Elastic Properties of Polycrystalline Solid Helium

Recent experiments have shown that the shear modulus of solid helium undergoes a large temperature variation in the range 20 to 200 mK, possibly due to changes in the pinning of dislocations. In this note we report on computer simulations of the elastic properties of polycrystalline solid helium. We calculate how the elastic coefficients of a sample made up of a large number of randomly oriented grains are affected by the changes in the shear modulus c ₄₄ of the individual grains.     

Acoustic Properties of Solid 4He in the Limit of Zero Impurity

We have studied the elasticity of solid ⁴He in relation with its possible supersolidity. For this we have measured acoustic resonance frequencies in a 1 cm³ cell filled either with polycrystals or with single crystals of ⁴He. We have observed a large stiffening at low temperature as first observed by Day and Beamish in polycrystals. The ³He impurity content has been varied from 300 ppb to 0.4 ppb. When kept in equilibrium with liquid helium, single crystals should be impurity free. In these crystals, a large stiffening is observed, which should not be the result of the pinning of dislocations by impurities.     

Isochoric Compressibility of Solid 4He

We have performed experiments in which we inject atoms into hcp, solid ⁴He contained in a cell of fixed volume at pressures greater than the bulk melting pressure. We measure the change in pressure of the solid in response to the injection, which gives a measure of the isochoric compressibility. We show that at T??700?mK the solid undergoes very little growth and is incompressible. With decreasing temperature the compressibility rises, saturates near T??400 mK and may show weak evidence of a decrease near T??250 mK. Measurements at lower temperatures are necessary to fully test the predictions.     

Elastic reflection of4He atoms from the surface of liquid4He

The reflection of incident⁴He atoms from the surface of liquid⁴He can yield information on the microscopic features of the liquid at the surface. Edwards et al. have measured this reflectivity and have developed a theoretical model which successfully described the measurements. However, the density profile of the liquid⁴He surface has recently been determined experimentally, and this can now be used to model the reflectivity without any freely adjustable parameters. We use this density profile and the experimentally-determined interatomic pair potential to derive an effective potential for the incoming atom, and then solve the single-particle Schroedinger equation to find the reflectivity as a function of wavevector perpendicular to the surface. Within the uncertainty in the density profile and interatomic potential, we have chosen values that give good agreement between the measured and calculated reflectivities.     

Charge Transport in Solid 4He

With the help of a new experimental technique strong anisotropy of the mobility of ions has been observed in hcp ⁴ He crystals. The mobility of positive ions in the direction of the six-fold axis is found to be 200 times higher than in the perpendicular direction. Activation energies of the mobility have been measured in both principal directions. They are equal to: 5.3K in the direction of the C₆-axis and 11K in the perpendicular direction. The behaviour of the ions' velocity in the strong electric field regime is also studied as a function of the orientation.     

Nuclear Magnetic Properties of Solid 3He Films

A brief review on the thermodynamic properties of ³ He films adsorbed on graphite is presented. The second solid layer of ³ He adsorbed on graphite is a particularly interesting two-dimensional system of localized identical spin- fermions, which evolves from antiferromagnetism to ferromagnetism as a function of increasing density. This striking behavior is interpreted within a generalized Heisenberg model including competing ring-exchange interactions. While ferromagnetic three-particle exchange dominates at the highest densities, higher order antiferromagnetic ring-exchange processes become significant at low densities leading to highly frustrated antiferromagnetic or ferromagnetic phases. At low temperature, the frustrated antiferromagnetic and ferromagnetic states may correspond to unique examples of new quantum phases as suggested by recent theoretical results. The relevance of this ring-exchange model for other systems of localized fermions is also discussed.     

Dielectric Constant Measurements of Solid 4He

Careful measurements of the dielectric properties of solid ⁴He have been carried out down to 35 mK, considerably lower than the temperature range of previous studies. The sample was prepared from high purity gas with ³He concentrations of the order of 200 ppb and were formed by the blocked capillary method. The molar volume of the sample was 20.30 cm³. The dielectric constant of the samples was found to be independent of temperature down to 120 mK before showing a continuous increase with decreasing temperature and saturating below 50 mK. The total increase in ?? is 2 parts in 10^?5. The temperature dependence of ?? mimics the increase in the resonant frequency found in the torsional oscillator studies and also the increase found in the shear modulus measurements.     

Flow of Solid 4He Near Melting

Torsional oscillator measurements on solid ⁴He have demonstrated non-classical rotational inertia (NCRI), indicative of a supersolid phase transition. Recent experiments indicate that the NCRI fraction depends on isotopic purity and perhaps on details of crystal growth and annealing, suggesting that defects may be involved. Our recent experiments have shown that solid helium does not flow in response to pressure gradients at low temperatures. Close to the melting temperature we do observe mass flow, but it decreases rapidly with temperature. For solid helium in the pores of Vycor the flow appears to be thermally activated and disappears below about half the melting temperature. Flow in bulk helium is restricted to a much narrower temperature range. Very close to melting (within 20 mK) the flow completely eliminates pressure differences in less than a minute. At slightly lower temperatures we saw flow, but significant pressure differences remained even after annealing.     

Kinetics of Liquid 3He Droplets in Solid 4He Matrix

Precise measurements of pressure in the crystal at constant volume were used to obtain the data on growth and dissolution kinetics of liquid ³ He droplets formed as a result of isotopic phase separation of solid ³ He- ⁴ He Mixtures. We studied several crystals with an initial ³ He concentration of 2.05% in the pressure range of 26–27 bar. It is shown that the growth of the liquid droplets during the stepwise cooling of the two-phase crystal is correctly described by the superposition of two exponential processes: diffusion decomposition with a small time constant and strain relaxation with a big time constant. The strain layer near the droplet boundaries is due to a great difference in molar volume between the droplets and the matrix, and leads to a plastic deformation of the matrix and to a non-equilibrium ³ He concentration in the matrix. Under such conditions quantum diffusion is significantly suppressed and ³ He atom transport occurs only as the strain is relaxed.     

Shear Modulus in Viscoelastic Solid 4He

The complex shear modulus of solid ⁴He exhibits an anomaly in the same temperature region where torsion oscillators show a change in period. We propose that the observed stiffening of the shear modulus with decreasing temperature can be well described by the response of glassy components inside of solid ⁴He. Since glass is an anelastic material, we utilize the viscoelastic approach to describe its dynamics. The viscoelastic component possesses an increasing relaxation as temperature decreases. The response functions thus derived are identical to those obtained for a glassy, time-delayed restoring back-action. By generalizing the viscoelastic equations for stress and strain to a multiphase system of constituents, composed of patches with different damping and relaxation properties, we predict that the maximum change of the magnitude of the shear modulus and the maximum height of the dissipation peak are independent of an applied external frequency. The same response expressions allow us to calculate the temperature dependence of the shear modulus?? amplitude and dissipation. Finally, we demonstrate that a Vogel-Fulcher-Tammann (VFT) relaxation time is in agreement with available experimental data.     

Low Frequency Elastic Measurements on Solid ^{4}He in Vycor Using a Torsional Oscillator

Torsional oscillator (TO) experiments involving solid \(^{4}\) He confined in the nanoscale pores of Vycor glass showed anomalous frequency changes at temperatures below 200 mK. These were initially attributed to decoupling of some of the helium’s mass from the oscillator, the expected signature of a supersolid. However, these and similar anomalous effects seen with bulk \(^{4}\) He now appear to be artifacts arising from large shear modulus changes when mobile dislocations are pinned by \(^{3}\) He impurities. We have used a TO technique to directly measure the shear modulus of the solid \(^{4}\) He/Vycor system at a frequency (1.2 kHz) comparable to that used in previous TO experiments. The shear modulus increases gradually as the TO is cooled from 1 K to 20 mK. We attribute the gradual modulus change to the freezing out of thermally activated relaxation processes in the solid helium. The absence of rapid changes below 200 mK is expected since mobile dislocations could not exist in pores as small as those of Vycor. Our results support the interpretation of a recent TO experiment that showed no anomaly when elastic effects in bulk helium were eliminated by ensuring that there were no gaps around the Vycor sample.     

A New Anomaly in Solid 4He

A new anomaly in the acoustic properties of solid⁴He has been observed when as little as a few parts per million of³He impurities are added. We show that the specific properties of the anomaly, can be explained by a continuous (second order) phase transition from a Bose condensed state above a critical temperature to a normal state below it. In this model the Bose particles which condense are long lived, thermally activated excitations.     

Vortex Dynamics in hcp Solid 4He

The peculiar features noted in (Penzev et al. in Phys. Rev. Lett. 101: 065301, 2008) we conjecture are evidence of a vortex fluid state in solid He. We suggest to analyze this state by means of the dynamics of quantized vortices, as used for the tangle of vortices in superfluid turbulence. We introduce parameters of the vortex tangle dynamics, e.g., relaxation time for the drift of lines in parallel to the torsional oscillation axis. We briefly discuss the transition from the supposed vortex fluid state into the supposed supersolid state (Shimizu et al. in Phys. Rev. Lett., arXiv:0903.1326).     

The Annealing Process in Solid 4He

We have used a torsional oscillator with square cross section and a resonance frequency of 185 Hz to confirm the nonclassical rotational inertia (NCRI) discovered by Kim and Chan (Nature 427:225, 2004; Science 305:1941, 2004). We have also found a strong correlation between the NCRI signal and a high dissipation Q ^?1 of 4×10^?6 of the oscillation above the transition temperature. Here, we present preliminary results of the annealing process in ⁴He at a pressure of 26 bar. When holding the temperature constant above 1 K we have observed a immediate rise in the period and a slow decay of the dissipation. The equilibrium value of Q ^?1 decreases with increasing temperature.     

Recent Experimental Studies on Solid 4He

In this article, we review the experimental studies in pursuit of supersolidity and on recent studies of mass flow through solid ⁴He samples.

     

Properties of 3He in thin 4He films

Substantial progress has been made in our understanding of the properties of ³He atoms in thin films of ⁴He. For such films the ³He occupies discrete quantum states in the film and the system is both rich and complex. Here we discuss progress in this field from several points of view; we briefly discuss early heat capacity and third sound results and concentrate on more recent NMR measurements of the magnetization and relaxation times T ₁ and T ₂. Further experimental work and theory for systems of finite ³He coverage is needed to fully understand this fascinating system.Presenter at the Elba Summer School; authors are listed alphabetically.     

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.     

Study of Solid 4He in Two Dimensions

Defects are believed to play a fundamental role in the supersolid state of ⁴He. We report on studies by exact Quantum Monte Carlo (QMC) simulations at zero temperature of the properties of solid ⁴He in presence of many vacancies, up to 30 in two dimensions (2D). In all studied cases the crystalline order is stable at least as long as the concentration of vacancies is below?2.5?%. In the 2D system for a small number, n _v , of vacancies such defects can be identified in the crystalline lattice and are strongly correlated with an attractive interaction. On the contrary when n _v ?10 vacancies in the relaxed system disappear and in their place one finds dislocations and a revival of the Bose-Einstein condensation. Thus, should zero-point motion defects be present in solid ⁴He, such defects would be dislocations and not vacancies, at least in 2D. In order to avoid using periodic boundary conditions we have studied the exact ground state of solid ⁴He confined in a circular region by an external potential. We find that defects tend to be localized in an interfacial region of width of about 15 ?. Our computation allows to put as upper bound limit to zero-point defects the concentration 3×10^?3 in the 2D system close to melting density.     

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.