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Size Effects in Superfluid Helium II - I Size effects in superfluid helium II - I. Experiments in porous systems E. Guyon, I. Rudnick To cite this version: E. Guyon, I. Rudnick. Size effects in superfluid helium II - I. Experiments in porous systems. Journal de Physique, 1968, 29 (11-12), pp.1081-1095. 10.1051/jphys:019680029011-120108100. jpa-00206747 HAL Id: jpa-00206747 https://hal.archives-ouvertes.fr/jpa-00206747 Submitted on 1 Jan 1968 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. LE JOURNAL DE PHYSIQUE TOME 29, NOVEMBRE-DÉCEMBRE 1968, 1081. SIZE EFFECTS IN SUPERFLUID HELIUM II I. EXPERIMENTS IN POROUS SYSTEMS By E. GUYON (1) and I. RUDNICK (2), Physics Department, University of California, Los Angeles, California, (Reçu le 22 avril 1968.) Résumé. 2014 Les propriétés de la phase superfluide de l’hélium liquide sont fortement modi- fiées par les effets de taille. Nous discutons dans ce travail une étude experimentale de l’hélium. contenu dans des poudres très fines (~ 100 à 104 Å) : abaissement de la température d’établis- sement de l’état superfluide, T0, et propriétés superfluides pour T To : vitesse d’écoulement critique, chaleur spécifique, densité superfluide. Cette dernière donnée est obtenue à partir de la mesure de la vitesse du son hydrodynamique qui se propage dans un tel système poreux 2014 le quatrième son. Nous discutons en détail les techniques et les propriétés physiques liées à la mesure du 4e son. Une discussion des résultats est présentée par analogie avec l’étude des effets de proximité dans les supraconducteurs. Abstract. 2014 The properties of the superfluid phase of liquid helium are modified by size effects. We discuss here experiments on helium contained in very fine compressed powders (~ 100 to 104 Å) : lowering of the onset temperature for superfluidity, T0, and superfluid pro- perties for T To : critical flow rate, specific heat, superfluid fraction. These last data are obtained from the measurement of the hydrodynamic sound velocity that propagates in such porous systems : 4th sound. We present in some detail the techniques of the measurements and the physical properties of 4th sound. A discussion of the results is presented in analogy with the study of the proximity effect in superconductors. IntroduCtion,. - The properties of the superfluid rikse [3] had measured the specific heat of helium phase of helium, He II, are strongly affected by adsorbed on a jeweller’s rouge powder and found the effects of size. These effects occur when the helium following properties : the singularity and discontinuity is in a nearly one or two dimensional container : of specific heat, which is observed in bulk helium II superfluid film of helium (Rollin film) or helium at T À is replaced by a peak having its maximum contained in the small channels of a porous system. at T p ( Tx). This peak becomes broader and This work will present some aspects of the modifica- shifted to lower temperatures for thinner films [4]. tion of superfluidity in this last case; the channels are In order to decide unambiguously the fundamental the tangled and interconnected pores of highly relevance of the temperature broadening from the compressed fine powders. Previous experimental experiments, one should have some information on the studies have described mostly the modification of the thickness distribution in the films. Unfortunately the onset temperature for superfluidity, To. We will also values of dF, obtained from adsorption isotherms present and discuss some properties of such systems measurements, are only of statistical nature and may in the superfluid state at T T0. vary with the substrate properties. The same charac- The problem of size effects in He II has been a teristic results of flow and specific heat measure- subject of considerable experimental interest in the ments [5, 6] were obtained for helium filling porous last 15 years. The first experiments of superfluid systems : To is smaller than Tx and the specific heat flow in unsaturated films [1] by Long and Meyer [2] has a broad maximum at a temperature Tp below Tx. show that To ( Tx) is an increasing function of the The same uncertainty remains in these results as the film thickness, dF. They also showed that the critical effect of the pore size distribution is certainly impor- flow rate goes smoothly to zero at To in contrast with tant in this case. The two sets of experiments were the sharp drop for the bulk sample. In 1949, Frede- done on the same samples of porous Vycor glass (solid perforated by interconnected channels). In (1) Permanent addyess : Laboratoire de Physique des the case of helium completely filling the pores of the Solides, associ6 au Centre National de la Recherche Vycor specimen, it was found on one sample that Faculté des France. Par- Scientifique, Sciences, Orsay, = = 2.06 OK. However in the case of unsa- tially sponsored by NATO. To TP (2) Research sponsored in part by the U.S. Office of turated films, it was observed that TP was larger than Naval Research, Acoustics Branch, Nonr 233-(48). To [2]. This contrasts with the case of bulk helium Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:019680029011-120108100 1082 where To = TP = Tx with an accuracy of the order velocity of the unattenuated 4th sound made is given of 10-6 °K. by [10] : A fundamental property of superiluid helium is its superfluid density. This quantity can be obtained from the velocity measurement of the hydrodynamic wave which propagates in helium II filled micropores : ul and U2 are the first and second sound velocity, This 4th sound wave was predicted by Pellam [7] P, is the isobaric isothermal expansion coefficient, and Atkins [8] and first observed by Shapiro and so the entropy of He II. E( T) is a small coefficient Rudnick [9] for coarse samples where the shift of To and is given in figure 1 for bulk helium. The correc- was too small to be detected. Similar experiments were performed in much finer powders by Rudnick et al. [10] and will be discussed and developed here. We will recall in Part I some essential results for 4th sound based on two fluid hydrodynamics. We discuss in Part II the properties of the powders and the experi- mental techniques. The determination of To, of flow measurement and of superfluid density, will be given in Part III. We present in Part IV a theoretical dis- cussion based essentially on the use of modified Gins- burg-Pitaevski [11] (G. P.) equations to discuss these results. Some analogies will appear with the case of superconductors where the corresponding Ginsburg- Landau [12] (G. L.) equations are known to describe well, within certain limits, the size effects. FIG. 1. - Correction to the simplified 4th sound velo- I. Summary of 4th sound properties. - The propa- city using (1.1). gation of sound waves in liquid helium II presents a number of which can be descri- interesting properties tion is maximum around 2 OK and decreases with bed accurately in terms of two fluid components, a zero near 1.17 OK where normal fluid and a of and temperature, becoming superfluid density PN pg [13] This correction should be different such that PN + Ps = P where p is the total density of PP changes sign. for a onset as the liquid. The superfluid carries no entropy and samples having depressed temperature the involved in it on The has no The sound wave which parameters depend To. viscosity. corresponds calculated variation is in to the sound is due to the vibration of the temperature of U4( T) given ordinary 2 with that of first and second sound two components in phase and is mainly characterized figure together in the case of "coarse" has to be smaller by density and pressure oscillations. Another mode powders : d then but not so small as to see a shift in the onset corresponds to the oscillation of the two fluids in XN 10-3 OK. The value of opposite phase such that the momentum density j temperature : Tx - T0 was taken from the disk measure- remains constant. This wave corresponds to an en- pg/p(T) oscillatory ments of Dash and We will not tropy (temperature) wave and is called second sound. Taylor [14]. repro- It is absent in bulk liquid helium above Tx. In the duce the calculation [9] leading to (I. 1). However limit where - 1 - 0 is the ratio of the one easily can understand the major contribution to y (y specific the 4th sound from the heats), which is a good approximation not too close expression (1.2) thermohydro- from the lambda point, the temperature (entropy) dynamics equations : changes are not coupled to the pressure (density) 1) The force on the superfluid is due to the variation of changes and there are no temperature changes in first the chemical potential y : sound and no pressure changes in second sound. Atkins [8] considered the case where the normal fluid does not move. This occurs when the viscous wave- length for the normal fluid, X,,, becomes large compa- The thermal fluctuations associated with the 4th sound red to the size of the system. Classically are small. 2) The continuity equation is : at the frequency m ; "1JN is the normal fluid viscosity.
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