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.     

Lattice Relaxation in Solid 4He: Effect on Dynamics of 3He Impurities

We present a new simplified derivation of the effect of lattice relaxation that accompanies the quantum tunneling of ³He impurities in solid ⁴He on the nuclear spin-lattice relaxation of the ³He impurities for very low impurity concentrations. As a result of the larger zero point motion of the ³He impurity compared to the ⁴He atoms, a significant lattice distortion accompanies the impurity as it moves through the lattice and the dynamics of the impurity depends on both the interaction energy between two ³He atoms and on the relaxation of the lattice for the tunneling impurity. Using a phenomenological model for the lattice relaxation we compare the nuclear spin-lattice relaxation rates observed at low temperatures with the dependence on temperature expected for a ⁴He lattice relaxation comparable to that observed by Beamish et al. (Phys. Rev. Lett. 96:195304, 2006).     

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.     

Thermal conductivity and isotopic impurities in single crystals of helium

We have utilized the enhancement of thermal conductivity by Poiseuille flow of the phonon gas to obtain highly sensitive measurements of phonon scattering by isotopic impurities in single crystals of helium. Crystal orientation, size, and quality may be inferred from the thermal conductivity data themselves. Our hcp ⁴ He crystals were grown at a constant pressure of 85.1 atm using apparatus and techniques that made possible some control over crystal orientation. An isotopic impurity concentration of 1.0×10^–5 decreases the peak conductivity in these crystals by a factor of 1.9 along a direction perpendicular to thec axis. In the Poiseuille region a relaxation time limit has been achieved experimentally that allows our data to be fitted as a function of temperature and concentration with only one parameter. The observed scattering strength is a factor of 2.7 greater than can be explained in terms of mass-defect scattering alone. A number of current theories are examined in the light of this result. Our pure ⁴ He data strongly support aT ^–3 dependence for the normal-process relaxation time. Measurements of the thermal conductivity parallel to thec axis reveal no anisotropy in either the normal-process relaxation time or the isotopic scattering strength.This work was supported in part by the National Science Foundation and the Office of Naval Research.     

4He Impurities in 3He: Energetics and Dynamics

We have developed the optimized Fermi Hypernetted Chain Theory of a single impurity atom in a Fermi liquid, and have applied the theory to a ⁴He atom in bulk ³He. Previous applications of the theory for one component have produced excellent agreement with the experimental equation of state of ⁴He; the resulting equation of state of bulk ³He is about 0.4 K above the experimental one. Within the same theory, we obtain the pressure dependence of the chemical potential of ⁴He in bulk ⁴He, ³He in ³He, as well as the chemical potential of a ⁴He impurity in ³He. The pressure dependence of the impurity chemical potential agrees well with the experimental data, but we have a constant energy offset of about 1.2 K that disallows conclusive statements. This offset is partly explained by the relative inaccuracy of the ³He equation of state. We then calculate the self-energy of a single ⁴He impurity in ³He. Our results for the effective mass m^* ₄ fall within the experimental error of the best available data; they increase from about m^* ₄/m₄1.4 at zero pressure, to m^* ₄/m₄1.6 at p=20 atm. We show that this effective mass enhancement is, to about equal parts, due to hydrodynamic backflow and to the coupling to particle-hole excitations. When the latter are turned off in the collective approximation of the impurity-background correlations one obtains a significantly lower effective mass, m^* ₄/m₄1.2–1.35.     

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.     

Supersolidity and Superfluidity of Grain Boundaries

We have looked for dc mass transport through solid ⁴He in a simple experiment with two communicating vessels filled with solid ⁴He in equilibrium with liquid ⁴He. Through good quality crystals, we have observed no mass transport, in contradiction with the hypothesis of a Bose–Einstein condensation of vacancies. Through crystals containing grain boundaries, we have found superfluid flow along these grain boundaries. We discuss these results in the context of other experiments on supersolidity.     

3He Impurities in 4He Systems Adsorbed on Curved Substrates

It is shown that ³He impurities in sufficiently large ⁴He systems adsorbed onto substrates with curved geometries form surface bound states, analogous to the Andreev state on a planar liquid--vapor interface. We report the analysis performed for superfluid ⁴He adsorbed on the external surface of the nano-fullerene C₆₀ and on cylindrical nano-wires of Au. It is found that a single ³He impurity diluted into such adsorbed structures behaves as on films on planar substrates and as on pure ⁴He clusters.     

Sub-boundaries in3He and4He single crystal and their migration below 1K observed by X-ray topography

The observation of alterations in crystal structure at ultra-low temperatures by X-ray diffraction, made possible by the realization of synchrotron radiation use after a quarter of this century, plays an important role in obtaining an understanding of the base structure of solids. For that, two types of³He-⁴He dilution refrigerators with a modified version of the top-loading facilities were installed at the BL-3C₂ and 6C₁ stations of the Photon Factory. In BL-3C₂, the behaviors of lattice defects in solid helium have been studied by X-ray topography. In this note, the migrations of sub-boundaries in³He and⁴He single-crystals are reported as being the result of an annealing effect. After annealing hcp⁴He single crystals for 80min at 0.5K, no change in crystallographic orientations could be easily observed from white SR X-ray topographs. In the same type topographs of bcc³He single crystals after annealing for several hours at 03K, migration of sub-boundaries were conspicuously discerned.     

Vacancy-induced transitions in hcp 3He

It is known from the work of Nagaoka that in hcp or fcc ³He a ferromagnetic alignment of nuclear spins does not give the lowest vacancy energy. We show that an ordered spin structure has a lower vacancy energy than either random or ferromagnetic structures. We study the possibility of vacancies inducing a transition to this spin structure, and of vacancies forming polarons. The latter is found to be more likely, and we estimate the fraction of vacancies forming polarons as a function of temperature. We briefly comment on the case of a vacancy in crystals of ⁴He with ³He impurity.Supported by the U.S. Department of Energy under Contract EY-76-C-02-1198.On leave from BARC, Bombay, India     

Disorder, Supersolidity, and Quantum Plasticity in Solid Helium 4

Several years after Kim and Chan’s discovery of an anomaly in the rotation properties of solid helium (Kim and Chan in Nature 427:225, 2004; Science 305:1941, 2004), the interpretation of the observed phenomena as a manifestation of supersolidity remains controversial. J.?Beamish and his collaborators have shown that the rotation anomaly is accompanied by an elastic anomaly (Day and Beamish in Nature 450:853, 2007; Day et?al. in Phys. Rev. Lett. 104:075302, 2010; Syshchenko et?al. in Phys. Rev. Lett. 104:195301, 2010): when the rotational inertia apparently increases, the shear modulus decreases. This softening is due to the appearance, in the solid, of a large reversible plasticity that is a consequence of the evaporation of ³He impurities from dislocations that become mobile. This plasticity is called “quantum plasticity” because the dislocations move by quantum tunneling in the low temperature limit. Since the main evidence for supersolidity comes from torsional oscillator (TO) experiments, and since the TO period depends on both the inertia and the stiffness of solid ⁴He, it is not totally clear if supersolidity really induces a change in inertia or if it is the disappearance of quantum plasticity that mimics supersolidity in TO experiments. In order to distinguish between supersolidity and quantum plasticity, we have studied the rotational and the acoustic properties of solid ⁴He samples with a variable amount of disorder and of ³He impurities. Of particular interest is the comparison of single crystals to polycrystals but the whole problem is not yet solved. This short review article is an opportunity to discuss several questions regarding the exact role of disorder in supersolidity and in quantum plasticity.     

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.      

Variational Study of a 3He Impurity Near a 4He Vortex Core

The system of kinetic equations for distribution functions of impurity excitations in solid 3He–⁴ He mixtures in the presence of phonons is solved. The results obtained allows us to calculate the spin diffusion coefficient of ³ He–⁴ He quantum crystals. The found expression differs from the results of the previous theoretical studies. A comparison of the obtained diffusion coefficient with experimental data makes it possible to determine the numerical values of the energy band width of impurity excitations.     

Variational calculation of the binding energy of one3He impurity in liquid4He

We present a variational microscopic study of the liquid⁴He with one³He impurity at zero temperature, within the framework of the average correlation approximation. In this approach all calculations can be referred to quantities of liquid⁴He. The chemical potentials of liquid⁴He and of a³He impurity are studied in the liquid range of densities and the results show an overall good agreement with the experimental data. Detailed comparisons with previous calculations are also presented. Due to the presence of the pressure term, the calculation of chemical potentials is a severe test to the capability of the wave function and the interaction to obtain a good saturation density. The calculation of the chemical potential of the impurity using the Lennard-Jones and the Aziz potentials, points out the different balance of kinetic and potential energies obtained in the variational minimization of these two potentials.Supported by a Fulbright Fellowship.     

Analysis of 3He Crystal Images Using a Computer-Generated Wire-Frame

Facetted crystals of bcc ³He have been observed with optical techniques in magnetic fields up to 9 T. Two-dimensional projections of the 3D crystals are obtained with a CCD camera. To analyze the growth rate of the various facets an interactive computer program is developed, which allows the user to analyze pictures made of crystals showing facets that have the 110-, 100- or 112-orientation. The working principles of this program are described and a picture taken from a ³He single crystal is analyzed as an example.PACS numbers: 67.80 −s, 81.10 Aj     

3He Impurity Effects on the Growth Kinetics of 4He Crystals

We report the growth kinetics of the⁴He crystals with a small amount of³He impurities around 0.8 K. The growth resistance was measured using the response of the charged interface with respect to an externally applied voltage. In 5 ppm and 10 ppm³He mixtures, it is found that (1) the relaxation process can be expressed as an exponential behavior, (2) the growth resistance becomes larger compared to pure⁴He and does not have a strong³He concentration dependence, and (3) the temperature dependence of the growth resistance is much the same as pure⁴He. We discuss several possible explanations of the present experiment.     

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.     

Pinning of Dislocation Motion in bcc Solid 3He

We have measured the dissipation of dislocation motion in bcc solid ³ He using the high-Q torsional oscillator technique at 1079 Hz. We observed a broad maximum in the temperature dependence of the dissipation. The maximum of the dissipation can be explained by the theory of Granato and Lucke in which the dislocation mobility depends upon the interactions of dislocations with point defects. ⁴ He impurities tend to bind to the dislocation lines at low temperatures and pin this dislocation motion. The maximum of the dissipation corresponds to the depinning of the dislocation motion. From the amplitude dependence of the depinning temperature we first obtained the activation energy of 1.03 K of the impurity ⁴ He atom trapped on the dislocations in bcc solid ³ He at a molar volume of 24.30 cm ³ /mol. The activation energy of the impurity atom in bcc ³ He was found to be larger than the value of 0.7 Kin hcp ⁴ He.     

Thin Helium Film on a Glass Substrate

We investigate by Monte Carlo simulations the structure, energetics and superfluid properties of thin ⁴He films (up to four layers) on a glass substrate, at low temperature. The first adsorbed layer is found to be solid and “inert”, i.e., atoms are localized and do not participate to quantum exchanges. Additional layers are liquid, with no clear layer separation above the second one. It is found that a single ³He impurity resides on the outmost layer, not significantly further away from the substrate than ⁴He atoms on the same layer.     

Comparative Study of Vacancies in the b.c.c. and h.c.p. Phases of 4He using Shadow Wave Functions

We use the shadow wave function formalism (SWF) to determine the energy of formation of single and double vacancies in ⁴ He crystals at T=0 K. Data is presented for both the bcc and hcp phases. The activation energy for single vacancies in bcc ⁴ He was found to be 6.7±3.9 K, about 43% of that in the hcp ⁴ He, 15.6±3.9 K. By determining the occupation of the Voronoi regions of the crystal sites, we determined the location of vacancies in the crystal and studied the relaxation of the neighboring atoms. We also present data on the correlations between vacancies, and between vacancies and ³ He impurities. Following the position of the vacancy through successive configurations we observed the motion of the vacancy as seen in our Monte Carlo simulations. On the shorter Monte Carlo time scales, greater vacancy motion was observed in the bcc phase than in the hcp phase.