Solidification and Superfluidity ofHe4in Confined Geometries

Abstract

The solidification of 4 He in Vycor glass and in sintered Ag powder has been studied between 0.8 and 2.5 K. At 0.8 K, elevation of the melting pressure by 12 bars is seen in Vycor and by 0.3 bar in the Ag sinter. In each material a range of melting pressures, corresponding to different pore sizes, is observed. The location of the \ transition in the liquid in Vycor is determined up to solidification pressure.PACS numbers: 67.40. Kh, 67.80.Gb Several studies have been made of the solidification and superfluidity of 4 He in confined geometries. 1 " 3 Experiments on helium in Vycor glass have indicated that it remained a liquid at pressures of ~-15 bars above the bulk melting pressure. 2 Recently Beamish et al 3 (BHTE) have observed solidification and the superfluid transition of helium in Vycor from changes in sound velocity. However, an accurate phase diagram has not been available because of uncertainties in the presence of the helium in the Vycor.We report measurements of pressure versus temperature along isochores and of the cooling rate (related to the heat capacity) of helium in Vycor. We identify solidification, melting, and the X transition and obtain a phase diagram up to P = 60 bars and T = 2.5 K. There is a range of pressures where both solid and liquid may exist, which, at r = 0.8 K, extends from 36.3 to 38.0 bars. Similar behavior is seen in the Ag sinter, but at only ~ 0.3 bar above bulk melting. The X transition of helium in Vycor has been followed to above solidification pressure, made possible by supercooling of the liquid.The cell is depicted in Fig. 1 (inset). Measurement of the pressure of 4 He in Vycor above bulk melting is difficult because of the long time constant required for communication to a transducer. We obtained a short time constant by grinding the Vycor into a powder with grains ^ 74 pm (200 mesh sieve) thereby reducing the distance for pressure communication. 4 The powder loosely filled the cell to a filling factor of 0.5, allowing individual grains to move with the bulk helium surrounding them and to transmit pressure to the capacitive transducer. 5 Bulk helium existed in the spaces between grains which were ~ 10 4 times the dimension of the 60-A pores in the Vycor.A layer of 700-A sintered Ag powder, pressed to a filling factor of 0.5, provided thermal contact to the helium. The cell was mounted on the still of a dilution refrigerator with a weak thermal link to allow slow cooling of the cell with a time constant ~ 500 times that for equilibrium within the cell. Temperatures were measured with a carbon resistor calibrated against the 4 He melting pressure. 6 Cooling along the bulk melting curve at T = 2 K was at a rate \dT/dt\^4 mK/min, with the cell reaching 0.8 K in ~5 h. The cooling rate is related to the heat current from the cell Q by ti-ll dt = Ceff dT dt where C/ and c s are the specific heats of the liquid 20.0 20.2 20.4 20.6 20.8 21.0 21.2 V(cm 3 /mole) FIG. 1. Upper-right inset, the cell: (a) thermal link, (b) heater, (c) thermometer, (d) Ag sinter, (e) Vycor powder...

Low Frequency Elastic Measurements on Solid $$^{4}$$ 4 He in Vycor Using a Torsional Oscillator

“…As in the other samples, a slow relaxation process occurred during the first cooling of each sample, after which the measurement was reproducible upon thermal cycling. The measurement was made at a strain of 10 −7 (Color figure online) dp of the TO is then related to a change in the shear modulus of the Vycor+helium dμ as dp = − 2π 2 3…”

“…For example, the melting curve and the lambda line of 4 He are both shifted by confinement in Vycor's nanoscale pores [1,2]. The superfluid critical behavior of thin helium films adsorbed on Vycor has been studied using an ultrasonic technique [3] and the torsional oscillator (TO) technique [4].…”

Formation of superfluid liquid pocket in aerogel and its solidification by cooling

“…Properties of superfluid 4 He in porous materials have been investigated extensively and variations in the static properties, such as reduction in the superfluid transition temperatures and elevation of the crystallization pressure have been revealed [1][2][3][4][5][6][7][8][9]. However, not much is known about the dynamical process of superfluid 4 He in porous materials due to the lack of an appropriate method to tackle the physics.…”

Thermal and quantum nucleation of4He crystals in aerogel

“…Crystallization of 4 He in porous materials is elevated to a much higher pressure than that in the bulk [16][17][18][19][20][21][22]. The crystallization has been believed to be initiated when the critical size of the nucleus becomes equal to the pore size with enough overpressure [16][17][18]. This crystallization process in pores is sometimes regarded as homogeneous nucleation because the depinning process would play a minor role in this activity at such high overpressure.…”

“…It is a heterogeneous nucleation, which is closely related to the depinning of a 4 He crystal pinned at that site on the wall [4][5][6][7][8][9][10][11]. Crystallization of 4 He in porous materials is elevated to a much higher pressure than that in the bulk [16][17][18][19][20][21][22]. The crystallization has been believed to be initiated when the critical size of the nucleus becomes equal to the pore size with enough overpressure [16][17][18].…”