HAL Id: jpa-00217551
https://hal.archives-ouvertes.fr/jpa-00217551
Submitted on 1 Jan 1978
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of
sci-entific research documents, whether they are
pub-lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
THE THERMAL EXPANSION OF HELIUM II IN
RESTRICTED GEOMETRIES
H. Wiechert, G. Wupperfeld
To cite this version:
JOURNAL DE PHYSIQUE Colloque C6, supplkment au
no
8, Tome 39, aofit 1978, page C6-324THE THERMAL EXPANSION O F HELIUM I1 IN RESTRICTED GEOMETRIES
H. Wiechert and G. Wupperfeld
I n s t i t u t fiir Physik, Johannes Gutenberg Universittit, 0-6500 Mainz, G e m y
Rdsum6.- Le coefficient de dilatation thermique de l'hllium I1 enferm6 dans une poudre ou dans le verre poreux "Vycor" est ddtermind entre 1,15 K et le point A sous la pression de vapeur saturante. Les donn6es montrent une transition de phase arrondie conforme aux mesures anterieures sur la cha- leur specifique dans les glom6tries restreintes.
Abstract.- The coefficient of thermal expansion of He I1 confined to powder samples and porous Vycor glass has been determined at temperatures between 1.15 K and the A-point under saturated vapor pres- sure. The data reveal an unsharp phas transition in accordance with previous measurements of the spe- cific heat in restricted geometries.
The phase transition of liquid helium I1 in restricted geometries is modified with respect to the transition of the bulk liquid. Experiments on the specific heat showed a considerable rounding and a shift of the A-anomaly /1-3/. The order parameter as derived from measurements on the superfluid frac- tion varies completely continuously across the tran- sition /4,5/. In this short communication, we will supplement the study of phase transitions in confi- ned geometries by presenting measurements of the coefficient of thermal expansion under saturated va- por pressure.
The coefficient of thermal expansion of He I1 confined in porous samples has been determined by a pycnometer technique. The experimental cell is shown in figure 1. EENED WIRES s r m s r CAPACITOR GAP IWIDTH : 0.51 MMI NEEDLE V ! E SAMPLE
-
1cmtrodes of the capacitor. Subsequently the needle valve in the filling capillary was closed and the capacity which is directly related to the filling fraction of the condenser was measured as a func- tion of temperature by a capacitance bridge (Gene- ral Radio 1615 A).
In order to measure the thermal expansion coefficient in matrices of various pore sizes and topologies, four samples have been investigated. Table I summarizes the main properties. The samples A and D were made by packing fine powder (aluminbu oxide and carbon black) under pressure into the cell The samples B and C consisted of porous Vycor glass. The mean effective diameters of the pores of the specimens were estimated by means of the BET method of analysis (see e.g. /5/)
Table I : Properties of the samples
Sam- Mate-, Aproximate Packing Porosity dBET ple rial grain size pressure
liml
&g em-qEl
A A1203 0.05 200 0.74 500
B Vycor I
-
-
0.30 130C Vycor I1
-
-
0.31 75D Carbon Black 0.015 1600 0.51 55
Fig. 1 : Schematic diagram of the experimental cell.
+~inde A1203 was supplied by Union Carbide Corp., porous Vycor glass (Code No 7930) by Corning Glass The whole system was immersed into a helium bath. Works and Carbon Black by Degussa
The experimental cell consists of a cylindrical ca-
pacitor on top of the sample cell which contained The results of our measurements are represen- the porous matrix and into which pure helium gas ted in the figures 2 and 3. Figure 2 shows the tem- was condensed until the level of the liquid had rea- perature dependence of the coefficient of thermal ched the lower section of the gap between the elec- expansion between 1.15 K and the A-point (upper sca-
le, circles). ples.
TEMPERATURE [K] . .
12 13 14 I5 I6 1.7 18 19 20 2 1
2 12 213 2 1L 2 15 2 16 2 17 TEMPERATURE [K]
Fig. 2 : The temperature dependence of the coeffi- cient of thermal expansion asvp of the He I1 contai- ned in sample A. The circles refer to the upper scale and the triangles to the expanded lower scale near the A-point. For comparison, the solid line indicates the results of the bulk liquid.
In order to elucidate the behaviour of the thermal expansion coefficient near the minimum of the curve, the data are likewise plotted in this figure on an expanded scale (lower scale, triangles). The arrow indicates the position of the minimum, the tempera- ture of which is assumed to be equal to the onset temperature of superfluidity T in completely filled pores / I / , as is the case here. It is apparent that the singularity of the thermal expansion coefficient of the bulk liquid shown by the solid line is smoo- thed and the transition in shifted to lower tempera- tures.
This behaviour becomes even more distinct for helium confined in the samplsB
-
D with smaller ef- fective pore diameters. Figure 3 shows the data of the thermal expansion coefficient as a function of temperature of these samples. The thermal expansion anomaly is progressively rounded and shifted to lo- wer temperatures with decreasing pore diameter. The depression of T with the pore diameter d may be described for all samples by the empirical relation-11 -1.5
TX
-
T = 12 x 10 d,
which is in order of magnitude agreement with mean-field-type theories /6,7/. The increase of the data at 1.2 K with de- creasing pore diameter implies that the temperatu- re, where the thermal expansion coefficient is ze- ro (T %1.14 K in the bulk liquid), is depressed to lower temperatures.It is interesting to note that there seems to be no principle difference between the behaviour of helium in porous Vycor glass and in powder sam-
n . . W
-10 -
12 13 IL 15 16 17 I8 19 20 21 TEMPERATURE [K]
Fig. 3 : The coefficient of thermal expansion as a function of temperature for the samples B (squares) C (triangles) and D (circles). The solid line re- presents the data of bulk helium.
This observation is in agreement with previous mea- surements of the specific heat in Vycor glass /I /, but in contrast to measurements of the superfluid fraction /8/, which indicated that due to the grea- ter homogeneity in the pore size distribution the superfluid transition in Vycor glass is relatively sharp as compared to packed powders.
We have attempted to analyze our data by con- sidering the influences of size effects and the den- sity variation in the capillaries as a function of the distance from the walls, which was recently cal- culated by Oestereich and Stenschke /9/ by taking into account the local compression of helium in the capillaries due to the Van der Waals forces of the walls. The results explain the shift and the roun- ding of the thermal expansion anomaly and the en- hancement of the data at lower temperatures quali-
tatively reasonably well. A more complete analysis of the experimental results is in progress.
References
/I/ Brewer,D.F.,J. Low Temp. Phys. 2(1970)205 /2/ Scott,S.A., Guyon,E., Rudnick,I., J. Low Temp.
Phys.
9
(1972) 389/3/ Chen,T.P.,Gasperini,F.M., Phys. Rev. Lett.
40
(1978) 331/ 4 / Kriss,M.,Rudnick,I.,J.Low Temp. Phys.3(1970)339 /5/ Gattert,H.,Lauter,H.J.,Wiechert, H.,J.Phys.C:
Solid State Phys.
10
(1977) 3737161 Ginzburg,V.L.,Pitaevskii,L.P.,Sov.Phys.JETP
36
(1 958)858/8/ Kiewiet,C.W., Hall,H.E., Reppy,J.,D.,'Pliys. Rev. Lett. 35 (1975) 1286
