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.     

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.     

Dynamical Transition of 4He Crystallization in a Very High Porosity Aerogel

Crystallization of ⁴He in aerogels of 90 and 96% porosities shows a dynamical phase transition at around 600 mK due to the competition between thermal fluctuation and disorder: crystals grow via creep at high temperatures and via avalanche at low temperatures. In a very high porosity 99.5% aerogel, however, the transition had not been observed in our previous publication (Nomura et al. in Phys. Rev. Lett. 101:175703, 2008). We improved the spatial resolution of the video image and found that the 99.5% aerogel did have the transition at around 200 mK, which is much lower than those of the lower porosities. The avalanche size is significantly smaller in the 99.5% aerogel. The reduction in the transition temperature and avalanche size may be the consequence of weaker disorder for the crystallization in the very high porosity aerogel.     

Elementary Excitations in Solid and Liquid 4He at the Melting Pressure

Recent discovery of a nonclassical rotational inertia (NCRI) in solid ⁴He below 0.2 K by Kim and Chan has revived great interest in the problem of supersolidity and initiated intensive study on the properties of solid ⁴He. A direct proof that the onset of NCRI corresponds to the supersolid transition would be the observation of a corresponding drop of the entropy of solid ⁴He below the transition temperature. We have measured the melting pressure of ultrapure ⁴He in the temperature range from 0.01 to 0.45 K with several single crystals grown at different pressures and with the accuracy of 0.5 μbar. In addition, supplementary measurements of the pressure in liquid ⁴He at constant volume have been performed, which allowed us to eliminate the contribution of the temperature-dependent properties of the pressure gauge from the measured melting pressure data. With the correction to the temperature-dependent sensitivity of the pressure gauge, the variation of the melting pressure of ⁴He below 320 mK obeys the pure T ⁴ law due to phonons with the accuracy of 0.5 μbar, and no sign of the transition is seen (Todoshchenko et al. in JETP Lett. 85:454, 2007). This sets the upper limit of ∼5⋅10⁻⁸ R for a possible excess entropy in high-quality ⁴He crystals below 320 mK. At higher temperatures the contribution from rotons in the superfluid ⁴He has been observed. The thermal expansion coefficient of the superfluid ⁴He has been measured in the range from 0.01 to 0.7 K with the accuracy of ∼10⁻⁷ 1/K, or by two orders of magnitude better than in previous measurements. The roton contributions to the melting pressure and to the pressure in liquid at a constant volume are consistent and yield the value of 6.8 K for the roton gap, which is very close to the values obtained with other methods. As no contribution due to weakly interacting vacancies to the melting pressure of ⁴He has been observed, the lower limit of about 5.5 K for their activation energy can be set.      

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     

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.     

On the Mobile Behavior of Solid 4He at High Temperatures

We report studies of solid helium contained inside a torsional oscillator, at temperatures between 1.07 K and 1.87 K. We grew single crystals inside the oscillator using commercially pure ⁴He and ³He-⁴He mixtures containing 100 ppm ³He. Crystals were grown at constant temperature and pressure on the melting curve. At the end of the growth, the crystals were disordered, following which they partially decoupled from the oscillator. The fraction of the decoupled He mass was temperature and velocity dependent. Around 1 K, the decoupled mass fraction for crystals grown from the mixture reached a limiting value of around 35%. In the case of crystals grown using commercially pure ⁴He at temperatures below 1.3 K, this fraction was much smaller. This difference could possibly be associated with the roughening transition at the solid-liquid interface.     

Impurity Scattering Effect on Superfluid Phases of 3He in 97.5% Porous Silica Aerogel

No Heading NMR studies of superfluid ³He in 97.5% aerogel have been performed in a magnetic field of 28.4 mT. A small-angle neutron scattering experiment on the structure of the aerogel shows that the average separation distance of silica strands is 54 nm. The aerogel strands were covered with a few layers of solid ³He whose magnetization shows Curie-Weiss behaviour. On cooling process A-like phase appeared at suppressed superfluid transition temperature T_C^aero and B-like phase appeared at lower temperatures although only the B-like phase was observed up to T_C^aero on warming process above 2.1 MPa. The superfluid transitions in aerogel always occur below the AB phase transition temperature of bulk liquid at all pressures. An isotropic inhomogeneous scattering model(IISM) proposed by Thuneberg et al. explained well the observed suppressed T_C^aero in 97.5% with the radius 59 nm of voids in this model. This radius is similar with the average strand separation distance of 54 nm measured in the structural analysis. This similarity of two lengths shows the connection of the suppression of T_C^aero with the actual average separation distance of the silica strands.PACS numbers: 67.57.Pq, 67.80.Jd     

Growth Rate of Frost Heave in Helium and Mass Transport in Solid 4He

Frost heave phenomena have been studied in ⁴He on porous vycor glass, in which ⁴He in the pores remained supercooled fluid below the bulk melting temperature, T _m . When we cool a bulk solid at T below T _m on the vycor, the bulk solid sucks the supercooled liquid in the pores and grows. We measured the maximum frost heave pressure over bulk melting pressure, P _m , as a function of ΔT=T _m −T. When temperature was suddenly lowered, the frost heave pressure increased in time to a next equilibrium pressure and we measured the time constant and derived the frost heave rate. The frost heave rate was measured as a function of temperature and decreased very rapidly as temperature was lowered. We propose models to explain the mass transport in solid either by vacancy or by amorphous solid between bulk solid ⁴He and vycor. From measured temperature dependence of the rate in comparison with our model, we conclude the frost heave rate is determined by mass flow in solid ⁴He due to thermally-activated vacancy diffusion.      

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.     

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.     

Melting Pressure Thermometry of the Saturated Helium Mixture at Millikelvin Temperatures

The melting pressure of a ³ He–⁴He mixture has a very simple quadratic temperature dependence below some tens of mK, determined by the entropy of the ³ He component in the liquid mixture. For undersaturated mixtures, the melting pressure also depends on the ³ He concentration x, which may vary in the course of the experiment as ⁴ He transfers between the liquid and the solid phases. On the other hand, if the mixture is saturated, the system is in a univariant state with a melting pressure that depends uniquely on temperature and, thus, offers a thermometric standard. However, the univariant state includes a pure liquid ³ He phase, which complicates the temperature dependence around its superfluid transition temperature T_c. In this paper, we analyze the melting pressure of the saturated mixture in simple terms and find an expression that is in good agreement with our experimental data, and is applicable across T_c down to very low temperatures. The obtained derivatives of the melting pressure with respect to the square of temperature are 0.92 Pa·mK⁻² above T_c and 1.52 Pa·mK⁻² in the zero-temperature limit. An erratum to this article can be found at     

Impurity Scattering Effect on Superfluidity of 3He in Aerogel

The impurity scattering effect on superfluid ³ He in aerogel is studied on the basis of the standard impurity theory within the weak coupling limit. We discuss the superfluid transition temperature and the superfluid density in the dirty Fermi liquid. The results are compared with recent experiments on the superfluidity of ³ He in aerogel. The low pressure data of the observed superfluid density are shown to be in better agreement with the results for the A-phase than for the B-phase. The B-phase results show considerable disagreement with the low pressure data.     

Superfluid helium three in aerogel

We report measurements of the superfluid density and transition temperature of³He confined within 98.2% open aerogel. Both the superfluid fraction and the temperature at which the superfluid is manifested are suppressed strongly from their bulk values. The results suggest that the aerogel reduces the order parameter by a mechanism other than as a diffusely scattering surface.     

The effect of pressure on the melting temperature and lamellar thickness of trans-1,4-polyisoprene crystallized at pressures of 1 bar to 3 kbar

The melting temperatures of both low-melting form and high-melting form trans-1,4-polyisoprene crystals grown at 1 bar pressure have been determined as a function of pressure. Equilibrium melting temperatures have been determined for specimens crystallized at pressure. All the melting temperatures increase by approximately 15 K kbar^–1. Lamellar thicknesses have been measured by both thin film transmission electron microscopy and via low-angle X-ray studies over the pressure range 1 bar to 3.0 kbar. The two methods of measurements give good agreement. Crystals of a given thickness melt at a given temperature, at 1 bar pressure, independent of temperature or pressure of crystallization. Crystals of a given thickness are formed at a given supercooling independent of the pressure of crystallization. At a given crystallization temperature the thickness of crystals formed decreases with increasing pressure. Crystals of the same form grow, at all pressures studied, by the same basic mechanism. Chain-extended type crystals were not formed.     

Effect of Crystal Quality on HCP-BCC Phase Transition in Solid 4He

The kinetics of HCP-BCC structure phase transition is studied by precise pressure measurement technique in ⁴He crystals of different quality. An anomalous pressure behavior in bad quality crystals under constant volume conditions is detected just after HCP-BCC structure phase transition. A sharp pressure drop of 0.2 bar is observed at constant temperature. The effect observed can be explained if we suppose that microscopic liquid droplets appear on the HCP-BCC interphase region in bad quality crystals. After the interphase region disappearance, these droplets are crystallized with pressure reduction. It is shown that this effect is absent in high quality thermal-treated crystals.     

Solidification of helium in confined geometries

Solidification and melting of helium in confined geometries has been studied in a series of in situ pressure measurements, using both³He and⁴He, in porous glass with pore sizes from 12 to 191 Å in radius. These measurements covered the temperature range from 0.04 to 2 K and pressures up to 6 M Pa. In³He, a pressure minimum is observed in the pores at the same temperature as for the bulk. At large pore sizes the elevation in pressure in³He is inversely proportional to the pore radius as predicted by the model based on homogeneous nucleation of solid as a result of density fluctuations. However, the magnitude of the pressure elevation does not agree with this model. In⁴He, comparison with the model is complicated by the strong temperaturedependence of the pressure elevation.     

Optical observation of growth and melting dynamics of3He-4He mixture crystals

Crystals grown from 2.1% and 9.3% solutions of³ He in⁴He were observed in a cryostat with optical access from two orthogonal directions (above and from the side). Video films of dynamic processes were recorded at temperatures between 0.5K and 1.8K. Facetted melting of crystals (in contrast with rounded melting which is the general case) was observed below 0.75K. This is in accordance with previous experiments which showed a higher³He concentration along the edges of the crystal. We also recorded morphological growth instabilities of the 9.3% b.c.c. crystals. In the temperature region below about 0.9K where the latent heat is negative no dendritic growth was observed, which we interpret as resulting from opposing effects of temperature and concentration gradients.     

Property of 4He Confined in 1D Nano-porous Medium FSM16 with 2.8-nm Channel Above Bulk Freezing Pressure

We have performed the freezing pressure and heat capacity measurements for ⁴He confined in a nano-porous medium FSM16 which possesses a one-dimensional 2.8-nm straight channel, in the pressure region above the bulk freezing pressure. At 2.8 MPa, where ⁴He in the channel remains a non-superfluid liquid down to the lowest temperature, the heat capacity decreases monotonically with decreasing temperature. It is in contrast to the heat capacity at 0.03 MPa with a broad bump at the temperature higher than the superfluid onset. At around the freezing onset in the channel, no clear heat capacity peak was observed. It suggests that the latent heat of the liquid?Csolid transition in the channel is quite small.     

Inelastic Neutron Scattering Studies of First Order Phase Transitions in bcc Solid 4He

We report inelastic neutron scattering studies of the [110] transverse phonon branches of bcc ⁴He near the bcc-hcp transitions on the solid-liquid coexistence line and near the melting transition. The question behind the experiment was whether these transitions in a quantum solid are in any way different from what one observes in usual materials. In contrast to large softening of the T₁ branch seen near the bcc-hcp transition in group IV metals, we found that the transverse phonons in bcc ⁴He do not soften at all. Altough visual studies of the crystals near the transition are consistent with a martensitic transformation, neutron scattering indicates that the transition in solid ⁴He is different than in metals. Thus, the mechanism of the bcc-hcp transition remains an open question. Similar study done near the melting transition indicates that none of the phonons measured in the present experiment is affected by melting, which rules out a mechanical instability of the bulk as a mechanism of melting. Finally, in addition to the phonons, we observed a new feature at q=0 and at an energy transfer of 1.23meV which we attribute to neutron scattering by point defects. Similarly to the phonons, this feature did not change near any of the phase transitions.