Fermi liquid behaviour of the viscosity of3He-4He mixtures

We have investigated³He-⁴He mixtures at³He-concentrations 0.98%x9.5% by the vibrating wire technique in the temperature range 1 mKT 100 mK and at pressures 0 bar p 20 bar. In the degenerate regime of the mixtures the Landau theory of Fermi liquids predicts a temperature dependence of the viscosity proportionalT ^–2. We report on the first observation of this behaviour at 3 mKT 10 mK for all investigated concentrations and pressures. At temperatures below about 20 mK slip corrections had to be taken into account due to the increase of the quasiparticle mean free path at very low temperatures. The low-temperature cut-off in T ² = constant indicates the transition into the ballistic regime of the mixtures, where the mean free path of the quasiparticles exceeds the radius of the vibrating wire. Our results for the pressure dependence of the viscosity as well as for its magnitude show substantial differences from predictions based on pseudopotential theory. However, a calculation of with the quasiparticle interaction potential of recent solubility measurements in mixtures agrees well with our experimental data, in particular the pressure independence of .     

Shear viscosity of liquid4He and3He-4He mixtures,especially near the superfluid transition

High-resolution measurements of are reported for liquid⁴He and³He-⁴He mixtures at saturated vapor pressures between 1.2 and 4.2 K with particular emphasis on the superfluid transition. Here is the mass density, the shear viscosity, and in the superfluid phase both and are the contributions from the normal component of the fluid ( _n and _n ). The experiments were performed with a torsional oscillator operating at 151 Hz. The mole fraction X of³He in the mixtures ranged from 0.03 to 0.65. New data for the total density and data for _n by various authors led to the calculation of . For⁴He, the results for are compared with published ones, both in the normal and superfluid phases, and also with predictions in the normal phase both over a broad range and close to T. The behavior of and of in mixtures if presented. The sloped/dT near T and its change at the superfluid transition are found to decrease with increasing³He concentration. Measurements at one temperature of versus pressure indicate a decreasing dependence of on molar volume asX(³He) increases. Comparison of at T, the minimum of _n in the superfluid phase and the temperature of this minimum is made with previous measurements. Thermal conductivity measurements in the mixtures, carried out simultaneously with those of , revealed no difference in the recorded superfluid transition, contrary to earlier work. In the appendices, we present data from new measurements of the total density for the same mixtures used in viscosity experiments. Furthermore, we discuss the data for _n determined for⁴He and for³He-⁴He mixtures, and which are used in the analysis of the data.     

Shear viscosity measurements of liquid 4He and 3He-4He mixtures near the tricritical point

A torsional oscillator cell is described, by means of which simultaneous precision measurements of () and of the molar volume can be made in liquid ⁴He-⁴He mixtures over the temperature range between 0.5 and 3 K. Here is the mass density, the shear viscosity and in the superfluid phase they become the contributions _n and _n of the normal component. The results of for ⁴He near the superfluid transition are compared with the predictions by Schloms, Pankert and Dohm, and by Ferrell. Measurements of () are reported for mixtures with 0.64X0.74, where X is the ³He mole fraction. Those for X = 0.67 and 0.70 are compared with data by Lai and Kitchens. The viscosity experiments show no evidence of a weak singularity at the tricritical point.     

Shear viscosity measurements of liquid 3He-4He mixtures above 0.5 K

Simultaneous measurements of () and of the molar volume are reported for liquid mixtures of ³He in ⁴He over the temperature range between 0.5 and 2.5 K. Here is the shear viscosity and is the mass density. In the superfluid phase, the product of the normal components, _n and _n , is measured. The mixtures with ³He molefractions 0.30 < X < 0.80 are studied with emphasis on the region near the superfluid transition T and near the phase-separation curve. Along the latter, they are compared with data by Lai and Kitchens. For X > 0.5, the viscosity singularity near T becomes a faint peak, which however fades into the temperature-dependent background viscosity as X tends to the tricritical concentration X _t. Likewise, no singularity in is apparent when T _t is approached along the phase separation branches _– and ₊. Furthermore, viscosity data are reported for ³He and compared with previous work. Finally, for dilute mixtures with 0.01 X 0.05, the results for are compared with previous data and with predictions.     

Diffusion mechanism in the quantum decay of metastable3He-4He mixtures at low temperatures

We study the quantum phase-separation kinetics of a supersaturated liquid mixture at temperatures down to absolute zero. The energy dissipation effect of diffusion is incorporated into the calculation of the nucleation rate in normal and superfluid liquid mixtures. Unlike single-component systems, diffusion is the principal process which governs both the quantum nucleation rate and supercritical droplet growth rate in mixtures near the demixing curve. The low temperature phase-separation experiments in supersaturated liquid³He-⁴He mixtures of³He-dilute phase are analyzed and discussed. The critical degree of metastability and at the same time the critical droplet radius are shown to be temperature-independent below about 80 mK, suggesting the temperature of the thermal-to-quantum crossover to be of the same order of magnitude. The critical radius of a demixed droplet is estimated as about 20 Å, being within reasonable values.     

Vibrating-wire measurements in vacuum,liquid3He and liquid3He-4He mixtures

In order to overcome the 200µK - barrier in the refrigeration of liquid ³ He- ⁴ He mixtures we have constructed an experimental cell using only pure materials to minimize possible origins for heat leaks into the liquid. With this arrangement we were able to cool a saturated6.8%- mixture to a temperature of 150µK. A vibrating wire which was immersed in pure ³ He floating on top of the phase-separated mixture was used as a thermometer. This wire was calibrated in a second experiment with pure ³ He only in the cell. In superfluid ³ He-B at T0.15 mK the damping of the wire due to the quasiparticles becomes very small, and we observe typical characteristics of the vacuum damping of the wire which was extensively examined before filling any liquid into the cell.     

Sound attenuation and3He-3He interaction in3He-4He liquid mixtures at saturated vapor pressure

The interaction potential between³He quasiparticles in³He-⁴He liquid mixtures is determined from the sound attenuation at saturated vapor pressure. Sound attenuation was measured in mixtures with³He mole fraction ranging from 0.0289 to 0.0573. The superfluid transition temperature of³He in mixtures and other properties were then estimated from the deduced interaction potential.     

Investigation of the dynamic behavior of 3He-4He mixtures at low temperatures using holographic interferometry

We describe a new optical interferometric technique which we have applied to ³He-⁴He liquid mixtures in the phase separation region. The formation and slow propagation of a concentration front is observed when the phase separation equilibrium is disturbed by sudden heating. The phenomenon is analyzed in terms of a concentration-dependent diffusion constant, and the results indicate critical behavior of the diffusion constant on the normal side of the lambda line. The application of the optical method to studies of interphase surface tension and crystallization is also indicated.This work was supported by the U.S.-Israel Binational Science Foundation.     

Nucleation of transitions in liquid 3He-4He mixtures

We present a complete set of data describing the nucleation both of superfluidity and phase separation at container walls in liquid ³He-⁴He mixtures. The appearance of superfluidity and the growth of phase-separated films are measured locally at the walls. A theoretical interpretation is given, important results of which are that the phase separation and superfluid transitions become uncoupled when the transitions are localized near the walls and that quantum fluctuations most probably strongly affect the nature of the superfluid nucleation transition at low temperature. Further, comparison of our results with data for transitions in pure ⁴He films demonstrates that a universality principle governs the transitions in both systems.Partly supported by NSF Grant No. DMR 75-21886.Laboratoire associé au CNRS.     

Theory of the osmotic pressure of dilute mixtures of3He in liquid4He at low temperatures

The osmotic pressure of dilute mixtures of³He in liquid⁴He is calculated and compared with experiment. One parameter, which is a measure of the difference between the mean potential energy of³He atoms and⁴He atoms in the mixture is determined from the experiments, and good agreement is obtained with the measured values of as a function of concentration and temperature. It is shown that the osmotic pressure does not provide any accurate information about the effective interaction between³He atoms. A comparison with earlier calculations of the osmotic pressure and of the³He chemical potential is made.Work performed under the auspices of U.S. Atomic Energy Commission.     

First viscosity of dilute3He-4He mixtures below 0.6 K

Starting with the Boltzmann transport equation, the first viscosity of dilute³He-⁴He mixtures for various³He concentrations x is evaluated up to around T 0.6 K by including the contribution from three-phonon processes (3PP) in the anomalous elementary excitation spectrum of liquid⁴He. Due to 3PP, the characteristic time for³He viscosity at high temperatures, i.e., T2T_F where T_F is the³He Fermi temperature, is evaluated as 5 × 10^–12/xT, which is smaller than the value estimated by Rosenbaum et al. This is interpolated with in the degenerate (quantum) region, TT_F. The obtained viscosities are in better agreement with experimental results than those of Baym and Saam, whose theory does not include 3PP. However, at very low concentrations there exists a discrepancy between the present theory and experiments, so that an alternate treatment should be considered.     

NMR Studies on 3He-3He and 3He-4He tunneling motions in solid 3He-4He mixtures

Helium-3 nuclear spin relaxation times T ₁, T ₂, and T ₁have been measured for ³He-⁴He solid mixtures at the exchange plateau region (~0.5K). The ³He concentrations X ₃of the samples were 7.2, 2.9, 1.8, 1.4, 0.67, 0.65, and 0.22%, and their molar volumes varied between 19.9 and 20.9cm³/mole in hcp phase. The spectral density function J() for dipolar field fluctuations was determined in the low-frequency branch from T ₁measurements and in the high-frequency branch from conventional T ₁measurements. It was found that J() is given by J() = cJ()|_3–4 + (1–c)J()|_3–3, where J()|_3–4 is the spectral density function due to the ³He-⁴He tunneling motions, and J()|_3–3 is that due to the ³He-³He tunneling motions. Using the Torrey theory, the correlation frequency of the ³He-⁴He tunneling motions was evaluated from T ₁data, and was found to be in good agreement with Landesman 's theory.Supported in part by the Japan Society for the Promotion of Science through a grant to Y.H.     

Heat release,refrigeration and thermometry in3He-4He solutions at very low temperatures

We report on our measurements performed in liquid³He-⁴He solutions in the microkelvin temperature range at the Bayreuth nuclear demagnetization cryostat. One aspect of our work is the application of the vibrating wire technique for thermometry in the ballistic regime of phase-separated solutions. The establishment of reliable thermometry along with the particular design of our experimental cells enables us to study two main limitations on the minimum temperature of about 100K achieved in³He-⁴He solutions so far: the thermal resistance between the liquid and the cell, and the origins of the heat leaks.     

NMR studies of highly polarized liquid3He-4He mixtures

An efficient technique for maintaining large³He nuclear spin polarizations in liquid³He-⁴He mixtures has been developed and used to polarize samples contained in narrow tubes. Results obtained in a U-shaped cell and a coil-shaped cell are compared. A systematic study of the effects of dipolar fields within the sample on the characteristics of the observed long-lived magnetostatic modes is in progress. NMR signals obtained in the coil-shaped cell reveal phase separation and the existence of a highly polarized³He-rich region in the sample.Laboratoire de L'Ecole Normale Supérieure et de L'Université Pierre et Marie Curie, associé au CNRS (URA 18)     

Measurements of the viscosity and the slip length on liquid3He at low temperatures

Measurements of the viscosity and the slip length are reported for both the normal liquid and superfluid³He within the slip approximation. We used the hollow torsional oscillator. For the normal liquid³He the slip length is shorter than the theoretical expectation and there is no anomaly near the superfluid transition, but the viscosity shows the anomalous deviation from the Fermi liquid behavior which is thought to be attributed to the superfluid fluctuation. For the superfluid³He, the temperature dependence of the slip length agrees with the theory qualitatively and the viscosity agrees well with the theory quantitatively as far as the slip approximation is valid.     

Sound attenuation in3He-4He liquid mixtures under pressure

The attenuation of sound was measured in³He-⁴He mixtures with³He concentrations ranging from 2.89 to 8.03% at pressures of 10 and 20 bar. The quasiparticle interaction potentials were then determined at each pressure by analyzing the sound attenuation data. The superfluid transition temperature of³He and other properties in the mixtures were then estimated from the interaction potentials.     

3He-3He quasiparticle interaction in3He-4He mixtures under pressure

Based on our recent phase separation curve of³He-⁴He solution at elevated pressures, we propose new³He-³He quasiparticle interaction potentials, which reproduce the existing experimental results pretty well except for³He effective mass under pressure.     

3He-4He mixtures in aerogel

Superfluid density and heat capacity experiments on³He-⁴He mixtures in 98% porous aerogel show that in this system the coexistence boundary is detached from the superfluid transition line. The tricritical point is removed, and there is a superfluid phase on the³He rich side of the phase diagram. The presence of heat capacity peaks along the transition line down to a⁴He concentration of only 8% indicates the 3-dimensional nature of this transition.This work is supported by NSF under grants DMR-9008461 and DMR-9311918.