Temperature-, concentration- and pressure-dependence of the viscosity of liquid3He-4He mixtures at low temperatures

We have investigated the viscosity of liquid³He-⁴He mixtures at various³He - concentrations (0.98%x9.5%) in the temperature range1 mK T 100 mK and at pressures 0 bar P 20 bar. At T10 mK the Fermi-liquid behaviour T² = const. as well as x^4/3 could be confirmed. However, there are significant deviations from theoretical predictions for the magnitude of the viscosity as well as for its pressure dependence.     

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.     

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.     

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.     

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.     

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.     

Transport properties of spin polarized3He-4He mixtures

We have calculated the viscosity, thermal conductivity, and longitudinal spin diffusion coefficient in³He-⁴He mixtures which are spin polarized. The calculation applies to all temperature regimes. We have also calculated the Onsager cross coefficient which arises because of the coupling between heat and longitudinal spin currents. The interaction between³He quasiparticles is taken to be a constant as a first approximation. We have also investigated the changes brought about by allowing the interaction to vary with the momentum of the quasiparticle.     

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 .     

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)     

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.     

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.     

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.     

Calculations of static properties of spin-polarized3He-4He mixtures

The theory of dilute mixtures of³He in⁴He that have been polarized by a strong magnetic field is developed. The interaction between the quasiparticles is taken to be constant, an approximation valid at low temperatures. The polarization of the mixture depends on the strength of the interaction. The internal energy, the specific heat, the osmotic pressure, and the velocity of second sound are also calculated. The specific heat is relatively insensitive to the interaction, but it does change significantly with magnetic field. The osmotic pressure is more sensitive to the effects of the interaction for some³He concentrations and temperatures. The velocity of second sound behaves qualitatively like the osmotic pressure. The measurement of these quantities as a function of temperature and magnetic field is discussed with a view to obtaining the strength of the interaction between quasiparticles.     

Magnetic susceptibility and collisionless spin waves in liquid3He and3He-4He mixtures

The transverse spin susceptibility for a Fermi liquid in a uniform magnetic field is calculated in the collisionless regime using the Landau theory of Fermi liquids. The singularities corresponding to the l=0 and l=1 spin waves are investigated in pure and dilute³He as a function of the wave vector q up to the threshold of the Landau damping.     

Transport properties in3He-4He mixtures near the superfluid transition

We report measurements of the temperature, density, and concentration gradients in³He-⁴He mixtures, induced by a vertical heat flux. The flat horizontal cell included two superposed capacitors and the density was determined by means of the dielectric constant method. The experiments were carried out on mixtures with mole fractionsX ₃=0.37, 0.15, and 0.05 at saturated vapor pressure, with special emphasis on the region near the superfluid transition. Our measurements under steady-state conditions give the conductivity , the thermal diffusion ratiok _T , and the coefficient of thermal expansion. We describe the singular behavior of these quantities in the neighborhood ofT (X). In the superfluid phase, we test with fair success a relation by Khalatnikov between gradX/ gradT and several static properties. From the relaxation times needed to attain steady-state conditions, and in combination with measured static and transport properties, we obtain in the normal phase the mass diffusionD, which diverges strongly asT is approached. In the superfluid phase, we test successfully a scaled relation that results from the solution of Khalatnikov's hydrodynamic equations. From our data the dispersion relations for scattered light are calculated: _o/q ² in both the normal and the superfluid phases and ₂/q ² in the normal phase.Research supported by NSF grant DMR 8024056.     

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.     

Refrigeration and thermometry of liquid3He-4He mixtures in the ballistic regime

The ballistic regime of liquid³He-⁴He mixtures is characterized by a large mean free path of the thermal excitations compared to the characteristic dimension of the experiment. We report on investigations of the transport properties of mixtures as well as superfluid³He in the ballistic regime by means of the vibrating wire technique. In order to avoid possible sources of heat leaks into the liquid, the experimental setup was built as far as possible of pure materials only. The contribution of a Ag sinter to the heat leak as well as its influence on the attainable minimum temperature of the mixtures were investigated by performing measurements in two similar setups which differed in the size of the heat exchanger by about one order of magnitude. Moreover, we have used the vibrating wire partly immersed in the superfluid³He-B phase of a phase-separated mixture as a very sensitive, continuously monitoring thermometer for liquid mixtures in their ballistic regime. The achieved minimum temperature of a 6.8%-mixture atp = 0.35 bar and of a 9.5%-mixture atp = 9.8 bar was 130 K. This value can be considered as an upper limit for the temperature of the mixtures as the damping of the vibrating wire thermometer saturates at this temperature due to its intrinsic properties.