Nucleation and Avalanche of 4He Crystals in Aerogel

Dynamical transition of ⁴He crystals in aerogel was reported recently (Nomura et al. Phys. Rev. Lett. 101:175703, 2008). Bare aerogel, which was placed in the bulk ⁴He crystals, was used in the report. ⁴He crystals inside the aerogel grew via creep at high temperatures and via avalanche at low temperatures owing to the competition between thermal fluctuation and quenched disorder. Crystal-liquid interface advanced from the edge to inside of the aerogel. Crystal has a greater density than liquid so that the extra mass has to be transported in the crystallization process. It is not known how the mass is transported in the aerogel. To find a clue to this issue, we did an experiment with aerogel in a glass tube so that the aerogel had contact with the bulk on only one surface. In this case, a similar dynamical transition was observed at low temperatures. In the avalanche region, however, ⁴He crystals did not grow from the outer surface of the aerogel but nucleated at various sites inside the aerogel. This means that crystallization in aerogel does not occur by the forced invasion of ⁴He crystal but by a process of the bulk crystal once being melted and transported to increase the pressure of the liquid in the aerogel. Thus, a mass transport mechanisms for the crystallization has been revealed by this observation.     

Observation of Shrinkage of Silica Aerogel during Capillary Condensation of 4He

Silica aerogels are highly porous and very compressible materials. They are transparent and suitable for observation of the liquefaction process in them. We reported that capillary condensation of ⁴He in a very light aerogel with a porosity of 99.5% proceeded with two steps under a nonequilibrium condition. The aerogel sucked outer liquid with two separated interfaces which were regarded as precursor films and avalanches (Nomura, R., et al. in Phys. Rev. E 73:032601, 2006). During the capillary condensation, shrinkage of the aerogel was large enough to be visually observable, shrinking about 1.5% in length by the capillary force. During the rapid evacuation at high temperatures, shrinkage was enhanced to as much as 7% and was easily seen. By repeated filling and evacuating of the liquid in the aerogel, the shrinkage became less. For denser aerogels with porosities of 95.8 and 90.4%, the shrinkage was not large enough to be observed by our method.     

Leftover Superfluid 4He in Aerogel and Its Crystallization by Cooling

Using a variable volume cell, we were able to crystallize ⁴He in aerogels at a constant temperature. The entire crystallization process was monitored visually owing to the transparency of the aerogel. Two different crystallization processes of ⁴He in aerogels were observed: creep at high temperatures and avalanche at low temperatures. In a 96 % porosity aerogel, we noticed that ⁴He remained liquid in some parts of the cell even though other parts of the aerogel were completely crystallized. Once such a situation was formed, the application of additional pressure did not further crystallize the liquid. This is presumably because a supply path of ⁴He atoms from the bulk crystal was blocked by the crystals in the aerogel. This leftover liquid, however, was found to begin to crystallize via avalanches when cooled below a particular temperature. If the crystallization pressure in aerogel is temperature independent at low temperatures as the bulk crystallization pressure, the crystallization by cooling is rather unusual. Possible explanations would be a decrease of the crystallization pressure in aerogel in the low temperature region, or the supersolidity of crystals in aerogel playing some role in mass transport.     

Effect of Strong Magnetic Fields on Superfluid 3He in 98% Porosity Aerogel

No Heading We report our results of shear acoustic impedance measurements performed on superfluid ³He in 98% porosity silica aerogel. Experiments in high porosity aerogel provide unique opportunity to study the influence of disorder on a p-wave superfluid and compare the behavior with that of the well understood pure bulk. Our experiment is designed to detect acoustic signatures from both bulk liquid and liquid in aerogel. In the past, experiments on ³He in aerogel have been conducted in zero or low magnetic fields (< 1 tesla). We made measurements in magnetic fields as high as 15 tesla at 28.4 and 33.5 bars and observed a new phase in aerogel induced by magnetic fields splitting the superfluid transition into two.PACS numbers: 67.57Pq, 67.80Mg     

Acoustic Properties of Normal Liquid 3He in 98% Aerogel

We have performed longitudinal ultrasound (9.5 MHz) attenuation and sound velocity measurements in the normal state of liquid ³He in 98% aerogel. The absolute attenuation and sound velocity were determined by direct propagation of sound pulses through the medium in a wide range of temperatures, 2 mK<T<200 mK. Due to the scattering off the aerogel, the sound excitation remains as first sound over the entire range of temperatures and pressures studied. Unlike pure liquid ³He, the sound attenuation shows a minimum around 30–50 mK, depending on the pressure. We report our results of absolute sound attenuation measurements at 29 bars of sample pressure.     

Sound Modes of Superfluid 3He in Aerogel

We present the results of experiments on sound propagation at audio frequencies in ³ He-filled aerogel. Sound modes were observed at temperatures of 0.8–100 mK in an aerogel sample of 98% porosity. We find that below T _c for superfluid ³ He in the aerogel matrix the speed of sound in the composite system increases by as much as 1.5%. Also below the aerogel T _c new modes appear which correspond to propagation speeds of up to 10 m/s.     

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.     

Critical Behavior of the Liquid Gas Transition of 4He Confined in a Silica Aerogel

We have studied ⁴He confined in a 95 % porosity silica aerogel in the vicinity of the bulk liquid gas critical point. Both thermodynamic measurements and light scattering experiments were performed to probe the effect of a quenched disorder on the liquid gas transition, in relation with the Random Field Ising Model (RFIM). We find that the hysteresis between condensation and evaporation present at lower temperatures disappears at a temperature T _ch between 25 and 30 mK below the critical point. Slow relaxations are observed for temperatures slightly below T _ch , indicating that some energy barriers, but not all, can be overcome. Above T _ch , no density step is observed along the (reversible) isotherms, showing that the critical behavior of the equilibrium phase transition in presence of disorder, if it exists, is shifted to smaller temperatures, where it cannot be observed due to the impossibility to reach equilibrium. Above T _ch , light scattering exhibits a weak maximum close to the pressure where the isotherm slope is maximal. This behavior can be accounted for by a simple model incorporating the compression of ⁴He close to the silica strands.     

Capillary Condensation and Hysteresis for 4He in Aerogel

When fluids are adsorbed in a porous medium, confinement and disorder can dramatically affect their critical behavior. Silica aerogels, with their high porosities and tenuous structures, provide an opportunity to study the effects of random impurities on the liquid-vapor transition. Previous measurements with helium and nitrogen confined in a 95% porosity acrogel showed no hysteresis between cooling and warming behavior near the critical temperature, T _c, allowing equilibrium behavior to be observed. T _c was suppressed and coexistence curves were much narrower than for bulk fluids. However, recent measurements further from T _c found long time constants and hysteresis between filling and emptying. We have made high resolution isotherm measurements near the critical point of helium in a 95% porosity aerogel, using a capacitive technique to measure the density directly. We also measured the pressure and bulk density in situ and used a ballast volume to control pressure. Thermal relaxation was very slow in the coexistence region, but our technique allowed us to directly check for equilibrium at each point. T _c was suppressed, but the coexistence curve was not as narrow as in the earlier measurements. However, we observed hysteresis and finite compressibilities at all temperatures below T _c, indicating the importance of surface tension and capillary condensation.     

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.     

The onset of superfluidity in4He films adsorbed in aerogel glass

We have completed a systematic study of the superfluid density of ⁴ He films adsorbed in 91% porosity aerogel glass. We have concentrated on the low-coverage regime (T_c<200 mK) in an attempt to address recent theoretical work on the onset of superfluidity in dirty boson systems. Our data are not in agreement with the predictions of a scaling theory of the onset transition developed by Fisher et al. ¹ We discuss the extent of this disagreement and the limitations of other models of the onset transition.     

Sound Experiments on Superfluidity of 3He in Highly Porous Aerogels

We have carried out sound experiments on superfluid ³ He in three highly porous aerogels with different porosities. Two of the acoustic cells contain aerogels inside the pores in roughly sintered silver powder to avoid the vibration of the aerogel. In these acoustic cells we have detected fourth sound, and extracted the superfluid density from the fourth sound velocity. The effect of the sintered silver on superfluid ³ He was examined by using another acoustic cell which contains the sintered silver without aerogel. The size of the pores in the sintered silver was large enough not to show the size effect of superfluid ³ He and small enough to observe fourth sound of ³ He. In another cell without sintered silver, we have observed second-sound-like signal. The superfluid transition temperatures of ³ He are suppressed more in higher density aerogel. The aerogel density dependence of the suppression of the superfluid transition temperature of ³ He in aerogel can be explained qualitatively by the simple s-wave scattering approximation. However, the superfluid density shows quite different pressure-dependence in different porous aerogels. The reason of this phenomenon is not understood yet.     

The Equilibrium A-B Transition in Low Density Aerogels

No Heading We have measured in detail the NMR spectra of superfluid ³ He inside two different silica aerogels, one with a porosity of 99.3% and the other 98.6%. From these spectra, we are able to determine the equilibrium A-B transition temperatures in both aerogel samples as a function of hydrostatic pressure. We find that the slope of the reduced A-B transition temperature, 1- T_AB/T_c, vs. pressure is only about one third that seen for the bulk A-B transition, despite the fact the T_c for the two samples is suppressed very modestly, by only 4% and 8% at 34 bars. We argue from this that the presence of the aerogel stabilizes an equal-spin pairing which is district from that stable in the bulk.PACS numbers: 67.57 Pq, 67.57 Lm     

An Experiment to Measure Heat Capacity of 3He in Aerogel

We describe an experiment to measure the heat capacity of ³ He in aerogel. A new cell improved over the previous design¹ is shown. The aerogel sample is situated inside an epoxy shell which is also the bob of a torsional oscillator. ³ He entrained in aerogel is cooled through a ³ He weak thermal link. Data are being taken at temperatures from 10 mK to below 1 mK. We describe a new analysis procedure that determines both the heat capacity of the cell and the thermal conductance of the weak link.     

Optical Study of 4He Condensation into a Silica Aerogel

We use optical methods to study condensation of ⁴He into a 95% porosity silica aerogel at temperatures below the bulk critical point. Simugtaneous pressure and optical measurements are performed along isotherms, as the cell is very slowly filled or emptied. We find that the pressure presents a quasiplateau below the bulk saturation pressure P _sat over a finite range of densities inside the aerogel. In this range, strong light scattering is observed, which shows that the helium density fluctuates on a microscopic scale. Quantitative analysis shows that the helium density is correlated over distances somewhat larger than the gel correlation length. We discuss our resugts in terms of two possible scenarios, capillary condensation and liquid-gas transition.     

Transverse Acoustic Spectroscopy of Superfluid 3He in Compressed Aerogel

The unique nanoporous structure of aerogel provides a rare opportunity to study the role of anisotropic disorder on an anisotropic superfluid ³He. It has been proposed that uniaxial deformation of compliant aerogel would induce global anisotropy and a few compelling effects of global anisotropy on nature of the superfluid phases have been predicted. We measured high frequency shear acoustic impedance in superfluid ³He at 32 bar in a commercially available 98% porosity aerogel under uniaxial compression. At 5% compression, we found evidence of an A-like phase stabilized in a wider temperature width than the A-like phase in uncompressed aerogel.     

Absolute Ultrasound Attenuation Measurements in Superfluid 3He in 98% Aerogel by Direct Transmission

Systematic investigations on the effect of static disorder on p-wave superfluid ³He have been made possible by utilizing the unique structure of high porosity silica aerogel. For the past 10 years, a burst of experimental efforts revealed that three distinct superfluid phases exists. We have performed longitudinal ultrasound (9.5 MHz) attenuation measurements in the B-phase of the superfluid ³He in 98% aerogel. The absolute attenuation was determined by direct propagation of sound pulses through the medium in a wide range of temperatures, down to 200 μK, for sample pressures of 10 and 29 bars. Our results provide direct information on the zero-energy density of states of the superfluid phase in aerogel originating from impurity scattering.     

Large Boundary Magnetism and Superfluidity of Liquid 3He in Nanometer-sized Porous Alumina

Continuous-wave NMR measurements were performed for liquid ³He in porous alumina with nominal pore size of 20 nm in diameter, at temperatures down to 0.3 mK. The signal is composed of two contributions: from the liquid and from the boundary solid layer of ³He on the alumina’s surface. The latter shows a well-known ferromagnetic tendency and signal intensities can be fitted to a Curie-Weiss law in the high temperature region. The obtained Weiss temperatures are 0.18 and 0.50 mK at 7.5 and 28 bar, respectively. ⁴He coverage (4 monolayers) completely eliminates boundary signal between 7.5 bar and 32.5 bar. The residual liquid signal shows frequency shift and broadening below superfluid transition temperatures depending on liquid pressures. The obtained P-T phase diagram well resembles that of bulk liquid ³He in spite of the very narrow pore-size comparable to the coherence length of superfluid ³He.      

3He-4He Mixtures in 95% Porous Aerogel

Torsional oscillator measurements of ³ He- ⁴ He mixtures in 95% porous aerogel found a phase diagram similar to that in 98% porous aerogel. The coexistence boundary on the ³ He rich side resides very close to, but nevertheless is detached from the superfluid transition line. Together with the findings in 98%, 87%, and 99.5% porous aerogel, this result supports the interpretation that the phase separation of ³ He- ⁴ He mixture in aerogel is induced by the capillary condensation of ⁴ He films from neighboring silica strands into ⁴ He rich domains.     

Preparation of carbon aerogel electrodes for supercapacitor and their electrochemical characteristics

A new process is presented for synthesizing the supercapacitor electrodes of carbon aerogel via pyrolyzing resorcinol-formaldehyde (RF) aerogel, which could be cost-effectively obtained by ambient drying of wet RF-gels instead of conventional supercritical drying. Defect free RF-aerogels instead of conventional supercritical drying. Defect free RF-aerogels with the linear shrinkage of less than 8% could be manufactured by ambient-drying of wet RF-gels. Carbon aerogels with high strength were prepared via pyrolyzing RF-aerogels in N₂ atmosphere. The specific surface area (< 600 m²/g) and the electrical conductivity ( 50 S/cm) of carbon aerogels varied in sensitivity with the pyrolysis condition, while their densities (0.6 g/cm³) and porosities (70%) were found to be almost constant. Post heat-treatment of carbon aerogels around 300^C in air atmosphere was very effective for improving the electrochemical properties of electrodes. The carbon aerogel electrode pyrolyzed at 800C showed the specific capacitances of about 40 F/g in H₂SO₄ electrolyte solution and 35 F/g in KOH solution.