Transition Of 4He Research Articles

Critical exponents and equation of state of three-dimensional spin models

Three-dimensional spin models of the Ising and XY universality classes are studied by a combination of high-temperature expansions and Monte Carlo simulations. Critical exponents are determined to very high precision. Scaling amplitude ratios are computed via the critical equation of state. Our results are compared with other theoretical computations and with experiments, with special emphasis on the λ transition of 4He.

New concepts on the A–B transition in superfluid 3He

There is no doubt that the A–B transition in 3He can be triggered by neutrons, or some other radiation, which locally heats the liquid into the normal state with consequent fast cooling through T c. Many experiments show a very small probability for this triggering process. In a new scenario that we call “Venice” we consider the fast local cooling through T c with simultaneous and independent creation of many superfluid seeds of different order parameter. The stochastic process of triggering the A–B transition can be explained as the formation of a sufficiently big cluster of B-phase seeds. We consider the statistical conditions required for the triggering of the A–B transition.

Universal amplitude ratios for the superfluid transition of 4He

We present the results of a three-loop calculation of amplitude functions within the O( n) symmetric φ 4 theory in three dimensions for general n below T c. An appropriate treatment of Goldstone modes avoids spurious singularities for n>1. Several universal amplitude ratios are calculated using Borel resummation. Application to n=2 yields the α-insensitive quantity for the specific heat amplitude ratio P= α −1(1− A +/ A −)=4.39±0.26. For the superfluid density we get R ξ T = ξ 0 T ( A −) 1/3=0.815±0.010. These results are significantly more accurate than previous theoretical estimates and agree well with experimental results for the superfluid transition of 4He. Accurate knowledge of these amplitude ratios is needed for testing the renormalization-group prediction of critical-point universality along the λ-line of superfluid 4He on earth and under microgravity conditions in space.

Scaling of the superfluid fraction and T(c) of 3He in aerogel

We have investigated the superfluid transition of 3He in different samples of silica aerogel. By comparing new measurements on a 99.5% sample with previous observations on the behavior of 3He in 98% porous aerogel, we have found evidence for a scaling of the transition temperature and superfluid density of 3He to the correlation length of the aerogel.

Decoherence under a heat flux near the superfluid transition in 4He

Measurements of heat transport at the transition from perfect thermal super-conductivity to nonlinear heat diffusion in pure 4 He provide a very sensitive probe of matter wave coherence. Superfluid heat transport is proportional to the product of the superfluid density and the superfluid velocity, which are both directly related to the superfluid order parameter. From dynamic scaling theory, the correlation length near the superfluid transition provides a measure of the length over which phase fluctuations of the order parameter persist. Our measurements suggest that both the hydrostatic pressure variation within the liquid helium column, together with the heat flux Q, limit the otherwise divergent correlation length near the superfluid transition. Future measurements planned for the microgravity laboratory will provide the first extensive experimental test of a renormalized, field theoretic description of heat transport near the superfluid transition. It will also provide a conclusive experimental study of the influence of hydrostatic pressure effects and dynamical effects on the correlation length. A new class of microgravity experiments is proposed that will permit measurements to within 10 pK of the superfluid transition temperature, allowing an entirely new class of ultra-accurate scientific investigations to be performed.

Scaling Properties of Superfluid 3He in Aerogel

We have investigated the superfluid transition of 3 He in different samples of silica aerogel. Several of these samples have been characterized using x-ray imaging, yielding information about the microstructure of the aerogel. In comparing new measurements on a 99.5% sample with previous observations on the behavior of 3 He in 98% porous aerogel we have found evidence for a scaling of the superfluid transition temperature to the correlation length of the aerogel. Furthermore, the superfluid density exhibits a similar universal behaviour over a range of values of reduced temperature. We discuss these new results in the context of superfluid pairing in the presence of a correlated disorder, specifically focussing on the fractal nature of the aerogel.

A pulse tube refrigerator below 2 K

Up to now, all pulse tube refrigerators operating at the liquid helium temperature range use 4He as the working fluid. However, the lambda transition of 4He is a barrier for reaching temperatures below 2 K. Theoretical analysis in this paper shows that, using 3He, the temperature limit is below 2 K, and the efficiency of a 4 K pulse tube refrigerator can be improved significantly. A three-stage pulse tube refrigerator is constructed. A compressor with input power of 4 kW and a rotary valve are used to generate the pressure oscillations. With 4He, a minimum average temperature of 2.19 K was reached. Replacing 4He by 3He, at the same valve settings and operating parameters, the minimum average temperature goes down to 1.87 K and the cooling power at 4.2 K is enhanced about 60%. After fine tuning of the valves, a minimum average temperature of 1.78 K was obtained. This is the lowest temperature achieved by mechanical refrigerators.

Superfluid Transition of 4He for Two-Dimensional Crossover, Heat Capacity, and Finite-Size Scaling

We report heat capacity measurements of confined films of4He. These studies were undertaken to test predictions of correlation-length scaling. They are the first measurements for completely confined films over a range of confinements, and represent a geometry where criticality changes from 3-dimensions (3D) to 2D. The finite system is realized with a4He film confined between two, 2″ diameter, silicon wafers, which are separated by a small gap. A new technique was developed to bond these wafers at a uniform separation. The gap size, which determines the film thickness, ranges from 0.05 to 0.7 μm in the present work, and has better than 1% uniformity. The bonded cells are used to conduct high precision heat capacity measurements using a modified ac technique. This involves oscillating the sample temperature, as in conventional ac calorimetry, but with simultaneous dc regulation of the average temperature. The data are analyzed using a modified Sullivan–Seidel equation, which takes into account in an empirical way the finite conductivity of the cell. This procedure yields heat capacity data with good absolute accuracy and high resolution. Scaling analysis of the data both above and below the bulk transition temperature shows collapse onto universal curves determined only by the ratio of the correlation length to the confinement size. This is true everywhere except near the heat capacity maximum. Here, and into the superfluid side there is lack of scaling which might be associated with 2D crossover. We compare this result with calculations of scaling functions and find that these tend to underestimate the effect of confinement. Comparison with earlier results for cylindrical confinement shows differences which are most striking in the region of the specific heat maximum. The cylindrical and planar confinement data follow similar trends above the superfluid transition of bulk helium. Below the transition, however, the present data show much more structure. Fits of the scaled planar data above the transition to an empirical scaling function yield a correlation length exponent of νeff=0.674±0.001.

Breakdown of Fourier's Law near the Superfluid Transition in4He

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Testing critical point universality along the λ-line

We are currently building a prototype for a new test of critical-point universality at the lambda transition in 4He, which is to be performed in microgravity conditions. The flight experiment will measure the second-sound velocity as a function of temperature at pressures from 1 to 30 bars in the region close to the lambda line. The critical exponents and other parameters characterizing the behavior of the superfluid density will be determined from the measurements. The microgravity measurements will be quite extensive, probably taking 30 days to complete. In addition to the superfluid density, some measurements of the specific heat will be made using the low-g simulator at the Jet Propulsion Laboratory. The results of the superfluid density and specific heat measurements will be used to compare the asymptotic exponents and other universal aspects of the superfluid density with the theoretical predictions currently established by renormalization group techniques.

Thermal conductivity measurements and self-organized criticality very close to the superfluid transition in 4He

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Gravitational Effects on Nonlinear Heat Transport Near the Superfluid Transition in 4He

We have recently observed nonlinear heat transport within 30 nK of the superfluid transition temperature using heat flux, Q, in the range 0.1 < Q < 2 erg/(s cm2). While Haussmann and Dohm (HD) accurately predict the initial departure of the thermal conductivity, κ, from the linear response region, κ is greater than expected very close to Tλ. We anticipate that the nature of the thermal conductivity's nonlinearity may depend upon Earth's gravity in the low heat flux limit (Q < 0.5 erg/(s cm2)). Comparison of our data to similar data to be taken in a microgravity laboratory will provide an experimental determination of the effect of gravity on nonlinear heat transport near the superfluid transition. The microgravity measurements will also permit the first experimental test of theories that do not consider gravitational effects, such as those by HD.

Opportunities for High-Resolution Measurements and Microgravity Research near the Superfluid Transition of Liquid 4He

Six years ago an experiment to determine the specific heat of liquid helium near the superfluid transition in a microgravity environment opened up a new era of very-high resolution measurements. Recently this led to the establishment of the Fundamental Physics Discipline by NASA for the support of microgravity research in low-temperature/condensed-matter physics, laser cooling and atomic physics, and gravitation and relativity. This paper describes very-high resolution and microgravity research in one particular sub-field of low-temperature physics, namely the superfluid transition of 4 He, in order to illustrate the diverse research opportunities which exist within the Discipline. The effect of gravity on this system will be illustrated. Projects carried out already and expected to be undertaken in the near future on critical phenomena, surface effects, and non-equilibrium phenomena, will be discussed. These include measurements of the specific heat and the thermal conductivity, both in bulk samples and finite geometries, of the singularity of the boundary resistance between helium and a solid surface, as well as of non-equilibrium effects due to finite heat currents.

3He in 99.5% Porous Aerogel at the Normal-Superfluid Transition

We have used a torsional oscillator to measure the superfluid density and dissipation near the superfluid transition of 3 He in aerogel of 99.5% porosity. We used a new cell (constructed at Penn State) for which the aerogel was grown in the pores of a ∼100 μm silver sinter. The cell was tested with 4 He and showed no signs of the second-sound resonances that have interfered with previous torsional oscillator measurements. The measurements with 3 He, presented here, were taken at pressures of 1.34 and 4.13 bars. We observed values of ρ s /ρ in the T→ 0 limit of 0.05 and 0.14 respectively. Our measurements show an increase in the dissipation on warming through T c . This series of measurements is ongoing and temperature sweeps at various pressures are planned.

Approaching the 4He lambda line with a liquid nitrogen precooled two-stage pulse tube refrigerator

We report on the design and test of a three-stage refrigerator, consisting of a liquid nitrogen bath with heat exchangers and two subsequent pulse tube stages. The liquid nitrogen bath serves for precooling the oscillating 4He-gas flow. The PTR stages are operated in orifice and double-inlet mode with the orifice valves, reservoirs and second-inlet valves located at ambient temperature. Er 3Ni shot is used for the regenerator matrix in the coldest stage. A minimum temperature of 2.13(1) K has been achieved, which, at the average operating pressure of 19.5 bar, is only 0.19 K above the λ-line for the superfluid phase transition of 4He.

Superfluid transition in4He in gravity and heat flow

When4He in a normal fluid state near the superfluid transition is cooled from the bottom below the transition, a superfluid region appears at the bottom and slowly expands in the upward direction. We performed simulations for this case in one dimension fixing the temperature Tb at the bottom and the heat flux at the top Q. We find densely distributed phase slip centers rapidly oscillating in time in the expanding superfluid region. Their role is to produce a temperature gradient compensating the transition temperature gradient (dTλ(p)/dp) pg in gravity and to produce a constant negative reduced temperature T-Tλ(p) with small fluctuations superposed. The superfluid velocity multiplied by the correlation length is found to be violently fluctuating around ħ/√3m.

Effect of gravity on the thermal conductivity measurement of4He nearT λ

Precision measurements near the superfluid (λ) transition of4He is limited by a gravity induced inhomogeneity inT λ. Critical Dynamics in Microgravity (DYNAMX, a NASA preproject) will study the thermal conductivity in the nonlinear region in Microgravity. Unlike the study of static properties, the thermal conductivity can be derived from the measurement of the spatial temperature profile which is essentially alocal measurement of the temperature gradient. We present a method which, in principle, fully removes the apparent impact of gravity from the measurement. The inevitably finite spatial resolution of the probe and temperature resolution of the thermometer, however, make microgravity essential to study the region of interest.

Absence of superfluidity in4He adsorbed in zeolite

We present the results of a torsion-oscillator experiment which has searched for the superfluid transition in4He adsorbed in chabazite. A novel non-destructive dehydration technique has been used to make the 10 A pores of the crystal accessible to4He. No superfluid transition has been observed to within our resolution for4He coverages ranging from 50% of the full pore to complete saturation at temperatures above 130 mK.

Frequency dependence of the superfluid onset in4He films on hydrogen

The superfluid transition in4He films adsorbed on solid hydrogen of 5 layers was studied by using two torsional oscillators for frequencies of 640 and 2250 Hz. We observed the frequency dependences of the onset temperature and the dissipation peak temperatureT p. The coverage dependence of the difference ΔT p between the two frequencies indicates that an intrinsic parameterb 2/3 l d of a superfluid vortex becomes a minimum at a coverage withT p=1.15 K, whereb is a coefficient of the correlation length andl d an effective diffuse-length of a superfluid vortex.

Thermal resistance below the superfluid transition of4He in a heat current

We report on the thermal resistivity of4He nearT λ in heat currents 20≲Q≲300 μW/cm 2. The temperature at the bottom of a layer was measured as a function of that at the top and compared with integrations of models for the conductivity λ(Q,t). The data reveal a new dissipative region belowTλ(Q) with a small but finite resistivity and a sharp onset which can not be explained by the usual “mutual friction” due to vortices.