Measurements of Non-classical Rotational Inertia of Solid 4He at Two Frequencies

We have developed a double resonance compound torsional oscillator for studying non-classical rotational inertia (NCRI) of solid ⁴He at two different frequencies. The torsional oscillator consists of two beryllium copper torsion members, and two masses. The two masses rotate in phase in the first mode and out of phase in the second mode at resonance frequencies, 496 Hz and 1173 Hz, respectively. Samples of solid ⁴He (commercial grade with ³He impurity level less than 1 ppm) are grown with the blocked capillary method at pressures between 27 and 42 bar. Temperature dependences of NCRI signals at two different frequencies are observed in identical solid ⁴He at 37 bar.      

Transverse Ultrasound Measurements in 4He Single Crystals

Recently, Kim and Chan (Science 305:1941, 2004; Phys. Rev. Lett. 97:115302, 2006) have reported an anomalous decoupling transition of solid ⁴He in a torsional oscillator measurement, and interpret their results as evidence for non-classical rotational inertia and a possible supersolid phase of ⁴He. The detailed nature and properties of such a “supersolid” state in ⁴He are still far from being clear, although there are clues from experiments involving ³He impurities, different sample cell geometries, annealing effects and grain boundary flow. Defects produced during crystal growth or deformation (e.g. dislocations) may affect supersolidity, or even produce it, and they are expected to have significant impact on the elastic properties of the solid. The supersolid fraction could also decouple from the lattice and produce a decrease in the transverse sound speed. We have begun the experiments in this laboratory to study such effects, measuring the velocity and attenuation of transverse ultrasound at 10 MHz in ⁴He single crystals grown at constant pressure.      

Ground-State Properties and Collective Excitations in a 2D Bose-Einstein Condensate with Gravity-Like Interatomic Attraction

We study the ground-state properties of a Bose-Einstein condensate (BEC) with the short-range repulsion and gravitylike 1/r interatomic attraction in two-dimensions (2D). Using the variational approach, we obtain the ground-state energy and show that the condensate is stable for all interaction strenghts in 2D. We also determine the collective excitations at zero temperature using the time-dependent variational method. We analyze the properties of the Thomas-Fermi-gravity (TF-G) and gravity (G) regimes.      

Scattering of Elementary Excitations at the Surface of Superfluid 4He

We study the scattering of atoms, rotons and phonons at the free surface of superfluid ⁴ He. We calculate the evaporation, condensation and reflection probabilities in the framework of linearized time dependent density functional theory accounting for elastic one-to-one processes. We explore the angular dependence of the scattering probabilities showing that most results are independent of the incidence angle and can be expressed in terms of a single energy dependent parameter.     

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.      

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.     

Crystallization of 4He in Aerogels

Static behaviors of crystallization of ⁴He in porous materials, such as the increase of melting pressure, have been studied extensively, but nonequilibrium dynamics of the phase transition is hardly known. Our interest was in how ⁴He crystals grow in a 90.4% porosity aerogel. Aerogels are transparent and the dynamics in them can be studied visually. A Pomeranchuk-type variable-volume cell was used to study crystallization at a fixed temperature with a blocked capillary condition. By continuously compressing a chamber, the pressure rose above the bulk melting pressure and at a pressure 1.7 bar above the bulk melting pressure these crystals began to invade the aerogel. A clear crystal-superfluid interface was moved smoothly by the steady compression. No macroscopic facets were observed in the aerogel well below the bulk roughening transition temperature.      

Diffusion of Impurity Excitations in Superfluid and Solid 3He–4He Mixtures

Starting from the system of linearized kinetic equations, the exact expressions for the spin and mass diffusion coefficients and thermal diffusion ratio in quantum mixtures of helium isotopes with any degree of degeneration is obtained. From the general expression the various limiting expressions have been obtained, which are determined by various relations between collision rates of quasiparticles. The results of the calculations are compared with available experimental data. It is shown that in the low-temperature region, where an impuriton gas is one-component, the relaxation of concentration of ³ He in superfluid ³ He– ⁴ He mixtures is determined by the acoustic and dissipative collective modes with an effective diffusion coefficient. From the general relation, the expression for a spin diffusion coefficient in solid ³ He– ⁴ He quantum mixtures is derived. The comparison of the results obtained with the experimental data makes it possible to find a numerical value for the width of the impuriton energy zone.     

Melting and Crystallization of 3He Inclusions in Two-phase Solid 3He-4He Mixtures

The peculiar features of the phase diagram for the ³ He- ⁴ He system make it possible to melt the ³ He inclusions formed during phase separation of the mixture by further cooling and to crystallize them in subsequent heating. The kinetics of these processes is studied on a sample with a molar volume of 20.54 cm ³ /mole (P=31.7 bar) using pressure measurements. The time dependence of the crystal pressure P(t) is measured on cooling at a rate of 10 mK/h followed by heating. The dependence P(t) has two distinct rises in pressure, the first rise being associated with the phase separation of the mixture and the second one with the melting of the ³ He inclusions formed. It is shown that the melting of the ³ He inclusions is almost complete after the fast cooling and the observed pressure jump is in good agreement with the corresponding change in the molar volume. The repeated crystallization of the inclusions is found to give rise to a large pressure gradient near the boundary of the inclusions, suppressing quantum diffusion considerably. This may result in an incomplete crystallization of the inclusions. The experimentally observed difference between the initial and final pressure in the sample corresponds to the fact that approximately 20% of the ³ He remains in the liquid state.     

Liquid Drop Excitations and the Size Dependent Surface Tension of Small 4He clusters

No Heading The elementary excitation levels and chemical potentials of small ⁴He clusters with less than N = 50 atoms have been calculated by the diffusion Monte Carlo method. The deviations of the excitation energy levels from predictions based on a simple liquid drop model are explained by the width of the density fall-off at the cluster surface and the size dependence of the surface tension.PACS numbers: 67.40.Db, 36.40.–c     

The Formation and Melting of 3He Clusters in Phase-Separated Solid 3He-4He Mixtures

Melting pressure measurements have been made on the ³ He-rich phase formed by cooling a solid mixture of 0.6% ³ He in ⁴ He through phase separation, at pressures between 2.78 and 3.56 MPa. For comparison, simultaneous observations were made with the mixture confined in the pores of a silver sinter and in an open volume connected to the same fill-line. Samples in the sinter cell solidify at higher pressures than the open cell and equilibrate more quickly. Both cells exhibit hysteresis between melting and freezing temperatures, and the transitions are broader in the open-volume cell. Relative to pure ³ He, the melting pressure is elevated by as much as 60 kPa in the sinter cell and 20 kPa in the open cell. The size of the pressure change on melting indicates that a large fraction of the ³ He remains solid at pressures below the melting curve, and this effect is more pronounced in the sinter cell. Measurements are in progress to measure the magnetisation through the magnetic ordering transition.     

Superfluid Vorticity and 1/f Noise in Melting of Solid 4He

One of the ways to reach a zero-vorticity state in superfluid ⁴ He is to melt solid helium slowly at temperatures well below T . This method takes advantage of the small density difference between the liquid and solid phases and of the high critical velocities for vortex formation at low T. However, pinning of the liquid-solid interface on the walls, revealed by 1/f-like pressure fluctuations of up to 1-10 bar in our setup, has consistently led to remanent vortex line densities of 4 · 10³ lines per cm ².     

Adiabatic Melting of 4He Crystal in Superfluid 3He at Sub-millikelvin Temperatures

Adiabatic melting of ⁴He crystal to phase separated ³He–⁴He solution (at T< 2 mK) is probably the most promising method to cool the dilute phase down to temperatures substantially below 0.1 mK. When started well below the superfluid transition temperature T _c of pure ³He, this process allows, in principle, to get the final temperature (T _f ) several orders of magnitude less than the initial one (T _i ). This work is the first practical implementation of the method below the T _c of ³He. The observed cooling factor was T _i /T _f =1.4 at 0.9 mK, being mainly limited by the bad performance of the superleak filling line, by incomplete solidification of ⁴He in the cell, and by the improper thermal contact between the cell wall and the liquid.     

Spin Diffusion Processes in Solid 3He-4He Mixtures Near the BCC-HCP Phase Transition at the Melting Curve

The spin diffusion coefficient of 1% ³He in solid of ⁴He has been measured in the vicinity of the BCC-HCP phase transition at the melting curve by pulsed NMR. The applied spin echo technique does allow to distinguish the contributions from all of coexisting phases. In addition to well-known diffusion in BCC, HCP, and bulk liquid phases the new fast diffusion process is observed and the diffusion coefficient of this process is shown to be close to that in liquid mixture being dependent on the time between the NMR pulses (bounded diffusion). The possible reason for the effect may be connected with formation of liquid droplets during the BCC-HCP transition.     

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.      

Excitations and Their Temperature Dependence in Superfluid 4He Beyond the Roton

The temperature dependence of the dynamic structure factor S(Q,) for superfluid ⁴ He has been measured by inelastic neutron scattering for wave vectors between 2.3 and 2.6 Å ^–l. S(Q,) has two peaks: one sharp peak at low energies whose dispersion flattens out and whose strength decreases with increasing Q, and one broader peak at higher energies with a stronger dispersion. The first peak disappears gradually with increasing temperature, while only part of the second peak vanishes at T . This indicates the existence of a third broad contribution, related to atoms above the Bose condensate. The two-peak structure can be interpreted in terms of a Bose-condensate induced coupling of the two-particle spectrum to the one-particle spectrum. The overall temperature dependence is consistent with the density-quasiparticle picture.     

Elementary excitations and sound speed in liquid 4He at negative pressures

No Heading We present neutron scattering measurements of the phonon-roton excitations of superfluid ⁴He at negative pressures in the porous medium MCM-41. The phonon and maxon energies decrease systematically below bulk values as the density is decreased below the bulk value due to stretching of the liquid. The negative internal pressures are estimated by comparison of the observed maxon energies with extrapolation of positive pressure values and from the sound speed. The maximum negative pressure realized, about –5.5 bar, is consistent with surface tension arguments and the MCM-41 pore diameter of 47 Å. Slight broadening of the intrinsic lineshape is observed, suggesting shorter lifetimes of the excitations.PACS numbers: 61.12.Ex; 61.25.Bi; 62.60.+v; 68.03.Cd; 68.03.Kn; 67.40.Mj     

Instability of the Solid-Liquid Interface of 4He during a Large Transformation

We report an instability of ⁴He crystal surface during a large modification of its shape observed by schlieren photography. ⁴He crystal was nucleated on an ultrasound transducer which was placed in the upper part of the sample cell facing the bottom. The crystal was grown on the transducer and the lowest part of it eventually touched the bottom of the cell. Almost immediately, the crystal started to change shape very quickly to adjust itself to the new boundary condition. During this large deformation, the hexagonal shape of the crystal surrounded by facets became unstable and the surface became corrugated. The corrugation pattern during the deformation was observed by a high-speed camera. The results were compared with Kelvin-Helmholtz type instability which Uwaha and Nozières predicted.      

An Experimental Technique for Liquid/Solid Thermal Conductivity Measurements at the Melting Point

Based upon the theory that the thermal conductivity can be determined by measuring the speed of the propagation of the solid/liquid phase interface during a phase transition, a system was developed to investigate the thermal conductivity of metals and alloys at the liquid/solid phase transformation point. Furthermore, a mathematical method was applied to represent the melting and solidifying process in the phase transformation chamber, by which the error could be analyzed. In order to test the feasibility of the method and the measuring system, a series of verification experiments on lead have been performed to estimate the precision and the applicability of the measuring system. From comparisons with recommended data from the literature, the uncertainty of the experimental results is estimated to be about 5% which means the measuring method is suitable to determine the thermal conductivity of eutectic alloys and metals at the liquid/solid phase transformation point. This work provides a relatively precise method for thermal conductivity measurements on new materials such as lead-free solders.Paper presented at the Seventh Asian Thermophysical Properties Conference, August 23–28, 2004, Hefei and Huangshan, Anhui, P. R. China     

Supersolidity and Disorder in Solid Helium 4

Supersolidity is a rather controversial issue which has been revived recently by a number of torsional oscillator (ac-rotation) experiments with solid helium 4. One possibility would be that the ground state of helium 4 crystals contains a Bose-Einstein condensate of mobile vacancies. However, the supersolid signal was shown to depend on sample history. In addition, dc-flow experiments show that superfluid transport of mass does not occur in solid helium, except if it contains appropriate grain boundaries. As a consequence, we believe that supersolidity is not an intrinsic property of helium single crystals, but that it is due to quenched disorder. We report experiments on pressure relaxation in and light scattering from solid samples, that give additional evidence for the existence of disorder in helium crystals. We also describe our recent study of the wetting properties of grain boundaries.