Fluctuating Surfaces of Growing 4He Crystals in Aerogel

Crystal-superfluid interface of ⁴He in aerogel was shown to advance smoothly in a high temperature creep growth region above 0.6 K. In this report, we focused on the shape of the growing interface in the region and attempted to analyze the roughness of interfaces. The growth of rough interfaces is very common in nature and is known to often follow a scaling law; roughness usually increases with time and saturates in the later stage. We measured the roughness w(t) defined as the standard deviation of the interface height as a function of time t. It was found that w(t) in 98 % porosity aerogel initially increased with t and decreased after a particular time in the later stage. The abrupt reduction of roughness in the end of crystallization is unusual if it is intrinsic in the crystallization in aerogel.     

Homogeneous Nucleation of 4He Crystals by Acoustic Waves

We have recently found experimental evidence for the homogeneous nucleation of crystals in metastable liquid ⁴He at high pressure. For this we combined the focusing of a high intensity spherical acoustic wave with a simple light scattering technique. We discuss the analysis used to distinguish between nucleation of bubbles in the negative pressure swings of the wave from nucleation of crystals in the positive swings. We also discuss the interest of our results and future developments of our experiment in the general context of the study of nucleation and instability limits in phase diagrams.     

Nucleation and Growth of bcc 4He and of 3He-4He Crystals on Cubic Substrates

We describe experiments on the nucleation and growth of bcc ⁴He and ³He-⁴He mixture crystals on several cubic substrates. In the case of pure ⁴He, the solid does not preferentially nucleate nor does it wet the substrates even when the lattice match is very close. In our view, the absence of preferential nucleation and wetting is a consequence of the interaction between the substrate and the He solid being excessively strong. In the case of mixture crystals, preferential nucleation is observed on a CsCl substrate. Even without preferential nucleation, complete wetting of all the substrates is observed. We suggest that the addition of ³He lowers the crystal-substrate interface energy due to a lower shear modulus of the mixture solid. The microscopic origin of this effect remains a puzzle.     

Superfluidity of Pure 3He and Mixtures of 3He and 4He in Aerogel

We describe new torsional oscillator experiments on ³ He confined in 98.2% open aerogel. In one, we monitored the superfluid fraction of pure ³ He at T << T _c while we gradually changed the sample pressure. The resulting change in density alters ₀ of the superfluid ³ He relative to the distribution of the length scales (correlations) of silica in the aerogel. We observed a T = 0 normal-to-super fluid transition at a pressure of about 6.5 bar, in marked contrast to the bulk where liquid ³ He is superfluid at all pressures. In the second experiment, we measured the temperature dependence of the ³ He _s at a pressure of 21.6 bar with different amounts of ⁴ He present in the cell. Adding 2-3% ⁴ He slightly increases both T _c and _s . We found that for ⁴ He concentrations between 2% and 34%, the ³ He T _c increases by a very small amount. However, _s , which for pure ³ He in aerogel at 0.5T _c is no more than 11%, falls by another factor of 7. This behavior (constant T _c , reduced _s ) is similar to that observed in granular superconducting films where the long-range order is controlled by phase coherence between adjacent grains.     

Tortuosity and Dissipation of Liquid 4He in Aerogel

No Heading Flow of liquid ⁴He through silica aerogel has been studied by means of a torsional oscillator. Preliminary results on the tortuosity and dissipation of the ⁴He flow in 88%-porous aerogel are compared with earlier measurements on a 92%-porous sample where a transverse sound resonant technique was used. A hydrodynamic model for saturated superfluid helium in porous media is presented and its predictions are compared with the experimental results.PACS numbers: 67.40.HF, 67.40 Pm, 61.43.Gt     

Vortex-Loops and Phase Nucleation in Superfluid 4He and 3He

We propose a new model for the nature of the nucleation of solid from the superfluid phases of ⁴ He and ³ He. A fast solidification event in the superfluid results in a local release of pressure and a velocity field in the superfluid. This in turn facilitates the nucleation of vortex-loops. The kinetic energy gain of this process balances the surface tension, as the solid surface is quickly covered by many vortex-loops (hairy snow-ball). We show that this scenario gives good agreement with experiments on heterogeneous nucleation.     

Vortex-Loops and Solid Nucleation in Superfluid 4He and 3He

We propose a new model for the nature of the nucleation of solid from the superfluid phases of ⁴He and ³He. Unique to the superfluid phases the solid nucleation involves an extremely fast solidification front. We depart from the usual quasi-static treatment of solid nucleation by proposing that the nucleation of a solid seed is helped by the simultaneous nucleation of vortex-loops in the superfluid around it. It is the composite entity which is nucleated out of the over-pressurized liquid. This occurs when the local release of pressure creates a velocity field in the superfluid which in turn facilitates the nucleation of vortex-loops. The kinetic energy gain of this process balances the surface tension, as the solid surface is quickly covered by many vortex-loops (hairy snow-ball). We show that this scenario gives good agreement with many experiments on heterogeneous nucleation, where the energy barrier is found to differ with the classical theory of homogeneous nucleation by 8 orders of magnitude. We propose several experiments that could show the involvement of vortices with solid nucleation.     

Transverse Resonances in Aerogel with Liquid 4He

We present preliminary studies of transverse resonances in a thin disk of aerogel filled with normal and superfluid ⁴ He in the temperature range 1.4 to 3 K. We observed a broad temperature independent mode in the normal phase and three narrow critical modes in the superfluid phase. The system was modeled by combining the equations of superfluid hydrodynamics of helium with those of elasticity of aerogel. Analytical solutions were obtained for a resonator of square profile and two types of boundary conditions at the transducers/aerogel interface. Comparison of the model solutions with the experimental data showed that the dynamics of the oscillation was dominated by compression rather than shear as in pure transverse sound. Recommendations for future improvements are made.     

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.     

Nuclear Magnetism of Normal 3He and 3He-4He Mixtures in Aerogel

We report NMR experiments at 8 T on ³ He and ³ He- ⁴ He mixtures filling the pores of 95% porous aerogel, for temperatures T 6 mK. Magnetization measurements of pure ³ He reveal a localized layer approximately one monolayer thick. The longitudinal relaxation includes a component logarithmic in time, which is apparently associated with a fraction of the localized ³ He atoms. When the localized ³ He is displaced by adding ⁴ He the logarithmic relaxation disappears and T ₁ for the dominant exponential relaxation increases. Measurements of the spin diffusion coefficient with the aerogel filled with dilute solution in equilibrium with bulk phase-separated mixture provide an unambiguous determination of the spin mean free path,_s = 58 nm     

Excitations Beyond the Roton of Liquid 4He in Aerogel

The dynamic structure factor, S(Q, ), for wavevectors, 2.0Q3.6 Å ^–1 of liquid ⁴ He in 95% porous aerogel has been measured by inelastic neutron scattering methods. The aerogel was grown with deuterated materials and the multiple scattering involving the aerogel was negligible. S(Q, ) in the superfluid phase consists of a single peak plus broad intensity at higher energy , as in bulk superfluid ⁴ He. The single peak is identified with the phonon-roton excitation at higher Q. The weight in the peak, Z_Q , and the excitation energy dispersion curve, _Q , has the same basic wavevector dependence as in the bulk. The energy _Q is 2–3% below the bulk value at the end point and the peak is unobservable beyond Q=3 Å ^–1 within the present statistical precision. No peak is observed at T=2.3 K in normal ⁴ He suggesting, as in bulk ⁴ He, that the characteristic excitation at higher Q is associated with the superfluid phase.     

Contact Angle Singularity in 4He Crystals

Equilibrium shape of the interface between superfluid and crystalline ⁴He near the (0001) orientation is analyzed. We observe a singular dependence of the contact angle on the wall inclination with respect to the gravity. The energy of a step on the basal plane is measured. From the analysis of the meniscus profile the step-step interaction constant is estimated.      

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.     

Stacking Fault Energy in 4He Crystals

Recently observed non-classical rotational inertial (NCRI) in solid ⁴He is most probably related to defects which appear during the sample preparation. We have measured the energy of the stacking fault (SF) in an hcp ⁴He crystal at 0.2 K. The SF creates a groove with a dihedral angle of 155±5° on the crystal surface in a quasi-equilibrium with the liquid. The obtained value for the SF energy is (0.07±0.02) mJ/m², which is ～0.4 of the surface tension of the liquid–solid interface of ⁴He. Our findings suggest that the phenomenon of burst-like creation of new atomic layers might be accompanied by the creation of SFs.     

Nucleation of Solid 4He by Acoustic Waves

When an acoustic wave pulse was applied to metastable superfluid ⁴He above the megting pressure, a bulk ⁴He crystal was nucleated in the superfluid at low temperatures. Overpressure in which the metastable liquid could exist was investigated by changing the acoustic wave power. A larger power pulse could nucleate the crystal in smaller overpressures, which decreased linearly in the acoustic wave power.     

Fast Mode in Dense Aerogel Filled with Superfluid He II and Dilute Mixture of 3He in 4He

Longitudinal sound wave propagation in 90% porous silica aerogel filled with superfluid He II and dilute mixture of ³He in ⁴He has been studied using a low frequency resonance method. The observed fast mode was identified as a mode intermediate between the sound in the aerogel matrix and first sound. It was shown that the behavior of the fast mode in dense aerogel differs from both high porosity aerogel and rigid porous medium. We discuss the obtained results within the framework of theoretical models available.      

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.     

Supersaturation and Nucleation in Superfluid 3He–4He Solutions under Elevated Pressures

Nucleation and phase separation kinetics of superfluid ³ He– ⁴ He solutions at various pressures and concentrations were investigated. The measurements of the first sound velocity and the attenuation as well as the liquid dielectric constant determination were used. The study was performed at a constant temperature and pressure and the phase transition was initiated by continuous increasing the ³ He concentration. It is shown that the pressure dependence of the attainable supersaturations is non-monotonic when passing through a maximum at pressure of about 0.1 Bar. The comparison has discovered great differences between the results obtained and theoretical predictions.     

Vortex Nucleation by Negative Ion in Superfluid He4

In superfluid He⁴, moving ions nucleate vortex loops by quantum tunneling through the barrier for T<0.3K, while thermal phonons activate the system over the barrier at higher temperature. The energy barrier height and the nucleation rate are calculated numerically, and these are well fitted with the experimental data for low pressures P<16bar and low electric fields E<10⁵V/m.     

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.