Ultrasonic measurements as a probe of3He/4He phase separation in aerogels

We have used ultrasonic velocity and attenuation measurements to study the phase separation of³He/⁴He mixtures confined in a silica aerogel with a porosity of 87%. We used both shear and longitudinal sound and varied the frequency between 4 and 20 MHz. The superfluid transition is accompanied by a velocity increase due to decoupling and by a critical attenuation peak which increases with frequency. At the phase separation there are changes in the velocity and attenuation, and hysteresis on thermal cycling. We show some recent results and discuss how they relate to the phase diagram inferred from torsional oscillator and heat capacity measurements on helium mixtures in aerogels.     

Acoustic Resonances in Helium Fluids Excited by?Quartz Tuning Forks

Ordinary quartz tuning fork resonators, operated at about 30 or 200 kHz frequency, couple to acoustic first and second sound resonances in helium fluids under certain conditions. We have studied acoustic resonances in supercritical ⁴He, normal and superfluid ⁴He, and in isotopic mixtures of helium. Suggestive temperature, pressure, and concentration dependences are given. Furthermore, we propose a thermometric reference point device based on second sound resonances in helium mixtures, and indicate possible differences in the nature of second sound resonances in superfluid ⁴He and helium mixtures.     

Fluid States of Helium Adsorbed in Nanopores

We have studied helium adsorbed in new nanopores which have regular structures from nano-cage to three-dimensionally (3D) connected pores. Adsorption potential and layer formation of the adsorbed helium are observed by the vapor pressure for the adsorption. New paradigms of zero-D and 1D helium fluids are realized in nano-cages and nano-channels, respectively. The superfluid onsets (transitions) in the 1D and 3D nanopores show obvious dependence on the pore connections. The superfluid in the 3D pores has properties similar to the Bose-Einstein condensation of the 3D Bose atomic gas. The films of the ³He gas formed in the ⁴He preplated nanopores show the dimensional crossover depending on the pore connection: from the 2D Boltzmann gas to a 1D or 3D gas state with decreasing temperature. This gas changes to the degenerate state in each dimension at the lower temperatures. Extremely high frequency measurements of the helium adatoms on flat substrate determined the superfluid vortex parameters of the ⁴He films, and revealed a slippage (decoupling) of the helium adatoms in the non-superfluid state.     

Thermal convection and thermal conductivity of nondilute3He-4He mixtures

We present measurements of the critical temperature difference for the onset of thermal convection and the effective thermal conductivity in two³He-superfluid-⁴He mixtures. The mixtures were 6.8% and 9.8% by molar volume of³He in⁴He and the measurements were made from 0.65 K to just above the superfluid transition temperature for each mixture. The measurements were made as part of an effort to visualize convective flow patterns in helium mixtures using optical shadowgraph techniques. We discuss the implications of our results for this effort.     

The Tricritical Region for Helium Mixtures in 0.87 Porosity Aerogel

We have used ultrasonic velocity measurements to study ³ He- ⁴ He mixtures in aerogel with a porosity 0.87. The phase diagram resembles that of bulk mixtures, with a single transition for ³ He-rich mixtures, in contrast to the detached phase separation curve seen in 0.98 porosity aerogel. A kink in the lambda line at a 3He concentration of X _C =0.51 suggests that the phase separation line meets it at a tricritical point. We have measured the amount of superfluid which decouples both at low temperature and close to the superfluid transition, as functions of ³ He concentration. Each showed a sudden change at the concentration where the kink appeared in the lambda line, suggesting an abrupt change in the morphology of the superfluid phase in the mixtures. Similar measurements were made for pure 4He films on the same aerogel. We discuss the nature of ³ He-rich mixtures in aerogels based on these experiments.     

Studies on Helium Liquids by Vibrating Wires and Quartz Tuning Forks

We present results of low-temperature experiments on dilute mixtures of ³He in ⁴He and on pure ³He, obtained by means of two kinds of mechanical oscillators immersed in the liquid sample: vibrating wires and quartz tuning forks. The helium sample was cooled either by adiabatic demagnetization of an immersed copper nuclear stage or by adiabatic melting of ⁴He in superfluid ³He. The measured effect of the surrounding fluid on the mechanical resonance of the oscillators is compared with existing theories. We also discuss resonances of second sound and the state of supersaturation, both observed by a tuning fork in helium mixtures.     

Onset of Convection in Superfluid 3He-4He Mixture Heated from Below

The thermal instability of ³He-⁴He mixtures caused by heating the liquid from below has been studied experimentally. The temperature gradients were measured which appeared in the mixture with initial concentration 9.8% of ³He below 0.5 K in the presence of different heat flows from the heater at the cell bottom. At a certain critical heat flow the effective thermal conductivity of the liquid was observed to increase sharply which was naturally attributed to the convective heat transfer. It is shown that the thermal convection develops at high temperature gradients. In this case the Rayleigh numbers exceed many orders of magnitude those for heating from above. Thus the convective instability develops in a system in which the light liquid is at the top and where no prerequisite for instability is seemingly available. The resugts obtained are analyzed in terms of the theory of convective instability in binary mixtures. It is suggested that the phase separation, of superfluid mixtures caused by a heat flow could be a destabilizing factor initiating convection. The vortex formation in superfluid helium and the related turbulent flows appearing at high temperature gradients can be another factor favourable for instability of the liquid.     

Absence of Slow Sound Modes in Supersolid 4He

Torsional oscillator experiments on solid ⁴He have been interpreted as showing mass decoupling similar to what one observes in a superfluid. Within the context of a two-component model for the supersolid one would expect the appearance of a second, slow acoustic mode. We have searched for this mode using an acoustic resonance technique. We have used porous membranes in bulk solid ⁴He analogous to a second sound experiment in the superfluid. We also investigated solid helium in Vycor using piezoelectrically driven titanium diaphragms (analogous to a fourth sound experiment in the liquid). Our measurements have shown no indication of an additional sound mode in the kHz range.     

NMR Study of Superfluid Phases of 3He Confined in 97.5% Porous Silica Aerogel

We have studied the scattering effect from aerogel strands on superfluid phases of ³He by a cw NMR method at 920 kHz. Liquid ³He at a pressure of 13 bar was confined in 97.5% porous aerogel from the same batch as that of a recent 4th sound study. The NMR experiment was performed in a magnetic field of 28.4 mT down to 0.3 mK. As temperature decreased, the NMR resonant frequency increased below 0.76 mK. The temperature of 0.76 mK agrees with the superfluid transition temperature T ^aerogel _c observed in the 4th sound study at the same pressure. Below T ^aerogel _c the behavior of thefrequency shift as a function of temperature indicates that there is no phasetransition to the other superfluid phase down to about 0.4 T ^aerogel _c . Owing to a very large surface solid ³He magnetization, we could not determine the superfluid phase of ³He in the aerogel in the magnetization measurement.     

Spin Pumping Effect in Superfluid 3He A1

A fountain effect is a common phenomenon in both ³He and ⁴He superfluids. Unique to superfluid ³He is the magnetic fountain effect, which has been used to determine the spin direction of the condensate in ³He A₁ phase. Here we present a pressure driven fountain effect in A₁ phase. The experimental cell is composed of a large reservoir connected to a small detector chamber through superleak channels of width of 20 μm. One wall of the detector chamber houses a movable circular 6 μm thick membrane which serves as a sensitive capacitive pressure sensor and also acts as a spin pump. In A₁ phase, a DC voltage applied on the capacitor induces a simultaneous mass and spin superfluid current into the small chamber. After equilibration, removal of the DC voltage causes a sudden pressure drop followed by a slow relaxation. The sudden drop is a consequence of reversed superfluid flow through the superleak. The observed decay times during the slow relaxation agree with those obtained in magnetically induced spin flow experiment. These observations show that the slow relaxation stems from spin relaxation in the absence of applied field gradient.     

Stabilization of High Concentrations of Nitrogen Atoms in Impurity-Helium Solids

Impurity-helium (Im-He) solids created by injecting gaseous helium with an admixture of nitrogen atoms and molecules into superfluid ⁴He have been studied via electron spin resonance (ESR). We have studied the efficiency of stabilization of N atoms in Im-He samples prepared from nitrogen-helium gas mixtures with different fractions of nitrogen varying from 0.25% to 4%. Some of the observed ESR spectra of N atoms in the Im-He samples are very broad. The highest local concentration of N atoms determined from dipole-dipole broadening of the ESR line is ～8×10²⁰ cm^?3. The highest average concentrations of N atoms in N-N2-He solids were much lower (of order 10¹⁹ cm^?3). The samples with high concentrations of N atoms were stable in liquid helium, and remained stable even after draining liquid helium from the sample at T≤3.5 K.     

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.     

Quenched bond randomness: Superfluidity in porous media and the strong violation of universality

The effects of quenched bond randomness are most readily studied with superfluidity immersed in a porous medium. A lattice model for³He-⁴He mixtures and incomplete⁴He fillings in aerogel yields the signature effect of bond randomness, namely the conversion of symmetry-breaking first-order phase transitions into second-order phase transitions, the λ-line reaching zero temperature, and the elimination of non-symmetry-breaking first-order phase transitions. The model recognizes the importance of the connected nature of aerogel randomness and thereby yields superfluidity at very low⁴He concentrations, a phase separation entirely within the superfluid phase, and the order-parameter contrast between mixtures and incomplete fillings, all in agreement with experiments. The special properties of the helium mixture/aerogel system are distinctly linked to the aerogel properties of connectivity, randomness, and tenuousness, via the additional study of a regularized “jungle-gym” aerogel. Renormalization-group calculations indicate that a strong violation of the empirical universality principle of critical phenomena occurs under quenched bond randomness. It is argued that helium/aerogel critical properties reflect this violation and further experiments are suggested. Renormalization-group analysis also shows that, adjoiningly to the strong universality violation (which hinges on the occurrence or non-occurrence of asymptotic strong coupling—strong randomness under rescaling), there is a new “hyperuniversality” at phase transitions with asymptotic strong coupling—strong randomness behavior, for example assigning the same critical exponents to random-bond tricriticality and random-field criticality.     

The generation of particles to observe quantized vortex dynamics in superfluid helium

We describe a method to prepare a sample of superfluid helium-4 with hydrogen particles suspended within it. The method is to dilute hydrogen gas with helium at room temperature, and bubble the mixture through liquid helium at a temperature above the superfluid phase transition temperature, T_λ ≈ 2.17 K. The procedure yields a suspension of micron-sized particles whose total volume is about 10⁵ times smaller than the fluid volume. The fluid and suspension are then cooled to a temperature below T_λ. We show that the particles, so prepared in superfluid helium, are useful for studying superfluid flows and, in particular, the dynamics of quantized vortices. In addition, the particle-superfluid helium system is rich in not yet fully explained interactions. We review preliminary investigations that include observing the vortex lattice in rotating helium, vortex reconnection in quantized vortex turbulence, and vortex ring decay. These data illustrate the basic mechanisms of dissipation in superfluid turbulence.     

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.     

Measurements of the Superfluid Joule–Thomson Refrigerator Using High Concentration 3He–4He Mixtures

The superfluid Joule–Thomson refrigerator (SJTR) uses a liquid superfluid ³He–⁴He mixture to provide cooling below 1 K. Performance measurements of the SJTR using 5% and 11% ³He concentration mixtures are reported. High concentration operation shows higher cooling powers at high temperature. Ultimate temperatures are seen to increase with increasing concentration due to a pinching of the temperature defect in the recuperative heat exchanger. This pinching effect is due to the variation of the heat capacity of the ³He–⁴He mixture with temperature and concentration and is discussed in detail and design changes are suggested to mitigate it.     

Effective Heat Conductivity and Relaxation Processes in Superfluid Mixtures of 3He-4He

The effective thermal conductivity coefficient'ceff in superfluid ³He-⁴He mixtures with concentration of 9.8% ³He has been studied experimentally between 100 and 500 mK, where the main contribution to the kinetic processes is made only by phonons and ³He impurity excitations. In this case the effective thermal conductivity is a combination of diffusivity, thermal conductivity and thermal diffusion. The κ _eff value was found from stationary measurements of the temperature gradients caused by the thermal flow and from the temperature relaxation kinetics. Both the methods provide consistent resugts which also agree with those on effective thermal conductivity calculated in terms of the kinetic theory of phonon-impuriton system.     

Ellipsometric Study of Superfluid Onset in Thin Liquid 4Helium Films

We have developed a modulated null ellipsometer capable of measuring single layers of adsorbed ⁴He films at 1.4 K. The small optical index of liquid helium, the extreme sensitivity to temperature gradients, and the requirement of sub-monolayer stability over many hours presents significant experimental challenges, which will be briefly discussed. The main goal of our experiments is to independently measure the superfluid and normal coverage in thin adsorbed ⁴He films. This is a particularly important issue for helium films on intermediate strength substrates such as rubidium and thin cesium, where previous measurements indicate that prewetting and the Kosterlitz-Thouless transition interact strongly, and the K-T transition appears to have nonuniversal features. Independent determination of the superfluid and normal fraction can be accomplished by using the ellipsometer in conjunction with a quartz crystal micro balance (QCM). QCM measurements rely on viscous coupling of the fluid layers, and therefore respond only to the normal component of a ⁴He film. In contrast, the ellipsometer is sensitive to the total thickness, independent of the state (superfluid or normal) of the film. By combining the QCM and ellipsometric measurements we can determine the total coverage, the normal fluid component and thus the superfluid fraction.     

Capture of Superfluid Helium by Porous Structures

We have studied superfluid helium capture in a sample of silica aerogel of 98.2% porosity in the temperature range from 1.22 K up to 1.89 K. The high retention of He in the aerogel sample corresponds to a similar phenomenon in impurity-helium condensates, in which very high values of the ratio of helium atoms to impurity atoms (up to 60) have been seen. We have observed that removing the aerogel sample from superfluid helium in a cylindrical glass beaker caused a decrease of the helium level corresponding to the geometrical volume of the sample (≈1 cm³). This observation has allowed us to conclude that superfluid helium is completely captured by the porous sample. Superfluid helium filling aerogel and impurity-helium samples (porous structures) serves as a dispersive medium of gel-like samples which interacts strongly with impurity nanoclusters forming the dispersing system.      

Quartz Tuning Fork Viscometers for Helium Liquids

Mechanical resonators, in the form of vibrating wires or torsional oscillators, have long been employed as sensors in liquid ³He and ³He–⁴He mixtures. The damping of resonators is due to the viscosity of the surrounding liquid which is a strong, well-known function of temperature for bulk Fermi liquids. It is therefore possible to use the viscous damping for thermometry in the millikelvin regime. An alternative sensor is the small quartz tuning fork which is driven by the piezoelectric effect and requires no external magnetic field. In this paper, we present measurements of the viscous damping of such a tuning fork when immersed in a 6.2% ³He–⁴He mixture, between 3 and 100 mK, and at zero and high (10 T) magnetic field. The measurements indicate that damping of the tuning fork resonance is dominated by the liquid helium properties and is insensitive to the applied magnetic field. The response of the tuning fork to the saturated helium mixture demonstrates that it could potentially be used for thermometry in any magnetic field. There is evidence of slip at the interface between the fork and the helium suggesting specular scattering from the smooth surface of the quartz. The fork is also able to detect the superfluid transition in pure liquid ³He.