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Helium-four transition in a restricted geometry below and above the bulk solidification pressure
Physica I07B (1981) 583-584 North.Holland PubfishingCompany
JE 8
HELIUM-FOUR TRANSITION IN A RESTRICTED G E O ~ T R Y BELOW AND ABOVE THE BULK SOLIDIFICATION PRESSURE D.F. Brewer t, Cao Liezhao*, and C. Girit
Physics Laboratory, University of Sussex, Brighton, Sussex. and J.D. Reppy tt Laboratory for Atomic and Solid State Physics, Cornell University, Ithaca, New York. Using a torsional oscillator technique, we have investigated the onset of superfluidity of ~He in Vycor at pressures in the liquid region and at higher pressures where bulk ~He is solid. The lower pressure data trace out the onset temperature for superflow in Vycor as a function of pressure, which is roughly parallel to the bulk lanbda line but about O.25K lower. At OK, calculated values of the superfluid fraction are about O.16 at 1 bar and O.12 at 25 bar; these numbers contain a geometrical constant. Higher pressure data indicate that superflow can occur in Vycor at pressures as much as 20 bar above bulk solidification. An unexplained decrease in period is observed below the b u l k solidification temperature. I.
INTRODUCTION
The van der Waals attraction between He and most solid surfaces is sufficiently strong that it binds the layer of helium in contact with it at solid density. Nevertheless, it is known that, on a macroscopic scale, the free energy at melting pressures of the liquid helium-substrate interface is lower than that of the solidsubstrate interface in some cases, and the solid does not wet the wall although the first helium monolayer must still be adsorbed at solid density. Using interfacial tension results (i) one can calculate that in Vycor glass whose pores have an average diameter of ~ 7 0 ~, liquid should be stable at pressures of about 1 bar above the bulk solidification pressure. We have investigated superfluidity of ~He in Vycor using a torsional oscillator technique (2)and find evidence for it at considerably higher pressures. These measurements supplement others on solidification in restricted geometries which are also presented at this Conference (3-5). 2.
substrate and contributes to the moment of inertia. Transition to the superfluid state is observed as a decrease in period due to decoupling of the superfluid, with a decrease in the moment of inertia. 3.
RESULTS AND DISCUSSION
Figure 1 shows the period as a function of temperature for two constant pressures, the smaller one (15 bar) being in the fluid region of the phase diagram, and the larger one (42.5 bar) being in the bulk fluid region at higher temperatures and the bulk solid reqion at lower
--lO0
150
l
APPARATUS
m
The torsional oscillator was a hollow cylinder of beryllium copper, about icm diame6er and lcm high t almost completely filled with a cylinder of Vycor porous glass. It was connected by a BeCu torsion tube to a massive block, and helium could be admitted to it through the imm diameter bore of the tube. Oscillations were excited and detected electrostatlcally at a frequency about 3KHz, with a Q factor of ~iO 5. The period P of the oscillator is related to its moment of inertia I by P = 2~J(I/k) where k is the rigidity modulus of the torsion tube. In the normal state all the fluid is locked to the
03784363/81/0000-0000/$02~0
© No~h-HoUandPublishingCompany
840
1.0
I
I
2.0
3.0
TIK
Figure i: Period as a function of temperature for two different pressures. The period digits s h o w n are preceded by the digits 297 and are then in nanoseconds. Note the two shifted scales.
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temperatures (see also Figure 2 which shows the melting curve of bulk ~He). At the lower pressure, the period increases slightly as the temperature is reduced below 4K, indicating a positive expansion coefficient for 4He in Vycor, like bulk 4He but somewhat smaller in magnitude. At the point labelled a the period decreases slightly; this occurs at the bulk liquid lambda line (see Figure 2) and is attributed to decoupling of the small amount of bulk superfluid in the bore of the torsion tube and in the oscillator itself. At a lower temperature (labelled b) the period decreases much more markedly as liquid inside the Vycor becomes superfluid. The onset temperature for superflow at pressures S 27 bar are shown in Figure 2; similar results have been obtained at Cornell (6). At the higher pressure (42.5 bar) in Figure 1 the expansion coefficient of 4He in Vycor is again positive. At the bulk melting curve the period immediately decreases very sharply: this striking phenomenon has been observed many times and at several different pressures, and is quite reproducible. We have not so far been able to account for it. At lower temperatures still, the period again decreases sharply (point ~ in Figure 1). The temperatures at which this second break occurs are plotted in Figure 2 as a function of pressure. They form a smooth extension of the curve in the bulk fluid region of pressures which we identify there as the temperatures of onset of suner-
40 ~_.~_ 3OI ~ _
,o
BULK SOLID
-
\
1.5
Z.O "IlK
l~igure 2 : Phase diagram of ~He showing the bulk 'lambda line and onset temperatures for superflow in Vycor. Points labelled -o- in the bulk solid region are those such as c in Figure i, at the corresponding start~n@ pressures. Actual pressures in the Vycor are less due to contraction of the small amount of bulk He in the oscillator when it solidifies hence the error bars.
fluidity in Vycor. These observations add support to those which indicate that superflow can exist in restricted geometries in the region where bulk 4He is solid (3-5) - in this case to quite high pressures. the measurements we can calculate values of XOs,'p, where X is a comPlicated geometrical constant which includes the tortuosity factor {= 0.3 as measured from the spin diffusion coefficient of ~He in Vycor (7)), the number of blind pores, and an effect due to varying pore size. At OK, XQs/p = O.16 at 1 bar and O.12 at 25 bar. It is not clear whether X is expected to be pressure-dependent. From
If it is correct to retain the same interpretation of the data above the bulk solidification curve, XPs/Q at OK extrapolates to zero at 50 bar. This work was carried out with part support from SRC Grant GR /A7526.2 ~Science Research Council Senior Fellow. *Royal Society/Chinese Academy of Sciences Exchange visitor. Permanent address: University of Science and Technology of China, Hofei, C h i n a %%S.R.C. Senior Visiting Fellow at University of Sussex. EI~[ J. Landau, S.G. Lipson, L.M. Maatanen, L.S. Balfour and D.O. Edwards, Phys. Rev. Letters 45 (1980) 31. E 2 ] J.E. Berthold, D.J. Bishop and J.D. Reppy, Phys. Rev. Letters 39 (1977) 348. [3- I E.N. Smith, D.F. Brewer, Cao Lieshao and J.D. Reppy, Bull. Am. Phys. Soc. April 1981. E4~I E.N. Smith, J.D. Reppy, D.F. Brewer and Cao Liezhao, this Conference. E 5 ~ A.L. Thomson, S. Hayes, D.F. Brewer and J.D. Reppy, this Conference. E6~ D.J. Bishop, Ph.D. Thesis 1978, Cornell (unpublished). E7[[ D.F. Brewer and J.S. Rolt, Physics Letters 48A (1974) 141.
JE 8
HELIUM-FOUR TRANSITION IN A RESTRICTED G E O ~ T R Y BELOW AND ABOVE THE BULK SOLIDIFICATION PRESSURE D.F. Brewer t, Cao Liezhao*, and C. Girit
Physics Laboratory, University of Sussex, Brighton, Sussex. and J.D. Reppy tt Laboratory for Atomic and Solid State Physics, Cornell University, Ithaca, New York. Using a torsional oscillator technique, we have investigated the onset of superfluidity of ~He in Vycor at pressures in the liquid region and at higher pressures where bulk ~He is solid. The lower pressure data trace out the onset temperature for superflow in Vycor as a function of pressure, which is roughly parallel to the bulk lanbda line but about O.25K lower. At OK, calculated values of the superfluid fraction are about O.16 at 1 bar and O.12 at 25 bar; these numbers contain a geometrical constant. Higher pressure data indicate that superflow can occur in Vycor at pressures as much as 20 bar above bulk solidification. An unexplained decrease in period is observed below the b u l k solidification temperature. I.
INTRODUCTION
The van der Waals attraction between He and most solid surfaces is sufficiently strong that it binds the layer of helium in contact with it at solid density. Nevertheless, it is known that, on a macroscopic scale, the free energy at melting pressures of the liquid helium-substrate interface is lower than that of the solidsubstrate interface in some cases, and the solid does not wet the wall although the first helium monolayer must still be adsorbed at solid density. Using interfacial tension results (i) one can calculate that in Vycor glass whose pores have an average diameter of ~ 7 0 ~, liquid should be stable at pressures of about 1 bar above the bulk solidification pressure. We have investigated superfluidity of ~He in Vycor using a torsional oscillator technique (2)and find evidence for it at considerably higher pressures. These measurements supplement others on solidification in restricted geometries which are also presented at this Conference (3-5). 2.
substrate and contributes to the moment of inertia. Transition to the superfluid state is observed as a decrease in period due to decoupling of the superfluid, with a decrease in the moment of inertia. 3.
RESULTS AND DISCUSSION
Figure 1 shows the period as a function of temperature for two constant pressures, the smaller one (15 bar) being in the fluid region of the phase diagram, and the larger one (42.5 bar) being in the bulk fluid region at higher temperatures and the bulk solid reqion at lower
--lO0
150
l
APPARATUS
m
The torsional oscillator was a hollow cylinder of beryllium copper, about icm diame6er and lcm high t almost completely filled with a cylinder of Vycor porous glass. It was connected by a BeCu torsion tube to a massive block, and helium could be admitted to it through the imm diameter bore of the tube. Oscillations were excited and detected electrostatlcally at a frequency about 3KHz, with a Q factor of ~iO 5. The period P of the oscillator is related to its moment of inertia I by P = 2~J(I/k) where k is the rigidity modulus of the torsion tube. In the normal state all the fluid is locked to the
03784363/81/0000-0000/$02~0
© No~h-HoUandPublishingCompany
840
1.0
I
I
2.0
3.0
TIK
Figure i: Period as a function of temperature for two different pressures. The period digits s h o w n are preceded by the digits 297 and are then in nanoseconds. Note the two shifted scales.
583
584
temperatures (see also Figure 2 which shows the melting curve of bulk ~He). At the lower pressure, the period increases slightly as the temperature is reduced below 4K, indicating a positive expansion coefficient for 4He in Vycor, like bulk 4He but somewhat smaller in magnitude. At the point labelled a the period decreases slightly; this occurs at the bulk liquid lambda line (see Figure 2) and is attributed to decoupling of the small amount of bulk superfluid in the bore of the torsion tube and in the oscillator itself. At a lower temperature (labelled b) the period decreases much more markedly as liquid inside the Vycor becomes superfluid. The onset temperature for superflow at pressures S 27 bar are shown in Figure 2; similar results have been obtained at Cornell (6). At the higher pressure (42.5 bar) in Figure 1 the expansion coefficient of 4He in Vycor is again positive. At the bulk melting curve the period immediately decreases very sharply: this striking phenomenon has been observed many times and at several different pressures, and is quite reproducible. We have not so far been able to account for it. At lower temperatures still, the period again decreases sharply (point ~ in Figure 1). The temperatures at which this second break occurs are plotted in Figure 2 as a function of pressure. They form a smooth extension of the curve in the bulk fluid region of pressures which we identify there as the temperatures of onset of suner-
40 ~_.~_ 3OI ~ _
,o
BULK SOLID
-
\
1.5
Z.O "IlK
l~igure 2 : Phase diagram of ~He showing the bulk 'lambda line and onset temperatures for superflow in Vycor. Points labelled -o- in the bulk solid region are those such as c in Figure i, at the corresponding start~n@ pressures. Actual pressures in the Vycor are less due to contraction of the small amount of bulk He in the oscillator when it solidifies hence the error bars.
fluidity in Vycor. These observations add support to those which indicate that superflow can exist in restricted geometries in the region where bulk 4He is solid (3-5) - in this case to quite high pressures. the measurements we can calculate values of XOs,'p, where X is a comPlicated geometrical constant which includes the tortuosity factor {= 0.3 as measured from the spin diffusion coefficient of ~He in Vycor (7)), the number of blind pores, and an effect due to varying pore size. At OK, XQs/p = O.16 at 1 bar and O.12 at 25 bar. It is not clear whether X is expected to be pressure-dependent. From
If it is correct to retain the same interpretation of the data above the bulk solidification curve, XPs/Q at OK extrapolates to zero at 50 bar. This work was carried out with part support from SRC Grant GR /A7526.2 ~Science Research Council Senior Fellow. *Royal Society/Chinese Academy of Sciences Exchange visitor. Permanent address: University of Science and Technology of China, Hofei, C h i n a %%S.R.C. Senior Visiting Fellow at University of Sussex. EI~[ J. Landau, S.G. Lipson, L.M. Maatanen, L.S. Balfour and D.O. Edwards, Phys. Rev. Letters 45 (1980) 31. E 2 ] J.E. Berthold, D.J. Bishop and J.D. Reppy, Phys. Rev. Letters 39 (1977) 348. [3- I E.N. Smith, D.F. Brewer, Cao Lieshao and J.D. Reppy, Bull. Am. Phys. Soc. April 1981. E4~I E.N. Smith, J.D. Reppy, D.F. Brewer and Cao Liezhao, this Conference. E 5 ~ A.L. Thomson, S. Hayes, D.F. Brewer and J.D. Reppy, this Conference. E6~ D.J. Bishop, Ph.D. Thesis 1978, Cornell (unpublished). E7[[ D.F. Brewer and J.S. Rolt, Physics Letters 48A (1974) 141.