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.      

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.     

BCC vs. HCP—The Effect of Crystal Symmetry on the High Temperature Mobility of Solid 4He

We report results of torsional oscillator (TO) experiments on solid ⁴He at temperatures above 1?K. We have previously found that single crystals, once disordered, show some mobility (decoupled mass) even at these rather high temperatures. The decoupled mass fraction with single crystals is typically 20–30%. In the present work we performed similar measurements on polycrystalline solid samples. The decoupled mass with polycrystals is much smaller, ～1%, similar to what is observed by other groups. In particular, we compared the properties of samples grown with the TO’s rotation axis at different orientations with respect to gravity. We found that the decoupled mass fraction of bcc samples is independent of the angle between the rotation axis and gravity. In contrast, hcp samples showed a significant difference in the fraction of decoupled mass as the angle between the rotation axis and gravity was varied between zero and 85 degrees. Dislocation dynamics in the solid offers one possible explanation of this anisotropy.     

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.     

Thermal behaviour of helium in silicon carbide: Influence of microstructure

We have studied the microstructure dependence of He bubble formation in silicon carbide. Helium accumulation in SiC was performed by 500 keV ³He implantation at room temperature with a fluence of 5 × 10¹⁵ cm^?2. Depth concentration profiles have been investigated in 6H-SiC single crystals and α-SiC polycrystals by NRA spectrometry. Cross-sectional TEM samples have been imaged to study bubble formation. After annealing at 1300 °C, results clearly demonstrate an influence of grain boundaries on He retention yield in α-SiC polycrystals while helium is totally released from single crystals. Polycrystals also display the formation of intragranular overpressurized bubbles while no bubbles are observed in single crystals. Interpretations are proposed on the basis of the nature of He traps.     

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.      

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.     

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.      

Anomalous spin-lattice relaxation in solid3He

Nuclear spin-lattice relaxation measurements have been carried out in bcc and hcp solid³He at low temperatures. The observed relaxation rates are anomalously high and indicate that a typical sample has a substructure of small domains at whose boundaries rapid spin-lattice equilibrium takes place. Experiments on the sample anisotropy show that these domains cannot be crystallites and we believe that they may be determined by stacking faults or small-angle grain boundaries. The magnetic field dependence of the spin diffusion coefficient and the effects of dissolved⁴He are also investigated.     

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.     

Observation of the morphology of thin films of solid helium deposited from the fluid onto sapphire

Thin layers of solid helium were grown on sapphire single-crystal substrates at pressures from about 500 bar to 9 kbar. Grain boundaries can be observed in these layer crystals. The morphology of the grains depends on the crystal modification. In the hcp phase (below about 1.13 kbar) a system of parallel bands is observed, probably due to slip and twinning. In the fcc phase (above 1.13 kbar) a polygonal structure similar to a helium froth is found. Melting of this froth in the fcc phase shows grain boundary melting; fluid helium is wetting the fcc grains. Grain boundaries in the hcp phase are, in contrast, not wetted by fluid helium. Near the triple point at 1.13 kbar and 15.0 K one can deposit both crystalline phases side by side. In such structures, the transition fcc hcp⁴He can be observed during isothermal holding. The transition proceeds by the parallel motion of low-energy grain boundaries.     

Optical Imaging of Helium Interfaces

This review describes the development work done in the Low Temperature Laboratory (LTL) at the Helsinki University of Technology which has yielded high-resolution interferometric measurements on various helium interfaces at ultra low temperatures. The optical project was started in the end of 1980s and the free surface of superfluid ³He was seen for the first time ever in 1991. Additionally to the liquid/vapor interface of ³He, also the liquid/solid interface of both ⁴He and ³He has been the object of investigations. In the course of these studies several important experimental results have been obtained like the discoveries of a new surface state and two new growth mechanisms with ⁴He crystals, or the observation of a multitude of different facets on ³He crystals. The most significant findings from all these measurements are presented together with the corresponding background information and the details of the experimental setup. At the end of the review we also indicate the plans for new measurements with a faster CCD camera we hope to realize in the near future. PACS numbers: 07.60.Ly, 67.57.-z, 67.80.-s, 81.10.Aj.     

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.     

Sorption studies of helium and neon by crystals of C60 and C70

We present sorption measurements for³He and⁴He in the temperature range of 1.5 K to 4.1 K, and for²⁰Ne in the temperature range of 22 K to 27 K by crystals of C₆₀, C₇₀ and crystals of the mixture of these two molecules, 80% C₆₀, 20% C₇₀ We analyze these data by taking into account the non-ideality of the gas in equilibrium with the adsorbate. We calculate chemical potentials and isosteric heats. We find that there is no obvious evidence of intercalation of helium in these crystals at low temperatures. At higher temperatures there are some anomalies in the helium isotherms, and indication of excess sorption. The isosteric heat shows a minimum in this region which can be interpreted as penetration of the helium into a region of repulsive potential. We also find that levels of sorption, at the same chemical potential difference from saturation, are higher for⁴He than for³He. They are also higher for⁴He on C₇₀ than for the other crystals. For neon our work is concentrated around the triple point. We find that the isotherms indicate the formation of liquid or solid films. Below the triple point, and above a few atomic layers, the neon film does not grow uniformly.     

Defects and Glassy Dynamics in Solid 4He: Perspectives and Current Status

We review the anomalous behavior of solid ⁴He at low temperatures with particular attention to the role of structural defects present in solid. The discussion centers around the possible role of two level systems and structural glassy components for inducing the observed anomalies. We propose that the origin of glassy behavior is due to the dynamics of defects like dislocations formed in ⁴He. Within the developed framework of glassy components in a solid, we give a summary of the results and predictions for the effects that cover the mechanical, thermodynamic, viscoelastic, and electro-elastic contributions of the glassy response of solid ⁴He. Our proposed glass model for solid ⁴He has several implications: (1) The anomalous properties of ⁴He can be accounted for by allowing defects to freeze out at lowest temperatures. The dynamics of solid ⁴He is governed by glasslike (glassy) relaxation processes and the distribution of relaxation times varies significantly between different torsional oscillator, shear modulus, and dielectric function experiments. (2) Any defect freeze-out will be accompanied by thermodynamic signatures consistent with entropy contributions from defects. It follows that such entropy contribution is much smaller than the required superfluid fraction, yet it is sufficient to account for excess entropy at lowest temperatures. (3) We predict a Cole-Cole type relation between the real and imaginary part of the response functions for rotational and planar shear that is occurring due to the dynamics of defects. Similar results apply for other response functions. (4) Using the framework of glassy dynamics, we predict low-frequency yet to be measured electro-elastic features in defect rich ⁴He crystals. These predictions allow one to directly test the ideas and very presence of glassy contributions in ⁴He.     

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.     

Instability of Vacancy Clusters in Solid 4He

The behavior of pairs and clusters of vacancies in solid ⁴He crystals is studied with diffusion Monte Carlo method. We use a trial function suitable for describing solid ⁴He with long range order, arbitrary number of unoccupied sites and explicit Bose symmetry. It is found that vacancy clusters are unstable and collapse in all considered systems. We find no signature of stability of bound vacancy clusters of any size. Vacancies are found to exhibit weak attraction and a rough estimation of the binding energy is reported.     

Absence of Slow Sound Modes in Supersolid 4He

Torsional oscillator experiments on solid ⁴He have been interpreted as showing mass decoupling similar to what one observes in a superfluid. Within the context of a two-component model for the supersolid one would expect the appearance of a second, slow acoustic mode. We have searched for this mode using an acoustic resonance technique. We have used porous membranes in bulk solid ⁴He analogous to a second sound experiment in the superfluid. We also investigated solid helium in Vycor using piezoelectrically driven titanium diaphragms (analogous to a fourth sound experiment in the liquid). Our measurements have shown no indication of an additional sound mode in the kHz range.     

Theory of the Phase and Twin Boundaries in Solid Helium and Reversibility of the bcc-hcp Phase Transition

The phase transition between bcc and hcp in solid ⁴He has martensitic-like features. The phase transition was investigated theoretically in terms of coherent lattice transformations. A theory with three order parameters is developed to take into account the changes in volume and pressure. The order parameters are the relative displacement, the stretching strain, and the compressive strain of the atomic planes. Also we introduce a thermodynamic parameter which characterizes the deviation from phase equilibrium. The parameter describes the fine structure of a 180° boundary and it’s split into two phase boundaries. The twin boundaries are nuclei of the original crystal phase. On this basis we explain the bcc-hcp phase transition asymmetry and pressure change, found in solid ⁴He experiments, and propose a new experimental scheme to inverse this asymmetry.