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.     

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.     

Bound states of3He in3He-4He mixture films

³He atoms dissolved in super fluid⁴He may form aimers (³He)₂ in twodimensional (2D) geometries. We study dimer formation in films of dilute³He-⁴He mixture. After designing a schematic³He-⁴He interaction potential we calculate the dimer binding energy for various substrates. It is shown that³He impurity states localized near the substrate give rise to the largest magnitudes of the binding energies.Unité de Recherche des Universités Paris XI et Paris VI associée au CNRS.     

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.     

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 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.     

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.     

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.     

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.     

A pulsed NMR study of 3He-4He solutions

We report a study of the Leggett-Rice effect in dilute ³He-⁴He solutions at a Larmor frequency of 71 MHz. We have measured the height and phase of the spin echoes following 2-pulse NMR sequences of three solutions with ³He concentrations of 0.56%, 1.4%, and 4.0%. The theory of Leggett fits the data extremely well and yields values of the parameter M ₀ and the transverse diffusion coefficient D. We are also able to evaluate M ₀ and D by analyzing multiple spin echoes and find good consistency between the two methods. From values of /(1+F ₀ ^a ) at various concentrations, we are able to determine the scattering length for ³He quasiparticles, a, quite accurately. We find a = –0.97±0.03 Å.     

NMR Study of Solid 3He Droplets In Phase-Separated 3He-4He Mixtures

We report measurements on solid ³ He droplets embedded in a solid ⁴ He matrix. A feature of our experiments is that the mixture crystals, of 1% ³ He concentration, are grown under constant pressure conditions to minimise the formation of defects. Upon cooling the mixture isotopic phase separation is clearly observed in both pressure and NMR data. At a pressure of 36 bar the ³ He separates as solid droplets. NMR measurements on these droplets indicate values of T ₁ and T ₂ similar to those in bulk solid ³ He at the same pressure in the temperature-independent régime. Measurements of the bounded diffusion in the droplets indicate a spin diffusion coefficient similar to that in bulk solid ³ He at the same pressure. These measurements also show the size of the droplets to be a few microns.     

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.     

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.     

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)     

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.     

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.     

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.