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.     

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.     

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.     

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.     

Equation of state of a3He-4He mixture near its liquid-vapor critical point

Measurements of the pressure coefficient (P/T)_,x are reported for a ³ He- ⁴ He mixture with a mole fractionX=0.805 of ³ He in the neighborhood of the liquid-vapor critical point. These include data on 16 isochores taken over the density interval–0.50.5 and over the temperature range–0.1 t0.1, where =(– _c )/ _c andt=(T-T _c )/T _c ,with _c andT _c ,respectively, the critical density and temperature of the mixture. From the discontinuity of (P/T)_,x at the boundary between the two-phase and the one-phase regions we determine the dew-bubble curve nearT _c with better precision than was done in recentPVT experiments. From the extrapolation of data not approachingT _c closer than1 mK, (P/T)_,x along the critical isochore appears to be discontinuous atT _c ,while for the isochore / _c 0.92, (P/T)_,x is continuous across the dew curve. It is found that this latter isochore cuts the dew curve at its highest temperature. These observations are discussed in terms of general thermodynamic arguments and theoretical predictions of the asymptotic behavior. We calculate (P/T)_,x from the scaling equation of state proposed by Leung and Griffiths for ³ He- ⁴ He mixtures, using their numerical parameters. In spite of some systematic deviations, especially in the two-phase region, there is in general good agreement with experimental results. In particular, the shape of the measured dew-bubble curve and the apparent discontinuity of (P/T)_,x along the critical isochore show excellent agreement with theory.Work supported by a grant from the National Science Foundation. A report of this work has been presented at the Washington Meeting of the APS [Bull. Am. Phys. Soc. 20, 618 (1975)].     

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.     

Shear viscosity of liquid4He and3He-4He mixtures,especially near the superfluid transition

High-resolution measurements of are reported for liquid⁴He and³He-⁴He mixtures at saturated vapor pressures between 1.2 and 4.2 K with particular emphasis on the superfluid transition. Here is the mass density, the shear viscosity, and in the superfluid phase both and are the contributions from the normal component of the fluid ( _n and _n ). The experiments were performed with a torsional oscillator operating at 151 Hz. The mole fraction X of³He in the mixtures ranged from 0.03 to 0.65. New data for the total density and data for _n by various authors led to the calculation of . For⁴He, the results for are compared with published ones, both in the normal and superfluid phases, and also with predictions in the normal phase both over a broad range and close to T. The behavior of and of in mixtures if presented. The sloped/dT near T and its change at the superfluid transition are found to decrease with increasing³He concentration. Measurements at one temperature of versus pressure indicate a decreasing dependence of on molar volume asX(³He) increases. Comparison of at T, the minimum of _n in the superfluid phase and the temperature of this minimum is made with previous measurements. Thermal conductivity measurements in the mixtures, carried out simultaneously with those of , revealed no difference in the recorded superfluid transition, contrary to earlier work. In the appendices, we present data from new measurements of the total density for the same mixtures used in viscosity experiments. Furthermore, we discuss the data for _n determined for⁴He and for³He-⁴He mixtures, and which are used in the analysis of the data.     

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.     

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.     

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.     

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.     

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.     

Anomalous nuclear spin relaxation in liquid 3He-4He mixtures near the lambda transition

The longitudinal nuclear spin relaxation time T ₁ was measured for liquid ³He-⁴He mixtures under saturated vapor pressure in an epoxy sample chamber in which the wall effect is emphasized. The molar concentration of ³He was 0.12, 0.20, 0.35, 0.45, and 1.00. The temperature was regulated to better than 5 K in the range 1.2–2.1 K. A decrease of T ₁ was clearly observed several millikelvins below T (the superfluid transition temperature). T ₁ had a cusp like temperature dependence as a whole where the temperature is far from. T . This anomalous behavior of T ₁ is discussed.Work based on part of a dissertation submitted to the University of Tsukuba in partial fulfillment of the degree of Doctor of Science by one of the authors (T.K.).     

Vibrating-wire measurements in vacuum,liquid3He and liquid3He-4He mixtures

In order to overcome the 200µK - barrier in the refrigeration of liquid ³ He- ⁴ He mixtures we have constructed an experimental cell using only pure materials to minimize possible origins for heat leaks into the liquid. With this arrangement we were able to cool a saturated6.8%- mixture to a temperature of 150µK. A vibrating wire which was immersed in pure ³ He floating on top of the phase-separated mixture was used as a thermometer. This wire was calibrated in a second experiment with pure ³ He only in the cell. In superfluid ³ He-B at T0.15 mK the damping of the wire due to the quasiparticles becomes very small, and we observe typical characteristics of the vacuum damping of the wire which was extensively examined before filling any liquid into the cell.     

Phase equilibrium in a polarized saturated3He—4He mixture

We present experimental results on the phase equilibrium of a saturated³He−⁴He mixture, which has been cooled to a temperature of 10–15 mK and polarized in a⁴He circulating dilution refrigerator to a stationary polarization of 15%, 7 times higher than the equilibrium polarization in the external field of 7 T. The pressure dependence of the polarization enhancement in the refrigerator shows that the molar susceptibilities of the concentrated and dilute phase of a saturared³He-⁴He mixture are equal atp=2.60±0.04 bar. This result affects the Fermi liquid parameters of the dilute phase. The osmotic pressure in the dilute phase has been measured as a function of the polarization of the coexisting concentrated phase up to 15%. We find that the osmotic pressure at low polarization (<7%) agrees well with thermodynamics using the new Fermi liquid parameters of the dilute 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.     

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.     

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.