Specific heat of amorphous3He films and confined liquid3He

We have measured the heat capacities of³He films and liquid³He in porous Vycor glass at 10 to 600 mK. With increasing the film thickness from 1 to 3 atomic layers, the specific heat evolves gradually from that typical to solid to that of liquid³He. At about 2 atomic layers, however, its low-temperature part is nearly temperature-independent; we interpret this as a result of gradual freezing of spins in an amorphous solid³He film with decreasing the temperature. The contribution of liquid³He in the center of the Vycor pores can be described as the specific heat of bulk liquid³He at corresponding pressures in the range 0 to 28 bar. The thickness of amorphous solid on the pore walls increases with external pressure roughly linearly. Preplating the walls with⁴He allows to determine the positions of³He atoms contributing to the surface specific heat at 10 to 50 mK. In addition, the contribution from the specific heat of³ He -⁴He mixing at 100 to 600 mK is discussed as a function of pressure and amount of⁴He.0n leave from ISSP Acad. Sci. of Russia, Chernogolovka, Russia     

Experiments with3He quasiparticles in the collisionless regime. I. A direct measurement of the Fermi velocity by heat conduction

Measurements of the thermal conduction of liquid ³ He in the collisionless regime, where the mean free path of the thermal carriers is much greater than the channel diameter, allow a direct measurement of the carrier velocity. These experiments have been done using Vycor porous glass as the channel (average diameter ～70 Å) at temperatures down to 16 mK. They show that the carrier velocity (～43 m/sec) is that of quasiparticles rather than of bare ³ He atoms, whose velocity would be a factor of m*/m (～3) greater, and thus confirm quite independently of any other measurement the validity of Landau quasiparticle theory. The data also strongly suggest a zero quasiparticle specular reflection coefficient, which allows an estimate to be made of the quasiparticle lifetime. This shows that the energy levels of quasiparticle states have a width more than ten times greater thankT at 20 mK. As an incidental result, a value for the low-temperature thermal conductivity of Vycor glass has been calculated.     

The preferential adsorption of 4He from 3He-4He mixtures onto Vycor glass

The preferential adsorption of ⁴He from liquid ³He-⁴He mixtures onto Vycor glass has been measured over a wide concentration range between 1 and 3 K. Over most of this temperature range the preferential adsorption extends beyond the second atomic layer, with a preferential binding energy of about 3.5 K/mole. Near 1 K and below, the thickness of the ⁴He layer increases rapidly as a precursor to the bulk liquid phase separation.     

Nucleation and phase separation in superfluid3He-4He solutions

The kinetics of the phase separation in³He-⁴He superfluid solutions is studied from anomaly in the first sound velocity and the dielectric constant. The histogram of experiments on solution supersaturation is obtained and used to study of phase separation probability. It was shown that above 50 mK the obtained temperature dependence of the supersaturation is qualitatively in accord with the thermal activation mechanism of nucleation. Below 50 mK the data may point towards a transition from classical to quantum mechanism of nucleation.     

Surface Magnetism of 3He in Grafoil

We report the magnetic susceptibility of ³He in Grafoil filled with pure liquid³He at 27.6 bar and at temperatures down to 0.1 mK with a cw NMR method. It is composed of two contributions: from the bulk liquid and from the adsorbed layer of ³He on the Grafoil surface. The latter shows a well-known strong ferromagnetic tendency and can be fitted to a Curie–Weiss law in the high temperature region. The obtained Weiss temperature is surprisingly large compared with the previous ones.     

Preliminary Heat-Capacity Measurements of 2D Solid 3He Adsorbed on Graphite Preplated with 4He

We describe preliminary resugts of heat capacity measurements of the 4/7 phase in two dimensional ³He adsorbed on graphite preplated with a ⁴He monolayer in a temperature range between 0.17 and 20 mK. In zero magnetic field, we observed a double-peak structure similar to that reported previously for the same phase in a different system (³He/³He/gr) in which the gapless quantum spin-liquid ground state is proposed. The exchange interaction deduced from the high temperature data is by a factor of 30% smaller than the previous one, presumably because of the smaller lattice constant for the ³He/⁴He/gr system. The present resugt provides strong evidence that such a peculiar temperature dependence of heat capacity is characteristic of the 4/7 phase. Application of magnetic fields up to 0.65 T on this phase does not seem to change appreciably the higher temperature broad peak at around 1.4 mK.     

Thin3He films on a disordered substrate: A Metal-Insulator transition

The heat capacity of thin³He films and of liquid³He underpressure up to 28 bar in porous Vycor glass has been measured at temperatures 10–600 mK. An evolution from solid (Insulator) to liquid (Metal) behaviour has been observed with increasing the film thickness from one to three atomic layers. At low temperatures the second layer has a temperature independent specific heat. Using a model of glassy second layer of³He on a rough substrate, that has a broad uniform distribution of the logarithm of nuclear exchange interaction, we calculate its specific heat and susceptibility and compare them with the available experimental data.On leave from the Institute of Solid State Physics, Russ. Acad. Sci., Chernogolovka 142432 Moscow distr., Russia     

Equilibrium phase diagram and kinetics of isotopical phase separation of 3%3He in HCP4He mixture

The isotopical phase separation in a weak solid mixture of³He in⁴He is investigated by 250 kHz pulsed NMR under a pressure of 3.7 MPa in the temperature range 100 – 240 mK. The equilibrium concentrations of³ He in HCP phase are found to be in a good agreement with classical regular solution theory for phases with different crystal structures. The time constant of decay at steplike cooldown along the separation line are shown to monotonously decrease. The linear dependence of the time on the concentration may point towards an important role of quantum diffusion.     

Phase Separation of Liquid 3He–4He Mixtures in Porous Vycor Glass

We report our recent investigations of the phase separation of liquid ³ He– ⁴ He mixtures in the restricted geometry of porous Vycor glass using pressure measurements. The experimental cell is entirely filled with a Vycor cylinder and closed by a cold valve. We are measuring the pressure versus temperature by means of a capacitive pressure gauge. The results are discussed in comparison with the phase separation of helium mixtures in aerogel, ¹ in particular with respect to the different ratio of substrate surface to liquid volume of both glasses.     

Search for superfluidity of3He in3He-4He solution

We have tried to cool a³He-⁴He solution down to the microkelvin temperature region to search for a superfluid transition of the³He component in the solution. The contact surface area between the solution and a sintered powder has been increased enormously by the use of a fine platinum powder, to reduce the effect of the residual heat leak directly entering into the solution. Although the heat leak was found to be time dependent, the ultimate ratio of the heat leak to the surface area is about 0.046 pW/m², improved very much from those by the other groups. But the lowest temperature of the solution is still around 0.2 mK, and no evidence of the transition has been observed yet.     

Evaporative Cooling of 3He-4He Mixture Films

Heat transport by saturated ³ He- ⁴ He films has been studied at temperatures 50..350 mK and the bulk concentration of ³ He ranging from 0.1 ppm to 5%. The cooling of the film, when locally heated above 160 mK, is mainly via 2D flow of surface ³ He from colder area followed by evaporation of ³ He. At certain heating power the 2D flow becomes a bottleneck, the heated spot runs out of ³ He and its temperature abruptly increases. The critical power is nearly proportional to the surface density of ³ He. For higher ³ He concentrations another distinct step in temperature has been observed at a lower heating power. It is attributed to the existence of an excited ³ He surface state whose population starts at ³ He surface density of 3.5×10 ¹⁴ cm^–2 . The second state is located about 1.2 K higher in energy than the ground state and provides an additional channel for the 2D flow of ³ He.     

Adiabatic Melting of 4He Crystal in Superfluid 3He at Sub-millikelvin Temperatures

Adiabatic melting of ⁴He crystal to phase separated ³He–⁴He solution (at T< 2 mK) is probably the most promising method to cool the dilute phase down to temperatures substantially below 0.1 mK. When started well below the superfluid transition temperature T _c of pure ³He, this process allows, in principle, to get the final temperature (T _f ) several orders of magnitude less than the initial one (T _i ). This work is the first practical implementation of the method below the T _c of ³He. The observed cooling factor was T _i /T _f =1.4 at 0.9 mK, being mainly limited by the bad performance of the superleak filling line, by incomplete solidification of ⁴He in the cell, and by the improper thermal contact between the cell wall and the liquid.     

The damping of a vibrating wire resonator in 0.003% and 0.1%3He-4He solutions below 120 mK. The effective viscosity of a 0.1% solution

We have measured the damping of a 13-µm diameter vibrating wire resonator in 0.1% and 0.003%³He-⁴He solutions at temperatures between 7 and 120 mK. This is a particularly interesting system since it involves a transition from Fermi-Dirac to Maxwell-Boltzmann statistics and also a transition from viscous to ballistic behavior. Contributions to the damping on the wire from sources other than the³He quasiparticle component in the solutions are determined by measurements in pure⁴He. The viscosity inferred from the data for the 0.1% solution spans the quantum to classical transition, with a minimum at around 13 mK. The temperature dependence of the viscosity is in close agreement with that obtained from recent measurements of the damping of second sound, although the absolute values differ by about 25%. In the 0.003% solution the quasiparticle mean free path is much larger than the wire radius, so that momentum density rather than viscosity is the determining physical quantity. Nevertheless the measured damping on the wire is to found be in excellent agreement with the predictions of a simple kinetic approach, with no adjustable parameters.     

Osmotic Pressure of 3He-4He Solutions at 25.3 Bar and Low Temperatures

The osmotic pressures of dilute ³He-⁴He solutions were determined at 25.3 bar from measurements of crystallization curves at temperatures from 5 mK to 60 mK, when the ³He component of the solution obeying the Fermi-Dirac statistics was deep in the degenerate state. We determine the shift of the crystallization pressure of the solution of interest relative to pure ⁴He when both these substances are present in the cell in two separate volumes at the same temperature. We used our novel ultra-sensitive capacitive gauge for measurements of small pressure differences between the two substances. We used a quartz resonator for determination of solution’s concentration in situ. The difference between the crystallization pressure of the saturated solution and pure ⁴He, both extrapolated to zero temperature, is (339±2) mbar.      

Specific heat of3He-4He mixtures in Vycor glass

The specific heat of a ³ He- ⁴ He mixture filling a narrow pore is calculated in the temperature range 0.5–1 K, including the effect of van der Waals forces due to the walls, and is found to be compatible with the enhancement over the bulk liquid value experimentally observed for mixtures in Vycor glass.     

A Summary of Mass Flux Measurements in Solid 4He

Here we provide a summary and brief review of some of the work done with solid ⁴He at the University of Massachusetts Amherst below a sample pressure of 28?bar. The motivation for the work has been to attempt to pass ⁴He atoms through solid ⁴He without directly applying mechanical pressure to the solid itself. The specific technique chosen is limited to pressures near the melting curve and was initially designed to provide a yes/no answer to the question of whether or not it might be possible to observe such a mass flux. The thermo-mechanical effect and direct mass injection have been separately used to create chemical potential differences between two reservoirs of superfluid ⁴He connected to each other through superfluid-filled Vycor rods in series with solid ⁴He, which is in the hcp region of the phase diagram. The thermo-mechanical effect is a more versatile approach. And, in a particular symmetric application it is designed to provide a mass flux with little or no net increase in the density of the solid. Our observations, off but near the melting curve, have included: (1)?the presence of an increasing DC flux of atoms through the solid-filled cell with decreasing temperature below ≈650?mK and no flux above this temperature; (2)?the presence of a flux minimum and flux instability in the vicinity of 75–80?mK, with a flux increase at lower temperatures; (3)?the temperature dependence of the flux above 100?mK and the dependence of the flux on the net driving chemical potential difference provide interesting insights on the possible mechanism that leads to the flux above 100?mK. The most recent data suggest that whatever is responsible for the flux in solid ⁴He, at least for T>100?mK, may be an example of a Bosonic Luttinger liquid.     

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

Torsional oscillator (TO) experiments involving solid \(^{4}\) He confined in the nanoscale pores of Vycor glass showed anomalous frequency changes at temperatures below 200 mK. These were initially attributed to decoupling of some of the helium’s mass from the oscillator, the expected signature of a supersolid. However, these and similar anomalous effects seen with bulk \(^{4}\) He now appear to be artifacts arising from large shear modulus changes when mobile dislocations are pinned by \(^{3}\) He impurities. We have used a TO technique to directly measure the shear modulus of the solid \(^{4}\) He/Vycor system at a frequency (1.2 kHz) comparable to that used in previous TO experiments. The shear modulus increases gradually as the TO is cooled from 1 K to 20 mK. We attribute the gradual modulus change to the freezing out of thermally activated relaxation processes in the solid helium. The absence of rapid changes below 200 mK is expected since mobile dislocations could not exist in pores as small as those of Vycor. Our results support the interpretation of a recent TO experiment that showed no anomaly when elastic effects in bulk helium were eliminated by ensuring that there were no gaps around the Vycor sample.     

Adiabatic expansion of3He in4He at very low temperatures

In this paper the results of the investigation of a one-shot cooling technique, called adiabatic expansion of³He in superfluid⁴He, are reported. The expansion cooler basically consists of an expansion cell and a⁴He reservoir connected by a superleak. In the expansion cell nearly pure³He is gradually diluted to a saturated mixture by the injection of superfluid⁴He from the⁴He reservoir. The expansion of the³He produces cooling, which, in the ideal (isentropic) case can lower the temperature by a factor 4.56. In practice, the performance of this cooling method is limited by irreversibilities and heat leaks. In this paper several irreversible processes such as heat conduction, viscous effects, and supercritical⁴He flow, have been analyzed. Furthermore the effect of³He in a sinter layer in the expansion cell is discussed. The experiments have shown that the fountain pressure in the⁴ He reservoir is very suitable for driving the⁴He in and out of the expansion cell. During an expansion/extraction the⁴He chemical potential difference across the superleak is zero. The realised cooling factor, defined as the ratio of the initial temperature and the final temperature, is about 3.5 for initial temperatures between 20 mK to 190 mK. This value is lower than the ideal factor of 4.56 that can be obtained for isentropic expansions. The discrepancy is mainly due to the relatively large heat leak. The lowest temperature obtained in this investigation was 5.7 mK. The analyses have revealed no fundamental limitations for obtaining lower temperatures.     

Influence of 4He Preplating on 3He Fluid Formed in One-Dimensional 28 Å-Pores

No Heading A degenerate Fermi fluid has been realized recently for ³He films adsorbed in one-dimensional (1D) pores 28 Å in diameter, preplated with ⁴He layers. In order to study the influence of the ⁴He preplating on the ³He Fermi fluids, heat capacity was measured down to 4 mK for two preplated ⁴He films of different thickness. At low temperatures, no substantial difference was found between the two cases. On the other hand, a large difference appeared above about 150 mK. The large ³He heat capacity for the thick ⁴He preplating suggests thermal excitation of the ³He atoms to the excited energy levels of the Andreev states in the ⁴He fluid layers.PACS numbers: 67.70 +n. 67.55 Cx.     

Growth Dynamics and Faceting of 3He Crystals

³He crystals start to show facets on their surface only at about 100 mK, well below the roughening transition temperature. To find out the reason for this discrepancy, we have performed the first quantitative investigation on the growth dynamics of the faceted and rough surfaces of ³He crystals in the temperature range of 60–110 mK. We have applied an original method to obtain the variation of the overpressure on the crystal surface by measuring its curvature and height locally using a Fabry–Pérot interferometer. The growth of the rough surface was found to be limited by the transport of the latent heat which elaborates in the liquid, in accordance with theoretical predictions (Puech L., et al. in J. Low Temp. Phys. 62:315, 1986; Graner F., et al. in J. Low Temp. Phys. 75:69, 1989 and 80:113, 1990) and previous measurements near the minimum of the melting curve (Graner F., et al. in J. Low Temp. Phys. 75:69, 1989 and 80:113, 1990). The mobility of an elementary step on a facet was shown to be limited by the latent heat transport as well. The values obtained for the step free energy are by two orders of magnitude smaller than at ultra low temperatures, which we show to be the result of quantum oscillations of the solid-liquid interface, which quickly become damped when temperature decreases below 100 mK.