nucleated in Vycor at the melting curve, and above the melting curve, when other parts of the apparatus might become bloc- ked with bulk solid). The observations are being extended to other temperatures and substrates

We are grateful for support for A. Dahm to the National Science Foundation and to the U.S.-U.K. Educational Commission who provided a FulbrightlHays Special Award.

References

/ I / Brewer, D.F., Mitchell, H. and Truscott, W.S., Proc. Symp. on Phys. of Ultralow Temp. (Hakone Japan 1977 : Japanese Physical Society (to be published) ; Brewer, D.F., Mitchell, H. and Truscott, W.S., Proc. IIR Conference on Advan- ces in Refrigeration at the Lowest Temperatures, Zurich, March 1978 (to be published)

/2/ Robinson, J.E., Phys. Rev.

82

Williams, D.N., this Conference

/4/ Franchetti, S., Nuovo Cimento

4

38

(1977) 23