NMR experiments on pure3He and3He-4He mixtures in silica aerogel

We have carried out a series of NMR experiments on³He systems filling the pores of silica aerogel with 95% porosity. The systems studied included³He-⁴He mixtures with a wide range of³He concentrations x₃ as well as pure³He. All experiments were conducted in an 8 T field and for temperatures T 6 mK. This resulted in strong spin polarization at the lowest temperatures (up to approximately 80%) for the localized layer observed for a pure³He sample. For pure³He, the magnetic behavior is dominated by the localized spins, which are found to constitute 6% of the sample. The coupled system of localized plus liquid spins displays rapid transverse magnetization relaxation with an anomalous temperature dependence. For intermediate x₃ magnetization measurements provide a preliminary indication of the phase diagram of mixtures filling this porous material. The magnetization is hysteretic over some ranges of x₃.     

The mobility of ions trapped on vortex lines in pure4He and3He-4He solutions

We present measurements of the mobility of positive and negative ions trapped on vortex lines in pure⁴He and dilute³He-⁴He solutions over the temperature range 1.6>T>0.3 K. In pure⁴He below about 0.7 K, we observe several new effects not seen at higher temperatures and not easily explained with existing theories. Most notable are an enhanced broadening of the ion pulse and a rapid increase in the mobility with decreasing temperature. Measurements of the electric field dependence of the drift velocity in pure⁴He at low temperatures show a limiting velocity for sufficiently large fields. This behavior can be explained using a simple resonance theory. The inverse mobility data for solutions show sharp increases at certain critical temperatures, which are interpreted as being associated with the condensation of³He atoms onto the vortex cores. The dependence of the critical temperature on the bulk³He concentration is found to be in good agreement with a simple condensation theory. An extension of arguments used in this theory to lower temperatures leads to the picture of a³He-rich core growing with decreasing temperature, consistent with our lower temperature experimental data.Supported in part by a grant from the National Science Foundation.     

Self Diffusion in Solid 4He and 3He-4He Mixtures Near the bcc-hcp Phase Transition

We report experiments on the plastic flow of solid ⁴ He and ³ He- ⁴ He mixtures of 1.4% and 2.8% near the bcc-hcp transition. Plastic flow was generated by moving a wire through a macroscopic single crystal. We found that the plastic flow rate both in pure ⁴ He and in mixture helium crystals is enhanced in vicinity of the bcc-hcp phase transition. The results are interpreted in terms of self diffusion in the solid. Values of the self diffusion coefficient D_s at the respective transition temperatures of pure ⁴ He and of the mixtures are very close, and reach that found in normal liquids. The activation energy for self diffusion in the mixtures is lower by up to 3 K than in pure ⁴ He. We suggest that similar to what is observed in bcc metals, self-diffusion in solid He takes place through phonon assisted atom-vacancy exchange. The enhancement of the diffusion near the bcc-hcp transition is a result of the softening of a short wavelength transverse phonon. The temperature dependence of the energy of the phonon calculated using our data is in accord with the Landau theory of a phase transition driven by a soft mode. Work hardening was observed in mixture crystals, but not in pure ⁴ He. This implies that ³ He impurities pin dislocation lines.     

Wetting of3He-4He mixtures on alkali metal substrates

From available information concerning the wetting behavior of pure³He and pure⁴He on alkali metal substrates, as well as the known properties of bulk³He-⁴He mixtures, the complete wetting phase diagrams for such mixtures, showing prewetting, isotopic separation and lambda transitions for the film phases have been derived. We predict new phenomena such as a triple-point induced dewetting transition, and the absence of a superfluid film wetting Cs, Rb and K walls under concentrated³He solutions.     

Thermal resistance between liquid3He and copper potassium tutton salt

The thermal resistance between liquid³He and copper potassium tutton salt (CPS) has been measured through its magnetic ordering temperature (T _c=29.6 mK). The thermal resistanceR for pure³He has a broad minimum near 60 mK and increases continuously throughT _cwith decreasing temperature, except for a dip atT _c. BelowT _c,R is proportional toT ^–1.5. Effects of⁴He coating have been studied by stepwise addition of⁴He into liquid³He. The thermal resistance increased drastically for the liquid containing 150 ppm⁴He and more for 95%⁴He. By sudden depressurization of the liquid³He containing 480 ppm⁴He, a considerable decrease ofR was observed. SinceR for pure³He was much smaller than the calculated Kapitza resistance, the present experimental results indicate the existence of surface magnetic coupling between liquid³He and CPS.     

Thermodynamics of the liquid-solid interface in dilute solutions of3He in4He

We show that the (p, T, x) phase diagram of⁴He close to melting pressure (25.3 bars) with small concentrations of³He and at very low temperatures has several unanticipated and novel features. For pressures between 25.3 bars and a triple point pressurep*, estimated to be 25.8 bars, we find a dilute liquid solution of³He in equilibrium with solid⁴He. The concentration of the liquidx _c increases from zero to the dilute liquid solubility limitx ₀ as the pressure increases from the pure⁴He melting pressure atT=0 top*. We explore the possibility of self-cooling by lowering the pressure throughp*. We also consider the effects of a strong magnetic field, and show that it lowersx _c. An estimate of the kinetic growth coefficient is given. Finally, we discuss the possible adsorption of³He on the melting front and the consequent faceting enhancement of the solid⁴He.     

Nuclear magnetic susceptibility of3He adsorbed on graphite below 4.2 K

The nuclear magnetic susceptibility of³He films adsorbed on graphite substrates was measured by means of pulsed NMR techniques at 10 and 20 MHz. Submonolayer, monolayer, and multilayer coverages were examined, as well as one monolayer of³He mixed with various amounts of⁴He. The temperature range of measurements extended from 0.35 to 4.2 K. For pure³He and for³He mixed with⁴He the nuclear magnetic susceptibility displays departures from Curie's law. The observed behavior in pure³He layers can be fitted to an ideal-Fermi-gas curve with an effective degeneracy temperature of 0.15 K. The nuclear magnetic susceptibility of³He–⁴He films is also found to fall below the values predicted by Curie's law as the temperature is lowered, but the results suggest that in this case the film is not uniform, possibly as a result of a phase separation in the film at low temperatures.Work supported in part by the National Science Foundation and a Navy Equipment Loan contract.     

3He-4He mixture films in Anopore membranes

We report recent heat capacity and phase shift measurements on a⁴He and a³He-⁴He mixture film adsorbed in Anopore membranes We discuss the effects of a 1.1%³He concentration at a heat capacity signature found for a pure⁴He film.     

Influence of4He impurities on nuclear spin relaxation in solid3He

The NMR properties of solid³He, mainly the ratio of the heat capacities of exchange and Zeeman energies and the exchange-lattice relaxation times are very sensitive to the presence of⁴He impurities, while the transverse relaxation timeT ₂ does not depend on the impurity concentration when the latter remains small. These properties can be explained in two different ways. (1) We assume an enhancement of exchange interactions around⁴He impurities. We derive the consequences of such an assumption and compare them with experimental results. For two molar volumes in the bcc phase, the locally enhanced exchange is equal to approximately7J, withJ being the exchange in pure³He. (2) Guyer and Zane introduce a mass fluctuation wave to explain the excess of heat capacity and the dependence of the longitudinal relaxation time with concentration. Both these models give rise to a four-energy bath system. As in the bcc phase, the exchange-lattice relaxation time in the hcp phase decreases when × increases at low enough⁴He concentrations. ForV=18.48 cm³ we deduce the coefficient for translational diffusion from high-temperature experiments with the help of Torrey's theory for spin-lattice relaxation.This paper is based on a thesis to be submitted in partial fulfillment of the requirements for the degree ofDocteur ès Sciences in Physics at theFaculté des Sciences d'Orsay in 1970. This thesis will be registered at the CNRS under the number AO 3704.     

Nuclear susceptibility of liquid3He-4He solutions along the demixing line

Pulsed NMR measurements of the nuclear magnetic susceptibility of liquid³He-⁴He solutions at saturated vapor pressure are presented. They extend over the whole temperature range between 50 mK and 825 mK, for both concentrations of the coexisting dilute and³He-rich phases. The results have been compared to those obtained with pure³He, and the temperature dependence of the ratio of molar susceptibilities of coexisting phases is derived. The consequences on the efficiency of fractional distillation as a method to enhance nuclear polarization are discussed.     

The influence of3He on the wetting of4He to a cesiated substrate

We report preliminary measurements of the influence of ³ He in the adsorption of ⁴ He to a cesiated substrate by the use of quartz crystal resonance techniques. When compared with the case of pure ⁴ He, the presence of ³ He in the apparatus induces the wetting of the mixture film to Cesium at low temperatures. The wetting is hysteretic, beginning at a concentration-dependent T_c on cooling with continued wetting for T>T_c on warming. The temperatures T_c are given as a function of the total concentration of ³ He in the apparatus.     

Superfluidity of Pure 3He and Mixtures of 3He and 4He in Aerogel

We describe new torsional oscillator experiments on ³ He confined in 98.2% open aerogel. In one, we monitored the superfluid fraction of pure ³ He at T << T _c while we gradually changed the sample pressure. The resulting change in density alters ₀ of the superfluid ³ He relative to the distribution of the length scales (correlations) of silica in the aerogel. We observed a T = 0 normal-to-super fluid transition at a pressure of about 6.5 bar, in marked contrast to the bulk where liquid ³ He is superfluid at all pressures. In the second experiment, we measured the temperature dependence of the ³ He _s at a pressure of 21.6 bar with different amounts of ⁴ He present in the cell. Adding 2-3% ⁴ He slightly increases both T _c and _s . We found that for ⁴ He concentrations between 2% and 34%, the ³ He T _c increases by a very small amount. However, _s , which for pure ³ He in aerogel at 0.5T _c is no more than 11%, falls by another factor of 7. This behavior (constant T _c , reduced _s ) is similar to that observed in granular superconducting films where the long-range order is controlled by phase coherence between adjacent grains.     

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.     

Effects of3He impurities on the4He solid-liquid interface

Using crystallization waves we have measured the interfacial stiffness, , and the temperature dependence of the growth resistance, (Km)^–1, of the⁴He solid-liquid interface in the presence of³He impurities. For the purest⁴He sample, (Km)^–1 is consistent at the lowest temperatures with the assumption that the growth velocity is limited by the scattering of ballistic phonons from the moving interface. At higher concentrations of³He, we observe that (Km)^–1 increases exponentially with temperature below 0.25 K. We observe that decreases with increasing³He concentration.     

Heat capacity and pressure at phase separation and solidification of3He in hcp4He

We have measured heat capacity and pressure of 0.45% and 0.9%³He-⁴He mixtures at pressures between 25 bar and 33 bar and temperatures between 20 mK and 250 mK. The data show the latent heats and the pressure changes associated with the phase separation (or remixing) and with the liquification (or solidification) of the resulting droplets in the hcp matrix. Above about 31 bar, the phase separation and the liquid-solid phase transition are separately observable. From these data, as well as from the heat capacity of the liquid droplets, we conclude that the droplets are filled with almost pure³He showing bulk behavior and that only a part of the separated³He is liquified. The amount of the liquid depends on the history of the sample. The phase separation is reproducible and lasted for many hours. In the pressure range of the hcp-L₁-L₂ univariant the sample moves along the univariant for a limited temperature range.     

Field dependence of the magnetization of adsorbed3He films at ultra low temperatures

We present measurements of the magnetization of pure³He films adsorbed on graphite at a density of p = 0.235 atoms/Ų, which corresponds to the 2D Heisenberg ferromagnetic regime. Different NMR frequencies (461.3kHz and 1.004 MHz) were used to study the magnetic field dependence of the nuclear magnetization. Measurements were performed on a Papyex sample to investigate the influence of the platelet size. The results are discussed in the context of theoretical models presented recently to describe these systems.     

3He diffusion in liquid isotopic mixtures

Spin echo techniques have been used to study the diffusion of³He in liquid isotopic mixtures with molar concentrations in the range fromX ₃=0.137toX ₃=0.850 over a temperature range from 3.0 to 0.4 K. AboveT the diffusive behavior is very similar to that of pure³He, although there is an increased scattering associated with⁴He. BelowT the diffusion coefficient increases with decreasing temperature and shows a dependence on the³He number density much like that of a classical gas. The excitations of⁴He have little influence on the³He diffusion coefficient, even at temperatures well above 1 K.The Rhodes Trust and the National Research Council of Canada supported one of us (R.B.H.) during the course of this research.     

Viscosity of saturated3He-4He mixture below 200 mK

The shear viscosity of saturated³He-⁴He mixture has been measured at temperatures between 7 mK and 200 mK using a vibrating-wire viscometer and a calibrated pressure cell. The reliability of the vibrating-wire technique was tested by measuring the viscosity of pure⁴He. The results are internally consistent. A phenomenological expression is given for the viscosity of saturated³He-⁴He mixture between 7 mK and 80 mK.     

Ground-State Properties of Two-Dimensional 3He-4He Mixtures: Energetics and Structures

Using a variational Jastrow wavefunction extended to include a three-body correlation function and a hypernetted chain (HNC) and Fermi hypernetted chain (FHNC) scheme with contribution from elementary diagrams, we analyze ground-state energies and structural properties of two-dimensional ³ He- ⁴ He mixtures. The mixtures are in equilibrium at lower density compared to a pure ⁴ He system because of the large zero-point energy and statistical correlations due to the fermionic nature of ³ He. We evaluate the lowering of ground-state energies as a function of the impurity concentration and total density of mixtures. Comparing the results with boson ³ He- ⁴ He mixtures, we evaluate the energy shifts coming from the statistics and analyze the enthalpy to study the miscibility and mobility of each component of the mixture.