Ultrasonic measurements as a probe of3He/4He phase separation in aerogels

We have used ultrasonic velocity and attenuation measurements to study the phase separation of³He/⁴He mixtures confined in a silica aerogel with a porosity of 87%. We used both shear and longitudinal sound and varied the frequency between 4 and 20 MHz. The superfluid transition is accompanied by a velocity increase due to decoupling and by a critical attenuation peak which increases with frequency. At the phase separation there are changes in the velocity and attenuation, and hysteresis on thermal cycling. We show some recent results and discuss how they relate to the phase diagram inferred from torsional oscillator and heat capacity measurements on helium mixtures in aerogels.     

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.     

The Fermi Liquid theory of4He in3He

The Zharkov-Silin Fermi Liquid theory of solutions of⁴He in normal (non-superfluid) liquid³He is reviewed and slightly extended. The theory is expected to be valid only below 0.1 K, and it predicts that there should be a hundred-fold increase in the diffusion coefficient as the temperature is lowered into this region. The limited range of validity explains the apparent disagreement between the recent very low temperature measurements of the phase separation line by Nakamura et al. and extrapolations from higher temperatures. In the low temperature experiments the⁴He concentration X₄ is so small that there is no macroscopic phase separation, only a gradual thickening of the⁴He-rich film on the walls. We confirm that the phase separation temperature T_ps(X₄) estimated from the thickening is close to the values which would be observed in an ideal experiment with a macroscopic phase. Fits to T_ps(X₄) including the new data show that the⁴He effective mass m ₄ ^* is close to, and may be equal to, the bare mass m₄. The difference in binding at zero pressure between⁴He in liquid⁴He and in liquid³He is (E₄₄–EE₄₃)/k_B=(0.21+0.03/–0.01)) K. Using the volume measurements of Laheurte to calculate the pressure dependence of E₄₃ indicates that the difference in binding has a minimum of (0.0±0.2) K near 11 atm. This implies that the solubility of⁴He in³He is enhanced in this region of pressure. The behavior of the spinodal line at low temperature, and the possibility of observing Bose condensation in a metastable solution of⁴He in liquid³He are also discussed.     

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.     

The solubility of4He in3He below 0.1 K

The Zharkov-Silin Fermi Liquid theory of solutions of⁴He in non-superfluid liquid³He has been applied to the recent phase separation data of Nakamura et al. At zero pressure, the difference in binding between a⁴He atom in liquid⁴He and in liquid³He is smaller than previous estimates, and the⁴He effective mass is close to the bare mass. The volume measurements of Laheurte show that the difference in binding has a minimum near 11 atm. This implies an enhanced solubility of⁴He in³He below 0.1 K at this pressure, although there is experimental evidence that the solubility at 0 K remains zero.     

Phase Separation Kinetics of Solid 3He-4He Mixtures

The kinetics of isotopic phase separation in solid mixture of ³ He in ⁴ He with the initial concentration 2.05 % at various molar volumes has been investigated by precise pressure measurements. It has been shown that during both stepped and fast cooldown into the metastable region the equilibrium of coexisting phases is described by the exponential law with a characteristic time constant , The value of is found to decrease as the molar volume increases and the temperature lowers. It confirms that the growth of the ³ He-rich phase is connected with nonthermally activated (quantum) diffusion in the gas of delocalized ³ He quasiparticles. The obtained experimental results can be described only qualitatively by current kinetic theory of binary quantum solid mixtures. The conditions permitting the realization of the isotopic phase separation during the time observed in the experiment are analyzed. The effective quantum diffusion coefficient providing required ³ He atoms transport is about an order of magnitude higher than the corresponding value measured in NMR experiments. These conditions are probably fulfilled at the big concentration gradient which takes place at isotopic phase separation. The corresponding kinetic theory should be developed.     

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.     

3He-4He Mixtures in 95% Porous Aerogel

Torsional oscillator measurements of ³ He- ⁴ He mixtures in 95% porous aerogel found a phase diagram similar to that in 98% porous aerogel. The coexistence boundary on the ³ He rich side resides very close to, but nevertheless is detached from the superfluid transition line. Together with the findings in 98%, 87%, and 99.5% porous aerogel, this result supports the interpretation that the phase separation of ³ He- ⁴ He mixture in aerogel is induced by the capillary condensation of ⁴ He films from neighboring silica strands into ⁴ He rich domains.     

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.     

Nucleation and growth of the new phase in the supersaturated3He-4He superfluid solutions

Phase separation kinetics and growth of the new phase in supersaturated superfluid³He-⁴He solutions was studied using the method of continuous change of³He concentration in situ and developed theory. Simultaneous measurements of the first sound velocity and the dielectric constant were carried out during the change of concentration. The velocity and attenuation of the first sound and the dielectric constant in supersaturated metastable solutions were calculated on the assumption that the excess³He in the solution is in the form of both atoms and droplets of the new phase. It was shown that the sound velocity, unlike the dielectric constant, is very sensitive to the formation of droplets. Comparison of the theory and the experimental data allowed us to elucidate the growth dynamics of the nuclei of the new phase from the metastable supersaturated mixture.     

NMR study of 3He bubbles in phase-separated solid 3He –4He mixtures

³ He droplets embedded in a solid ⁴ He matrix have been studied by NMR and pressure measurements. One feature of the experiment is that the mixture crystals, of ³ He concentration 1%, are grown under constant pressure conditions to minimise the formation of defects. A number of sample pressures below 34 bar have been studied. Isotopic phase separation and the melting of the bubbles are clearly observed. Measurements of T₁ , T₂ and magnetisation give detailed information on the structure of the droplets. At an initial sample pressure of 28.3 bar preliminary measurements of the T₁ of the liquid bubbles show a temperature dependence of the form (A+ B/T²)^–1. This indicates that the expected relaxation in the liquid is augmented by a constant contribution, probably from the surface of the droplets.     

Evolution of the Concentrated Phase in Separated Solid 3He–4He Mixtures

Experimental and theoretical investigations of the growth kinetics of BCC ³ He precipitates in isotopic phase separation of HCP ³ He– ⁴ He are carried out. Low frequency pulsed NMR is used to study the mixture with an initial ³ He concentration of 3.18% at a pressure 3.7 MPa on stepped cooling down into the separation region. The separation time constant is shown to decrease monotonically with cooling. The evolution of heterophase structure resulted from separation is investigated by solving an equation for spatially non-homogeneous order parameter of decomposing mixture. The obtained temperature dependence of separation time constant is found to be in good agreement with the experiment.     

Fluctuation effects in the phase separation of solid3He-4He mixtures

We analyze the excess specific heat above the phase-separation temperature in solid mixtures of³He and⁴He as due to the fluctuations that represent the symmetry of the condensing state. In a³He-rich solid, the fluctuations of the⁴He-rich phase are two-dimensional, while in an even mixture they are three-dimensional. The density fluctuations are characterized by a length scale that is essentially the interparticle spacing.     

Phase separation of3He-4He mixture in aerogel

Torsional oscillator measurements of ³ He- ⁴ He mixtures confined in aerogel show evidence of a well defined phase separation region. This region is detached from the superfluid transition line, opening up a region of miscible superfluid mixture at high ³ He concentration.     

Surface tension and mass density of dilute solutions of4He in3He

We report the first precise measurement on the surface tension of dilute solutions of⁴He in³He from 2.6 K to the phase separation temperature as well as the mass density of the solutions. Compared to liquid³He, the surface tension of dilute⁴He solutions increases by 3.5 ± 0.1 mdyne/cm for 2.5%⁴He and 7.4 ± 0.2 mdyne/cm for 5.2%⁴He at 1 K. The increase of the surface tension means a negative adsorption, i.e.,⁴He atoms are excluded from the free surface. The surface adsorption, which is calculated on the basis of the⁴He quasiparticle model, was compared with the data. Assuming that the effective potential near the surface for the⁴He quasiparticle is long-range, the temperature dependence of the surface adsorption is well explained.     

Magnetic Susceptibility of 3He nano-Clusters

Using pulsed NMR, we have measured the magnetic susceptibility versus temperature of ³ He nano-clusters embedded in a matrix of ⁴ He, following phase separation of the mixture. Measurements were made in the temperature range from 2 mK to 35 mK at three different pressures, 3.647 MPa, 3.410 MPa and 3.075 MPa, for which the samples remain all solid, undergo partial melting, or are separated as a liquid, respectively. For 3.410 MPa, for which partial melting occurs near 15 mK, measurements up to 35 mK suggest a positive Weiss , which would indicate a ferromagnetic tendency.     

NMR Studies of 3He Droplets in Dilute 3He-4He Solid Solutions

We have performed measurements of the temperature dependence of the nuclear spin-lattice relaxation times (T ₁) for a wide range of ³He concentrations for dilute mixtures of ³He in solid ⁴He. The temperatures for phase separation are determined for ³He concentrations 500<x ₃<2000 ppm for a molar volume V _M =20.7 cm³. We report the temperature dependence of the nuclear spin-lattice relaxation times for ³He in the droplets formed after phase separation at low temperatures. The temperature dependence suggests that the interface ³He atoms responsible for the relaxation are degenerate, not solid-like.     

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     

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.     

NMR study of the solidification and melting of3He in porous glasses

TheP-T phase diagrams of the liquid-solid phase transition of³He in three porous glasses with different pore sizes have been determined from spin-lattice relaxation measurements in the temperature range 0.5–4.2 K. The onset of solidification of³He in the pores occurs at excess pressure over the bulk phase transition. The excess pressure depends on the pore size. A model of the phase transition in small pores which takes into account the contribution of the surface energy to the free energy is described and compared with experimental results. TheT ₁ relaxation mechanism of³He in the pores is found to be due to the surface relaxation when³He is in the liquid phase and due to the relaxation of bulk solid³He when it is in the solid phase.