Ultrasonic propagation in3He-4He mixtures near the tricritical point

We present measurements of the singular sound attenuation _sing in liquid mixtures of³He and⁴He near the superfluid transition and at temperatures above the phase separation curve. The mole fractionX of³He ranged from 0.55 to 0.73 and the frequency /2 varied between 1 and 45 MHz. The temperature range was 0.75–1.4 K, with the greatest emphasis on the tricritical region nearX _t=0.67 andT _t=0.87 K. From the change in slopedU/dT of the sound velocityU, we present a new determination of the phase separation curve, which is compared with previous measurements. The sound attenuation peak along the superfluid transition becomes broader in temperature asT is decreased. In addition, there is also an increase in sound attenuation as the phase separation temperatureT is approached. ForX<X _t these two peaks merge into one asX _t is approached. For a given frequency, the attenuation has a maximum value at the tricritical point. Estimates of the contribution _D of mass diffusion to the attenuation for³He-⁴He mixtures with 0<X<0.55 and comparison with experimental values show that _D becomes relatively more important asX increases, and that atX=0.55 it effectively accounts for all of the observed singular attenuation, at least at megahertz frequencies. Hence we assume that for mixtures withX>0.55 the observed attenuation can be analyzed solely in terms of the diffusive relaxation mechanism. The mass diffusion parameterD is then determined from the data. AtX=0.55,D diverges asT is approached, which is consistent with theoretical expectations and experimental results. NearT _t, there is a crossover to a tricritical regime, and it is found that approximatelyD(T–T _t) ^Z withZ=0.32±0.1. Mode coupling predictions are thatZ=1/2 while recent renormalization group calculations giveZ=1/3. The attenuation curves in the tricritical region at the various frequencies can be represented satisfactorily but not perfectly by a scaling function with a characteristic relaxation time (T–T _t) ^–x withx=1.7±0.15. This time corresponds to order-parameter fluctuations. Its temperature dependence is in excellent agreement with renormalization-group calculations that givex5/3, while expectations from dynamic scaling are thatx=3/2. Our analysis also gives the variation of the amplitudes of andD with the direction of approach toT _t. A comprehensive theory for interpreting all the data, in the normal as well as in the superfluid phase, is lacking at this time.Supported by a grant from the National Science Foundation. A preliminary account of this work was presented inBull. Am. Phys. Soc. 21, 229 (1976).     

Interfacial tension near the tricritical point in3He-4He mixtures

The interfacial tension ₁ of phase-separated³He-⁴He mixtures has been measured between 0.5 K and the tricritical point. The observed decrease of _i on approaching the tricritical point is much stronger than for ordinary critical points. Our data are consistent with a critical exponent =2.     

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.     

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.     

Phase diagram and concentration susceptibility of 3He-4He mixtures near the tricritical point

The inverse concentration susceptibility (/\x) _T of ³He-⁴He mixtures has been calculated from high-resolution vapor-pressure measurements and in situ measurements of the dielectric constant very close to the tricritical point. The measurements have been fitted to a scaling-law equation of state. In the normal fluid a logarithmic correction term was necessary to obtain a good fit. In the superfluid a regular correction term, proportional to (x – x _t)², was evaluated. New measurements of the phase-separation curve confirm our earlier measurements on the ³He-rich side and extend the measurements much closer to the tricritical point on the ⁴He-rich side. The tricritical point is at temperature T = 0.8669 ± 0.0005 K and mole fraction x = 0.6716 ± 0.0014.Work performed under the auspices of the U. S. Department of Energy.     

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.     

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.     

Thermal concentration gradients and the thermal diffusion ratio in3He-4He mixtures near the tricritical point

We report a study of transient effects in sound velocity measurements in several³He-⁴He mixtures near the tricritical point, from which by extrapolation we derive the equilibrium thermal concentration gradient and the thermal diffusion ratiok _T . In the superfluid phase, the thermal concentration gradient is found to be proportional to the concentration susceptibility.Research supported by a grant from the National Science Foundation.     

Vibrating superleak transducers in3He-4He mixtures

We generate second-sound resonances in a cylindrical cavity in³He-⁴He mixtures using vibrating Nuclepore filters. The properties of the cavity resonances are well described by the theory proposed by d'Humieres et al. The theory predicts the strength of cavity resonances as well as the phase shift between in- and out-of-phase components of the signal. By fitting these quantities we are able to get information about the compliance of the membrane, the distance of the membrane to the backplate, and the resistance to flow through the membrane. This enables us to predict the reflection coefficient of second-sound waves off the transducer. We also study the effect of a strong magentic field on the resonances.     

Two-phase sound in stratified3He-4He mixtures

The hydrodynamic boundary conditions at the normal liquid-superfluid interface in stratified³He-⁴He mixtures are formulated and applied to the propagation of low frequency two-phase sound. Coupling between the first- and second-sound modes occurs at low temperature because of the large increase of the Fermi-liquid transport coefficients. Starting with a normal homogeneous mixture, a coupling in a narrow range of temperature near the phase separation point is also predicted.     

Dynamics near the tricritical point of a3He-4He mixture

By means of mode-mode coupling we compute damping constants near the tricritical point of a ³ He- ⁴ He mixture. Both on the coexistence curve and in the tricritical region we find : mass diffusion constant≈|?T _t | ^+1/2 , thermal diffusion constantDK _T ～|T?T _t | ^?1/2 , and third viscosity～|T?T _t | ^?3/2 , whereT is the temperature andT _t is the tricritical temperature. These results imply that damping constant of second sound～|T?T _t |S| ^?1/2 in the ordered phase.     

Interfacial tension near the tricritical point of3He-4He solutions

In a recent paper we made a calculation of the interfacial tension in a binary liquid solution. This involved consideration of the effects of composition gradient, and involved a characteristic length z giving the distance up or down the gradient over which a molecule was influenced by its neighbors. An equation was derived which related to z, the coexistence curve, properties of the critical point, and the thickness z of the interface. This equation has now been applied to³He-⁴He solutions, and its relation to scaling laws for the tricritical exponents has been discussed. This requires estimates of effective values of the tricritical exponents in the temperature range actually used from measurements in the literature of and other quantities, and from an estimate of z from the de Broglie wavelength, z has been estimated to be about 80Å at0.022 deg below the critical temperature. This has been compared to an estimate of the correlation length.Supported by the National Science Foundation.     

Enhancedp-wave pairing in polarized3He-4He mixtures

The potential model of Bardeen, Baym, and Pines is generalized to describe polarized³He-⁴He-mixtures. The zero-field strength and range of the potential as a function of³He-density and pressure are determined by transport data and, for the first time, the magnetostriction. It is found that at higher pressures the magnetostriction leads to a³He-density-dependence in the strength of the potential, an effect which only negligibly appears when fitting the transport data. The model predicts ap-wave superfluid transition with a transition temperatureT _c ^p which is highest at the maximum solubility. Including the correction for the polarization-dependence of the maximum solubility, a large increase inT _c ^p with polarization is found. The size of the enhancement depends on the zero fieldT _c ^p which in turn depends on which set of normal state data we fit.     

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.     

The dielectric formalism for3He-4He mixtures

The microscopic theory of³He-⁴He mixtures with a Bose condensate is formulated in terms of the dielectric formalism. By expressing all correlation functions in terms of proper, irreducible contributions, one sets the stage for approximate calculations that will be consistent with various exact sum rules and Ward identities, just as in the case of pure⁴He. The present analysis includes a symmetry-breaking term that allows us to deal with the continuity equations properly, and is valid at finite temperature. As a specific application, we express the normal fluid density _N in terms of the static⁴He current-current correlation function. We also give the first formal proof that in the presence of a moving condensate, the³He atoms make no direct contribution to the superfluid flow.     

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.     

Compression of3He by refluxing4He: HEVAC effects in3He-4He mixtures

The effect of a refluxing ⁴ He gas facing a Rollin film on the concentration distribution of ³ He atoms is described. In some situations, a large concentration enhancement of the colder part can result. Possible applications are briefly discussed.Unité de recherche de l'Ecole Normale Supérieure et de l'Université Pierre et Marie Curie, associé au CNRS (URA 18).     

A new method for measuring the osmotic response function of3He-4He mixtures near the tricritical point

A new method of measuring the osmotic response function in³He-⁴He mixtures near the tricritical point is described. The method has been used to measure the tricritical divergence of this quantity in the normal phase. The values of the tricritical exponent and amplitude are in fair agreement with those obtained by other methods.Boursier du CNRS Libanais     

The solubility of spin-polarized3He in4He and the superfluidity of3He in3He-4He mixtures

We investigate the possibility of a large enhancement of the T = 0 finite solubility of³He in⁴He due to spin-polarization. The size of the effect depends on the fraction of³He atoms in the system. We present two different approaches for the limits of a small and a large number of³He atoms compared to the number of⁴He atoms. Since the possible³He superfluid phase transition depends on³He density, we calculate the consequences of this change in the solubility for its superfluid transition temperature. It is shown that for small fractions of³He, the transition temperature is enhanced mostly due to the enlargement of the up-spin Fermi sphere. In the opposite limit the transition temperature is enhanced as a result of the increased³He solubility.