Heat flow through superfluid4He at low temperatures

The heat conductivity of superfluid⁴He has been measured as a function of temperature between 0.1 and 0.7 K at different pressures between zero and 24 atm. The experiment gives direct evidence that the heat conductivity varies asT ³ at very low temperatures.     

The melting pressure of helium-3 at very low temperatures

The melting pressure of³ He at very low temperatures was shown earlier to be determined overwhelmingly by the solid phase. Using an extended solid³He model based on isotropic effective first-neighbor-pair antiferromagnetic and second-neighbor-pair ferromagnetic exchange interactions, the melting process is reinvestigated here. One of its motivating aspects may be said to be tied to its possible use, suggested by us earlier, for the establishment of a thermodynamic temperature scale at very low temperatures. As a consequence of the assumed multineighbor interactions, spin ordering is accelerated and, at the same temperature, the extended-model solid entropy falls below that of the simpler nearest-neighbor-pair interaction model. Equivalently, the spinordering critical transition temperature is raised over that associated with the simpler interaction scheme. The overall result is a decrease in the melting pressure variations at very low temperatures below those arising from the simple solid model. In the absence of a reliable experimental temperature scale at very low temperatures, only a qualified and cursory comparison is justified with recent experimentally estimated melting pressures. Discrepancies arise between theory and preliminary data on the temperature derivatives of the melting pressure or the entropy of the solid at melting. They might be due in part to the tentative experimental temperatures, which appear shifted toward too low temperatures when compared with the theoretical temperature scale implicit in the treatment of the generalized solid model. However, from the viewpoint which accepts the rather preliminary, scarce, very low temperature melting pressure data at face value, failure of the extended exchange model of solid³He at those temperatures must be kept in mind.Work performed under the auspices of the U.S. Atomic Energy Commission.     

Turbulence generated by vibrating wire resonators in superfluid 4He at low temperatures

No Heading We have measured responses of vibrating wire resonators in superfluid ⁴He at millikelvin temperatures. We find evidence for turbulence generation above a critical velocity on the order of a few cm/s. At the critical velocity for the onset of turbulence, the resonator velocity abruptly decreases and shows hysteretic behavior. Surprisingly we find that the resonant frequencies of the resonators increase in the turbulent regime. We also find that the critical velocity may be reduced by the presence of turbulence generated by a neighboring vibrating wire resonator, allowing the detection of existing turbulence in the low temperature regime.PACS numbers: 67.40 Vs, 67.40 Pm     

NMR in superfluid3He at very low temperatures

Just a few years ago it was generally believed that the NMR properties of superfluid³He far below T_c would not be qualitatively different from those found at higher temperatures. Surprisingly, the strange enhancement of relaxation processes at around 0.4 T_c named catastrophic relaxation, was then found. Recently an extremely long lived induction signal with new dynamical properties was discovered in the region of 100 K. Some of the newly discovered properties can be partly explained, although there are still many unsolved problems. The main aim of this article is to raise new questions for future investigations at the lowest temperatures presently possible.     

Quantum cavitation in superfluid helium 4 ?

We have observed the nucleation of bubbles in superfluid helium-4 at negative pressure and at temperatures down to 65 mK. Cavitation is found to be a random process. Above 1 K, its probability varies with temperature in a manner consistent with classical activation by thermal fluctuations. Below 0.4 K, Cavitation is still random but temperature independent, in agreement with a recent theory of quantum tunneling. We also consider another possible interpretation involving turbulence in the focal region.     

Noncompact groups and the excitation spectrum in superfluid helium-4

It has been shown that the underlying symmetry algebra in the superfluid ⁴He can be extended to the spectrum-generating noncompact groups. This method furnishes the excitation energy of this system, exact in the framework of the symmetry algebra.     

Thermodynamics and nucleation of bubbles in normal and superfluid liquid helium-4 at negative pressures

We report on a theoretical investigation of liquid helium-4 at negative pressures. For normal liquid helium we estimate the thermodynamic functions for negative pressure via extrapolation of measurements made for positive pressures. We determine the free energy as a function of density and temperature and find the location of the liquid-vapor spinodal. The results of these calculations are used to construct a temperature-dependent density-functional scheme to describe the inhomogeneous liquid. This density functional is then applied to calculate the rate at which bubbles nucleate in the liquid at negative pressures. We include a discussion of the properties of the superfluid phase based on the use of Landau's quasi-particle model.     

The one-dimensional excitation gas in superfluid3He-A at very low temperatures

By setting up an experiment with a static A-B boundary stabilised by a magnetic field, we have been able to cool the liquid to the regime where the A-phase excitation gas is almost one-dimensional. We have measured the damping of a vibrating wire resonator in the A-phase while simultaneous measuring the damping in the B-phase. The response in the A-phase is found to follow an exponential temperature dependence and not a power law as might be naively expected. This effect is a result of the bending of the texture by the wire which excludes a large fraction of the bulk low energy excitations from the surface.     

An equilibrium theory of the dilute solutions of3He in superfluid4He at very low temperatures

An equilibrium theory of the dilute solutions of ³ He in superfluid ⁴ He is derived systematically. The theory is based on a model which (a) goes beyond the parabolic Landau-Pomeranchuk approximation for the ³ He quasiparticle energy by taking into account the fourth-order term in the momentum expansion of this quantity, (b) disregards contributions to the ³ He quasiparticle effective interaction whose order in the momentum is higher than two, and (c) allows the effective interaction to be nonlocal. The simplicity of the model enables the development of a unified parametrization of the various equilibrium properties of the solutions. The expressions obtained for these properties are both easy to apply and highly accurate over a wide temperature range spanning from T=0 to temperatures of the order of the ³ He quasiparticle degeneracy temperature. It is shown that the parameters appearing in the expression for the ³ He quasiparticle effective interaction at fixed ⁴ He number density are replaced in the fixed-pressure, low-temperature expansions of the equilibrium properties by other parameters whose appearance in the theory seems to be due to the renormalization of this interaction by the interactions between the ³ He quasiparticles and the virtual fluctuations of the ⁴ He number density Finally, a comparison is made between theory and experiment. Three quantities are considered in detail : the ³ He osmotic pressure and the ³ He quasiparticle inertial and specific heat effective masses. The analysis of the experimental data makes it possible to determine the parameters associated with the effective interaction at several pressures. It is found that the theory is, in general, in a very good accord with the experimental situation and that, within its framework, the experimental values of the osmotic pressure and the two effective masses are indeed consistent with one another.     

A mechanical measurement of textural relaxation in superfluid3He-A at very low temperatures

We have studied superfluid³He-A textures by a mechanical method in the very low temperature limit, T/T_c 0.14. The damping of a vibrating wire viscometer is affected by the structure of the 1-vector texture near the wire. The texture is disturbed by a violent motion of the wire. The relaxation of the texture, back to equilibrium, is then observed through changes in the damping of the wire's motion.We gratefully acknowledge discussions with G.R. Pickett and J.R. Hook. J.D.Close helped with early preparation of the experiment. This work was supported by NSF grant DMR 9120277.     

Tensile strength and visible ultrasonic cavitation of superfluid4He

Motion picture photographs of cavitation in He II revealed new characteristics pertinent to the liquid's tensile strength and bubble dynamics. A cylindrical acoustic standing wave with a frequency of 50.58 kHz induced the cavitation in He II at a temperature of 2.09 K. Analysis of light diffracted by the sound gave measurements of the acoustic pressure amplitude which were used both for selecting the best drive frequency and for obtaining the tensile strength. Bubbles appeared to originate on pressure antinodes, expanded to a diameter of 0.5–1.0 mm in about 0.3 msec, and eventually fragmented into smaller bubbles. They originated where the negative pressure extremum was as small as –0.6 bar (+0, –50%), a tensile strength much smaller than the predictions of theories developed for the homogeneous nucleation of bubbles in classical liquids. The bubble fragments were frequently nonspherical and had widths of 0.1–0.2 mm. Small bubbles also displayed an unexpected preference to originate on the surface of a stainless steel tube inserted in the sound field. Subsequent to nucleation, bubbles were frequently attracted to acoustic pressure nodes in agreement with a theory of vibrations and forces originally developed for bubbles in normal liquids. Attempts to detect first and second sound radiated by cavitation are described.Work supported by the National Science Foundation Grant DMR75-15628.NSF Predoctoral Fellow.     

The velocities of first and second sound in dilute solutions of3He in superfluid4He at very low temperatures

A unified theory of first and second sound in dilute solutions of ³ He in superfluid ⁴ He at very low temperatures is presented. The theory is based on the detailed semimicroscopic model for the ³ He quasiparticle excitations described by Disatnik and Brucker a few years ago. In contrast with Khalatnikov's macroscopic theory, the application of this model enables the derivation of relatively simple expressions for the sound velocities in which no omissions of terms representing contributions due to the thermal expansion are made. The sound velocities are given in the final expressions in terms of various parameters of the ³ He quasiparticle spectrum and effective interaction. These expressions are both highly accurate and easy to use over a wide temperature regime spanning from the quantum limit to temperatures of the order of the ³ He quasiparticle degeneracy temperature. The actual application of the theory to measurements of the sound velocities is described in detail. Numerical values or estimates for various characteristic parameters of the ³ He quasiparticle system, including in particular the ³ He quasiparticle effective mass, are obtained from the comparison between the theory and the experiment. The example of the second sound velocity is used to illustrate a procedure for analyzing data from very low-temperature measurements of the equilibrium properties of the solutions, which is expected to produce meaningful information regarding the parameters of the basic model. In practice, the theory is found to be in a very good accord with the measurements of the sound velocities. The result obtained for the zero concentration limit of the ³ He quasiparticle effective mass (m ₀ =2.19m ₃ ) is somewhat lower than the empirical estimates reported in the past. On the other hand, this result is in very good agreement with variational calculations based on the detailed microscopic theory of the solutions. A discussion of this and other results obtained from the comparison between theory and experiment is included.Work supported in part by the United States-Israel Binational Science Foundation.Killed in action, 16 October 1973.     

Nucleation of negatively charged vortex rings in superfluid helium-4 near its solidification pressure

The rate at which negative ions nucleate vortex rings in He II has been measured at 25 bar for electric fields E up to 12 kV/cm and temperatures T down to 0.4 K. A strong temperature dependence of v observed for T 0.6K and E<5kV/cm is attributed to the influence of isotopic impurities. Although the temperature-independent behavior found for T 0.6K and 5<E< 12 kV/cm is consistent with a theoretical prediction by Bowley, the relatively very much larger values of measured near 1 K indicate a serious deficiency in the model on which the theory is based.Supported by the Science Research Council under grants GR/A/0388.3 and GR/A/4874.7.     

Dynamics of superfluid helium-3 in flow channels with restricted geometries

The dynamics of superfluid helium-3 in flow channels with transverse sizes smaller than the mean free path of quasiparticles with respect to collisions with each other is considered, taking into account the diffusive reflection of quasiparticles from the walls. For quasiclassical Green functions the boundary conditions obtained by Ovchinnikov for the similar problem in superconductors have been used. Equations are derived defining the behavior of the difference between chemical potentials of normal and superfluid components of helium-3. These equations describe a phenomenon similar to the branch imbalance (or charge imbalance) in superconductors, and determine the relaxation depth of the pressure gradient in superfluid helium-3. The time-dependent Ginzburg-Landau equations are also obtained for the order parameter in the case when the transverse size of the channel is close to the critical value when the superfluid transition temperature goes to zero. The approach makes it possible to study theoretically effects related to the overcritical flows of superfluid helium-3 through narrow channels under pressure.     

Phase separation in solid mixtures of helium-3 and helium-4

Phase separation temperatures have been determined in bcc³He-⁴He mixtures as a function of³He concentration and melting pressure from measurements of changes in the X-ray lattice parameter and Bragg peak shape. A new rigid tail dilution refrigerator cryostat was used to study³He-⁴He crystals with³He concentrations of 0.10, 0.20, 0.30, 0.45, 0.60, and 0.70 and melting pressures between 3.0 and 4.3 MPa. The phase separation temperatures determined are in good agreement with regular solution theory and give little support for an asymmetry in the coexistence curve expected from a Nosanow-type model and reported from previous experiments using other signatures of phase separation. At a given concentration, differences in phase separation temperatures determined from slow cooling and warming data, respectively, are as much as 25 mdeg, but this is less than half the differences reported from previous experiments. A bcc-hcp transformation was seen in a crystal with 10%³He at aboutT=0.3 K for a melting pressure of3.7 MPa.     

Acoustic attenuation in superfluid3He-B at low pressures

The attenuation of zero sound in superfluid³He-B has been measured up to 160 cm^–1, at pressures less than 4 bar and at frequencies 34.2, 44.2, and 54.0 MHz. The contribution of pair breaking to the attenuation has been measured for the first time. The gap (J=1 ^–) mode has been studied in magnetic fields up to 80 mT and the structure of its Zeeman components revealed. Coupling to the gap mode in the applied field allows a direct spectroscopic measurement of the energy gap. In zero magnetic field, the attenuation is well described by the theory of Wölfle, showing agreement with the magnitude of the attenuation and the frequency of the squashing mode resonance, for an appropriate choice of the parameterz=(c ₀–c₁)/c₁, wherec ₀, c₁ are the velocities of zero and first sound. This provides a determination of the Landau parameterF ₂ ^s and indicates that thef-wave interaction is negligible at these low pressures.     

Adiabatic expansion of3He in4He at very low temperatures

In this paper the results of the investigation of a one-shot cooling technique, called adiabatic expansion of³He in superfluid⁴He, are reported. The expansion cooler basically consists of an expansion cell and a⁴He reservoir connected by a superleak. In the expansion cell nearly pure³He is gradually diluted to a saturated mixture by the injection of superfluid⁴He from the⁴He reservoir. The expansion of the³He produces cooling, which, in the ideal (isentropic) case can lower the temperature by a factor 4.56. In practice, the performance of this cooling method is limited by irreversibilities and heat leaks. In this paper several irreversible processes such as heat conduction, viscous effects, and supercritical⁴He flow, have been analyzed. Furthermore the effect of³He in a sinter layer in the expansion cell is discussed. The experiments have shown that the fountain pressure in the⁴ He reservoir is very suitable for driving the⁴He in and out of the expansion cell. During an expansion/extraction the⁴He chemical potential difference across the superleak is zero. The realised cooling factor, defined as the ratio of the initial temperature and the final temperature, is about 3.5 for initial temperatures between 20 mK to 190 mK. This value is lower than the ideal factor of 4.56 that can be obtained for isentropic expansions. The discrepancy is mainly due to the relatively large heat leak. The lowest temperature obtained in this investigation was 5.7 mK. The analyses have revealed no fundamental limitations for obtaining lower temperatures.     

Fibre-epoxy composites at low temperatures

The thermal and mechanical properties of carbon, glass and Kevlar fibre reinforced epoxy composites are discussed, with particular reference to the behaviour of these materials at cryogenic temperatures. The effects of production techniques and various fibre arrangements are determined.