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.     

Third sound in3He-4He mixture films

We report third-sound studies of³He-⁴He mixture films for 0.3T1.8 K carried out in two different experimental situations. In one experiment detailed measurements of the amplitude of both the temperature and thickness variation of the film were made for pure⁴He and the results for |T/d| are in good agreement with the predictions of Bergman. Mixture studies in this apparatus were made difficult due to the presence of capillary condensation. In spite of this a number of interesting results are reported. Subsequent measurements were made in a new apparatus where capillary condensation effects could be demonstrably avoided. Helium films of 5.7 layers of⁴He were studied as a function of added amounts of³He. BelowT0.7 K the third-sound measurements are consistent with model calculations based on a bilayer film. We conclude that for 0.3T0.6 K films of the type we have studied are isotopically layered in the van der Waals field provided by the substrate.     

Spin diffusion and magnetization studies of3He in3He-4He mixture films

The longitudinal spin diffusion coefficient and magnetization of a submonolayer coverage of ³ He, n ₃ =0.0066 Å^–2, in a thin adsorbed ⁴ He film has been measured as a function of temperature0.024 K T0.5 K and ⁴ He coverage0.21 Å ^–2 n ₄ 0.32 Å ^–2.     

Universal behavior of3He-4He mixture films near the Kosterlitz-Thouless transition

We report measurements of the convective thermal conductance of³He-⁴He mixture films near the Kosterlitz-Thouless transition. The thickness of our⁴He films is 14.7 and 19.1 Å above the inert layer and the³He concentration ranged from 0.033 to almost 2%. The thermal response is tested for the critical behavior as observed in pure films, and it is found to be preserved in the mixture films case. However, the parametersb, D/a ² andT _c exhibit a strong dependence on the concentration. The mixture film conductance at fixedT-T _c is found to decrease upon addition of³He implying a decrease in the 2D correlation length. Mixture films thus exhibit 2D behavior over a narrower temperature range than pure films. Further, for temperaturesT _c , the largest measurable conductance decreases sharply with the addition of³He. We attribute this behavior to a³He-⁴He scattering mechanism and a³He induced free-vortex density.     

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.     

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.     

First-sound measurements in a 5%3He-4He mixture

Precision first-sound measurements at 17.1 kHz are presented for a 5%³He-⁴He solution. Measurements near the transition are analyzed with a modified Pippard-Buckingham-Fairbank relation using recent³He-⁴He heat-capacity measurements. The analysis takes into account the effects of gravity and dispersion. An accurate determination of (P/)_T is obtained from velocity measurements in the range 1.1–2.0 K.Work at the University of California was supported in part by the U.S. Office of Naval Research.Part of this work was performed during the author's postdoctoral year (1967) at the Physics Department of the University of California at Los Angeles.     

The proximity effect between superfluid3He and a3He-4He mixture

The quasiclassical theory is used to study the proximity effect between superfluid ³ He and a mixture of ³ He- ⁴ He. The order parameter and the surface tension are calculated, and their dependence on temperature and on the hypothetical transition temperature of the ³ He- ⁴ He mixture is discussed.     

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.     

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.     

Novel behavior of3He-4He mixture films on a cesium coated substrate at low temperatures

We report quartz crystal measurements of the adsorption of³He —⁴He mixture films to gold and cesium substrates as a function of temperature and concentration. Measurements for higher concentrations than reported earlier show steps in the adsorption at low temperatures. Speculations as to the origin of these steps are presented.     

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.     

Convective instability of a superfluid3He-4He mixture in a superleak

The convective instability of a superfluid³He-⁴He mixture in a porous medium confined between parallel horizontal planes is studied. It is shown that this system behaves as a pure classical liquid in a porous medium from the point of view of the convective instability in the whole range of the phase diagram between the λ line and the coexistence curve. It is predicted that two-fluid effects become important for the convection onset and can be observed experimentally in this system at moderately low temperatures. This system is supposed to be the most convenient one to study experimentally convection in a porous medium.     

3He-3He and 4He-4He Cross Sections in Matter at Low Temperature

The Galitskii-Migdal-Feynman (GMF) formalism is applied to liquid ³He and (for the first time) to liquid ⁴He. The effective total, diffusion and viscosity cross sections, as well as the effective scattering length and the effective range, are calculated. For liquid ³He, it is found that S-wave scattering dominates for wave number k<0.5 Å^?1. At the Fermi momentum k _F, the effective partial cross section σ _? (and thus the total cross section σ _T) has a singularity (virtual state). This singularity may be interpreted as a signature of superfluidity or a quasi-bound state. For k>2 Å^?1, the effective total cross section is nearly constant. On the other hand, it is found in liquid ⁴He that S-wave scattering dominates for k<0.3 Å^?1, and a peak exists in σ _T arising from a peak in the effective D-wave cross section. This resonance corresponds to a quasi-bound state trapped by the ?=2 centrifugal barrier. The most prominent features of our calculations are a resonance and a Ramsauer-Townsend minimum in the matter cross section at low temperatures. This effect is absent in the ³He gas. It is, therefore, a purely many-body effect in liquid ³He. With increasing energies, the matter results approach the vacuum results. This indicates that the high-energy behavior is dominated by the self-energy contribution; the many-body effects can be neglected.     

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.     

Optical observation of growth and melting dynamics of3He-4He mixture crystals

Crystals grown from 2.1% and 9.3% solutions of³ He in⁴He were observed in a cryostat with optical access from two orthogonal directions (above and from the side). Video films of dynamic processes were recorded at temperatures between 0.5K and 1.8K. Facetted melting of crystals (in contrast with rounded melting which is the general case) was observed below 0.75K. This is in accordance with previous experiments which showed a higher³He concentration along the edges of the crystal. We also recorded morphological growth instabilities of the 9.3% b.c.c. crystals. In the temperature region below about 0.9K where the latent heat is negative no dendritic growth was observed, which we interpret as resulting from opposing effects of temperature and concentration gradients.     

Structure Properties of the 3He-4He mixture at T = 0 K

The spatial structure properties of³ He-⁴ He mixtures at T = 0 K are investigated using the hypernetted-chain formalism. The variational wave function used to describe the ground-state of the mixture is a simple generalization of the trial wave functions for pure phases and contains two- and three-body correlations. The elementary diagrams are taken into account by means of an extension of the scaling approximation to the mixtures. The two-body distribution (g(^,)(r)) and the structure functions (S(^,)(k)) together with the different spin-spin distribution functions of the ³He component in the mixture are analyzed for several concentrations of³ He. Two sum-rules, for the direct and the exchange part of the g ^{(3, 3)}(r), are used to ascertain the importance of the full treatment of the Fermi statistics in the calculation. The statistical correlations are found responsible for the main differences between the several components of the distribution function. Due to its low concentration, ³He behaves as a quasi-free Fermi gas, as far as the statistical correlations are concerned, although it is strongly correlated with the ⁴He atoms through the interatomic potential.     

Search for superfluidity of3He in3He-4He solution

We have tried to cool a³He-⁴He solution down to the microkelvin temperature region to search for a superfluid transition of the³He component in the solution. The contact surface area between the solution and a sintered powder has been increased enormously by the use of a fine platinum powder, to reduce the effect of the residual heat leak directly entering into the solution. Although the heat leak was found to be time dependent, the ultimate ratio of the heat leak to the surface area is about 0.046 pW/m², improved very much from those by the other groups. But the lowest temperature of the solution is still around 0.2 mK, and no evidence of the transition has been observed yet.     

Adsorbed films of 3He-4He mixtures: A systematic experimental study

The results of a systematic study of helium thin-film adsorption are presented. Measurements are reported, obtained with a 24-MHz crystal adsorptometer, on the adsorbed mass per unit area as a function of the three independent variables temperature, concentration, and pressure of the gas of ³He-⁴He atoms generating the adsorbed film. The investigations span concentrations from zero to unity, all pressures up to the dew point for each mixture, and temperatures from 1.3 to 2.1 K. From the experimental results we display the detailed form of the van der Waals attractive potential holding the helium atoms to the surface. The expected dependence on the cube of the distance from the substrate is confirmed over the range of distances explored. The strength of the van der Waals potential is measured and reported. This attractive potential is demonstrated to be of the same form and of the same strength both for the ³He atoms and for the ⁴He atoms in the mixture at all concentrations. We further deduce, directly from our measurements, the detailed relationship between , the mass per unit area of film absorbed, and d, the thickness of the film.German Academic Exchange Service (DAAD) leave from the Free University of Berlin.