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.     

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.     

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.     

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.     

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.     

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.      

Dendritic crystal growth in pure4He

Dendritic crystal growth of pure hcp and fcc⁴He was observed at pressures between 210 and 6500 bar. Dendrite morphology depends on fluid supercooling and crystal phase. At large supercooling, dendrites with side arms are observed, whereas at low supercooling dendrites grow without side arms. The morphology of hcp⁴He dendrites is strongly influenced by crystalline anisotropy. Comparison with present theories of dendrite growth show good agreement with the power law dependencies of velocity, tip radius, and Péclet number on supercooling. Numerically, theory predicts much larger velocities than are observed. The stability parameter is found to be much smaller than theoretically predicted.     

Investigation of the lifetime of longitudinal phonons at GHz frequencies in liquid and solid4He

The attenuation of longitudinal 1-GHz phonons was measured as a function of temperature in liquid ⁴ He at svp and at 23 bar as well as in hcp ⁴ He at 36 bar. The lifetime of the phonons which were generated by stimulated Brillouin scattering was determined optically by a probing light pulse. The results in liquid ⁴ He are discussed in terms of relaxation processes in the phonon and roton gas and are in good agreement with existing work. The attenuation in hcp ⁴ He, which approximately shows aT ⁴ temperature dependence, is attributed to three-phonon processes with longitudinal thermal phonons. A quantitative comparison with Landau-Rumer theory gives satisfactory agreement with the data. No effect of phonon dispersion on sound attenuation is found down to 0.8 K.     

Rapid growth of single crystals in the solid state utilizing a massive transformation

A method is described for rapidly growing single crystals in the solid state, utilizing the massive transformation. The technique involves moving a necked specimen through a thermal gradient and it has been shown to be successful in alloys of the Ag-Al system near 24.5 at. % Al. Single crystals of the hcp phase have been grown from the b c c phase at rates between 0.01 and 1.2 cm sec^–1. X-ray observations indicate the development of misorientations and a substructure with increasing crystal growth velocity. Metallographic observations on numerous crystals demonstrate that the occurrence of single crystal growth is closely related to the relationship between the undercooling at the transformation interface and the interface velocity. Favourable conditions require that the velocity of the transformation interface be near the maximum value possible under the imposed thermal conditions. Success in growing a single crystal decreases with increasing undercooling and no crystals could be grown when the undercooling exceeded about 20°C. Solid state crystal growth utilizing the massive transformation has many features in common with crystal growth resulting from undercooled liquids.     

4He Crystals on an Oscillating Plate

Shape and motion of ⁴He crystals in superfluid placed on a transversely oscillating plate were investigated visually. The plate was glued onto a piezo post which was driven in a shear mode electrically. The purpose of the experiment was to drive a ⁴He crystal by a piezoelectric device which can be used to drive ordinary solids by the inchworm method. Facets of a single ⁴He crystal 3 mm in width were destroyed by a single sawtooth pulse of 1 ms duration at 0.4 K. In case of a larger crystal 7.5 mm in width and 0.8 mm in height, only one side of the crystal moved toward the center of the crystal, while the other side never moved despite application of 100 pulses at 10 ms intervals. Therefore, the crystal grew vertically and its height varied from 0.8 mm to about 1.4 mm during the pulses. This anisotropic behavior had nothing to do with the direction of the sawtooth driver. Many of the observed behaviors were puzzling, but it can be said that the crystals responded to the oscillation sensitively and the sawtooth pulse induced a very anisotropic motion of the crystal surface.     

Effects of a 3He impurity on the Elastic Anomalies of 4He at T=0

Effects on the elastic constants of a system formed from ⁴He atoms with a ³He impurity concentration of 0.14 % are investigated in a range of densities varying from 0.029 to 0.035 Å^?3. A model wave function of the shadow class is used to compute elastic constants and quantities defined through relations satisfied by them. The linear compressibility assumes the isotropic character expected for an hcp crystal with a constant value of the structure axis ratio c/a. This is in contrast with bulk ⁴He where an anisotropic behavior is observed.     

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.     

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.     

Vacancy motion in solid helium

A model calculation of the vacancy tunneling frequency in bcc ³ He, hcp ³ He, and hcp ⁴ He is presented. Only the Debye temperature (and its volume dependence) and vacancy activation energies (from NMR data) are used; comparison with experiment is made. The relative tunneling rates in the three systems along with NMR and specific heat data provide evidence for the nature of vacancy motion in each of these systems.This work submitted in partial fulfillment of the requirements for Ph.D. degree, University of Massachusetts (1975).     

Etch pits in flux-grown corundum

Procedures have been developed for chemically polishing and etching {0001}, {10¯11}, {10¯12}, {11¯20}, and {1¯100} planes in crystals of ruby and sapphire grown from a PbF₂ flux. The shape and the orientation of the etch pits were found to be characteristic for each plane and the density of the pits was 10² to 10⁴/cm². Similar pits were produced in flame-fusion material, but the density was 10⁶ to 10⁸/cm². Ruby and sapphire crystals grown by the same process behaved similarly. There is evidence that etch pits reveal dislocations which emerge normally to the basal or to the prismatic planes, since similar patterns of pits were produced after the removal of successive layers of material parallel to these planes, and a correlation was found between the pit patterns on opposite {0001} faces. Inconclusive evidence on this point was obtained for the rhombohedral planes.     

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.     

Elastic Properties of Solid 4He

The shear modulus of solid ⁴He increases below 200 mK, with the same dependence on temperature, amplitude and ³He concentration as the frequency changes recently seen in torsional oscillator (TO) experiments. These have been interpreted as mass decoupling in a supersolid but the shear modulus behavior has a natural explanation in terms of dislocations. This paper summarizes early ultrasonic and elastic experiments which established the basic properties of dislocations in solid helium. It then describes the results of our experiments on the low temperature shear modulus of solid helium. The modulus changes can be explained in terms of dislocations which are mobile above 200 mK but are pinned by ³He impurities at low temperature. The changes we observe when we anneal or stress our crystals confirm that defects are involved. They also make it clear that the shear modulus measured at the lowest temperatures is the intrinsic value—it is the high temperature modulus which is reduced by defects. By measuring the shear modulus at different frequencies, we show that the amplitude dependence depends on stress in the crystal, rather than reflecting a superfluid-like critical velocity. The shear modulus changes shift to lower temperatures as the frequency decreases, showing that they arise from a crossover in a thermally activated relaxation process rather than from a true phase transition. The activation energy for this process is about 0.7 K but a wide distribution of energies is needed to fit the broad crossover. Although the shear modulus behavior can be explained in terms of dislocations, it is clearly related to the TO behavior. However, we made measurements on hcp ³He which show essentially the same modulus stiffening but there is no corresponding TO anomaly. This implies that the TO frequency changes are not simply due to mechanical stiffening of the oscillator—they only occur in the Bose solid. We conclude by pointing out some of the open questions involving the elastic and TO behavior of solid helium.     

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.     

Studies on synthesis,growth and characterization of a novel third order nonlinear optical 4-Dimethylaminopyridinium p-Toluenesulfonate single crystal

Good quality single crystals of 4-Dimethylaminopyridinium p-Toluenesulfonate (4DMAPPTS) possessing third order nonlinearity were grown by slow evaporation solution technique (SEST). Single crystal X-ray diffraction analysis reveals that 4DMAPPTS belongs to monoclinic crystal system with centrosymmetric space group P2₁/n. FT-IR spectral studies were carried out to identify the functional groups present in 4DMAPPTS. NMR spectral study confirms the molecular structure of the grown crystal. Dielectric measurements were made over a wide range of frequencies for different temperatures. The grown crystal was subjected to Vickers microhardness test to study the mechanical property. The etching studies reveal the growth pattern and dislocations present in the grown title crystal. The important optical parameters such as absorption coefficient, extinction coefficient, refractive index and optical band gap were estimated from UV–Visible spectral analysis. The negative third order nonlinear optical parameters like refractive index (n₂), absorption coefficient (β) and susceptibility (χ⁽³⁾) were estimated by Z-scan studies.     

The Roughening of Crystal Surfaces in Helium: Comments on Quantum Fluctuations and the Coupling Strength

I review the problem of the coupling of a crystal surface to the underlying lattice in the light of recent measurements by Todoshenko et al. in ³He. A comparison of ⁴He and ³He crystals illustrates the role of quantum fluctuations.PACS numbers: 67.80 −s, 81.10 Aj