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.     

Improved Optical Setup to Measure Growth and Megting of Solid 3He Below 1 mK in Magnetic Fields Up to 9 Tesla

Recent experiments on crystal growth and crystal shape in ³He at zero magnetic field at 0.55 mK by Tsepelin et al. ^{1, 2} in Helsinki have revealed many new facets and strong anisotropy in the growth rates. Since ³He presents the unique possibility of investigating the influence of a magnetic field on crystal growth properties, we intend to extend our experimental studies of the shape and growth rate of solid ³He to magnetic fields up to 9 T at temperatures as low as possible.For that purpose our optical access cryostat with low temperature CCD has been upgraded and modified. The low temperature LED is replaced by a room temperature source coupled to the cell with an optical fiber to obtain clear images of the growth process. Our Pomeranchuk cell has been fitted with a new optical section with pure quartz windows. It has a larger diameter, a larger distance between the optical windows, and an improved thermal link. Also the heat switches between the nuclear stage and the dilution refrigerator were replaced according to a more sturdy design. Initial resugts show clear crystals with sharp facet edges down to T=0.4 mK.     

First Observation of the Critical Size of Facets on 3He Crystals near 1 mK

We have been able to obtain the step free energies of the basic (110) and (100) facets on ³He crystals near 1 mK by using a new method in which the critical radius of facets is measured on slowly melting crystals. The critical radius is obtained by tracking optically the moment that the facet collapses. Our findings confirm that at such low temperatures the liquid–solid interface of ³He is indeed strongly coupled to the crystal lattice, as was suggested in our previous studies.     

Measurements on the Surface Tension of 3He Crystals near 100 mK

No Heading ³He crystals start to show facets on their surface only at about 100 mK, well below the roughening transition temperature, and the reason for this change of the surface state is not clear yet. However, the most important characteristics of the crystal surface, the surface tension, was not measured in this temperature range before. We report our observations on the equilibrium shape of the ³He crystals in the temperature range of 77...100 mK. The surfaces tension was found to be isotropic and temperature—independent, and the corresponding value of the capillary length, = 0.93 ± 0.10 mm, is in a good agreement with the value measured at higher temperatures by Rolley et al.²PACS numbers: 68.35.Md 68.08.–p 67.80.–s     

Observations on Faceting of 3He Crystals at T=0.55 mK

We report on our recent observations on growing ³ He crystals in which altogether eleven different types of facets were found. The crystals were imaged with a novel low-temperature Fabry-Pérot interferometer. Intensity based analysis methods combined with a phase shift technique were used to identify the observed facets.     

Thermal expansion coefficient of 3He near 1 mK

A measurement of the thermal expansion coefficient of ³He at 0 bar from 0.6 to 3 mK is presented. At the superfluid transition the expansion coefficient changes by 1.1 × 10^\s-6 mK^\s-1. This change is consistent with predictions based on thermodynamic arguments and existing heat capacity data.This work was supported by NSF grant DMR 79-25098.     

Growth Dynamics and Faceting of 3He Crystals

³He crystals start to show facets on their surface only at about 100 mK, well below the roughening transition temperature. To find out the reason for this discrepancy, we have performed the first quantitative investigation on the growth dynamics of the faceted and rough surfaces of ³He crystals in the temperature range of 60–110 mK. We have applied an original method to obtain the variation of the overpressure on the crystal surface by measuring its curvature and height locally using a Fabry–Pérot interferometer. The growth of the rough surface was found to be limited by the transport of the latent heat which elaborates in the liquid, in accordance with theoretical predictions (Puech L., et al. in J. Low Temp. Phys. 62:315, 1986; Graner F., et al. in J. Low Temp. Phys. 75:69, 1989 and 80:113, 1990) and previous measurements near the minimum of the melting curve (Graner F., et al. in J. Low Temp. Phys. 75:69, 1989 and 80:113, 1990). The mobility of an elementary step on a facet was shown to be limited by the latent heat transport as well. The values obtained for the step free energy are by two orders of magnitude smaller than at ultra low temperatures, which we show to be the result of quantum oscillations of the solid-liquid interface, which quickly become damped when temperature decreases below 100 mK.     

Visualization of 3He Nucleate Boiling Below 1 K

Boiling behavior of liquid ³ He below 1 K was visualized as shadowgraph image. A light source and a video camera (or still camera) were arranged at room temperature. The light was guided to the ³ He cell by an optical fiber, and the shadowgraph image was transferred to the camera by an image fiber. The ³ He bubble formed on the heated copper surface was spheroid-like due to the low surface tension. The size at departure from the surface and the relative bubble formation rate were measured as a function of heat flux. The previously obtained heat transfer curve could be explained qualitatively by this boiling behavior.     

Cryostat for Optical Observations Below 1 mK and in Strong Magnetic Fields

We developed a cryostat for optical observations at ultralow temperatures and in strong magnetic fields. The optical system consisted of a LED, a light transmission path and a CCD chip, with all components installed inside the inner vacuum can of the cryostat. We have been able to cool a ³He sample to a temperature of 0.6 mK in zero magnetic field and to 2 mK in 9 Tesla, while looking at the crystallization and melting of the solid ³He. The CCD chip gives a heat leak of only 200 pW to the ³He in our Pomeranchuk cell. The performance of the nuclear demagnetization cryostat as well as the optical system are described.     

3He melting pressure temperature scale below 25 mK

Using⁶⁰Co -ray anisotropy radiation as a primary thermometer, with a Pt NMR susceptibility secondary thermometer, we have made high-precision measurements of the³He melting pressure versus temperature from 500 K to 25 mK. Temperatures obtained for the fixed points on the melting curve are: the superfluid A transition T_A = 2.505mK, the A-B transition T_AB = 1.948 mK, and the solid ordering temperature T_N = 0.934 mK. We provide a functional form for P(T), which, with the fixed points, constitutes a convenient temperature scale, based on a primary thermometer, usable to well below 1 mK.     

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.     

Observation of3He crystallization down to 1 mK using a cooled CCD camera

We describe a new setup for optical observations (particularly of helium crystals) at ultralow temperatures. It is conceptually different from the usual optical setups, which require the use of optical windows in the cryostat. Our optical system, including the light source and camera, is placed inside the vacuum can of a dilution refrigerator cryostat. We have succeeded in filming the growth of³He crystals in contact with the superfluid B phase, down to 1 mK. The optical system can easily be combined with a nuclear demagnetization stage, and a simple extension of the image transport system will allow us to study³He crystals in high magnetic fields. The entire setup is described, and some typical images are shown.     

Magnetic properties of solid 3He down to 0.3 mK

Nuclear magnetization of solid ³He has been studied by static magnetization measurements from 10 mK down to 0.3 mK for molar volumes ranging from V = 24.14 to 21.02 cm³/mole in the bcc phase and from V= 19.83 to 19.26 cm³/mole in the hcp phase. In the bcc phase, both the antiferromagnetic transition temperature T _N and the reciprocal of the maximum magnetization V _max ^–1 at T _N vary in proportion to V ^16.5±1, and the magnetization below T _N is constant. The magnetization reduced by M _max is found to be represented by a universal function of the reduced temperature T/T _N. In the hcp phase, the magnetization can approximately be represented by Curie's law, and the estimated Weiss temperatures are below 50 K. We also observed that the boundary magnetism of liquid ³He depends considerably on pressure. The transition temperature of solid ³He to the antiferromagnetic phase coexisting with liquid in a restricted geometry is 15% higher than that of the bulk solid on the melting curve.     

Viscosity of saturated3He-4He mixture below 200 mK

The shear viscosity of saturated³He-⁴He mixture has been measured at temperatures between 7 mK and 200 mK using a vibrating-wire viscometer and a calibrated pressure cell. The reliability of the vibrating-wire technique was tested by measuring the viscosity of pure⁴He. The results are internally consistent. A phenomenological expression is given for the viscosity of saturated³He-⁴He mixture between 7 mK and 80 mK.     

The viscosity and some related properties of liquid3He at the melting curve between 1 and 100 mK

The viscosity of liquid ³ He has been measured along the melting curve from 1 to 100 mK by means of a vibrating wire viscometer. In the normal Fermiliquid region we find 1/T² = 1.17–3.10T, where is in P and T in K. At the transition temperature T _A = 2.6 mK a rapid decrease occurs in _n , the viscosity of the normal component. Within 0.3 mK below T _A , _n decreases to about 25% of _A, but then becomes essentially constant. In the B phase _n first decreases to 20% of _A and then seems to increase below 1.4 mK. Data on _n , the density of the normal component, are also presented in the A and B phases. The results show that viscous flow is accompanied by a flow of zero dissipation, thus proving superfluidity in the A and B phases. The viscosity data at magnetic fields up to 0.9T have been related to theoretical calculations of the energy gap of superfluid ³ He near T _A . The splitting of the A transition and the suppression of the B phase in an external field were also measured.     

Characterization of spin polarized dilute3He-4He solutions below 500 mK

We have prepared a large sample of spin polarized liquid ³ He- ⁴ He at 500 mK. Polarization is obtained by laser optical pumping, and studied by pulsed NMR. We have observed a nuclear magnetization lifetime T ₁ longer than 1 hour, and an anomalously long, non linear decay of tranverse magnetization.Unité de recherche de l'Ecole Normale Supérieure et de l'Université Pierre et Marie Curie, associé au CNRS (URA 18).     

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.