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.     

Elementary Excitations in Solid and Liquid 4He at the Melting Pressure

Recent discovery of a nonclassical rotational inertia (NCRI) in solid ⁴He below 0.2 K by Kim and Chan has revived great interest in the problem of supersolidity and initiated intensive study on the properties of solid ⁴He. A direct proof that the onset of NCRI corresponds to the supersolid transition would be the observation of a corresponding drop of the entropy of solid ⁴He below the transition temperature. We have measured the melting pressure of ultrapure ⁴He in the temperature range from 0.01 to 0.45 K with several single crystals grown at different pressures and with the accuracy of 0.5 μbar. In addition, supplementary measurements of the pressure in liquid ⁴He at constant volume have been performed, which allowed us to eliminate the contribution of the temperature-dependent properties of the pressure gauge from the measured melting pressure data. With the correction to the temperature-dependent sensitivity of the pressure gauge, the variation of the melting pressure of ⁴He below 320 mK obeys the pure T ⁴ law due to phonons with the accuracy of 0.5 μbar, and no sign of the transition is seen (Todoshchenko et al. in JETP Lett. 85:454, 2007). This sets the upper limit of ∼5⋅10⁻⁸ R for a possible excess entropy in high-quality ⁴He crystals below 320 mK. At higher temperatures the contribution from rotons in the superfluid ⁴He has been observed. The thermal expansion coefficient of the superfluid ⁴He has been measured in the range from 0.01 to 0.7 K with the accuracy of ∼10⁻⁷ 1/K, or by two orders of magnitude better than in previous measurements. The roton contributions to the melting pressure and to the pressure in liquid at a constant volume are consistent and yield the value of 6.8 K for the roton gap, which is very close to the values obtained with other methods. As no contribution due to weakly interacting vacancies to the melting pressure of ⁴He has been observed, the lower limit of about 5.5 K for their activation energy can be set.      

Crystallization of 4He in Aerogels

Static behaviors of crystallization of ⁴He in porous materials, such as the increase of melting pressure, have been studied extensively, but nonequilibrium dynamics of the phase transition is hardly known. Our interest was in how ⁴He crystals grow in a 90.4% porosity aerogel. Aerogels are transparent and the dynamics in them can be studied visually. A Pomeranchuk-type variable-volume cell was used to study crystallization at a fixed temperature with a blocked capillary condition. By continuously compressing a chamber, the pressure rose above the bulk melting pressure and at a pressure 1.7 bar above the bulk melting pressure these crystals began to invade the aerogel. A clear crystal-superfluid interface was moved smoothly by the steady compression. No macroscopic facets were observed in the aerogel well below the bulk roughening transition temperature.      

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.     

3He constant-volume gas thermometry: Calculations for a temperature scale between 0.8 and 25 K

A discussion is presented on the possibilities of a³He gas thermometer for defining a temperature scale below 30 K, based on recent new measurements of the virial coefficient. The influence of all corrections of interest is given in comparison with⁴He gas thermometry and with⁴He and³He vapor pressure thermometry. It is shown that a³He gas thermometer can be operated down to temperatures <1 K, with an estimated inaccuracy of less than ±0.5 mK, thereby obviating the explicit need of the³He and⁴He vapor pressure scales below 5 K, and directly joining a possible scale based on the³He melting curve.     

Phase separation in solid mixtures of helium-3 and helium-4

Phase separation temperatures have been determined in bcc³He-⁴He mixtures as a function of³He concentration and melting pressure from measurements of changes in the X-ray lattice parameter and Bragg peak shape. A new rigid tail dilution refrigerator cryostat was used to study³He-⁴He crystals with³He concentrations of 0.10, 0.20, 0.30, 0.45, 0.60, and 0.70 and melting pressures between 3.0 and 4.3 MPa. The phase separation temperatures determined are in good agreement with regular solution theory and give little support for an asymmetry in the coexistence curve expected from a Nosanow-type model and reported from previous experiments using other signatures of phase separation. At a given concentration, differences in phase separation temperatures determined from slow cooling and warming data, respectively, are as much as 25 mdeg, but this is less than half the differences reported from previous experiments. A bcc-hcp transformation was seen in a crystal with 10%³He at aboutT=0.3 K for a melting pressure of3.7 MPa.     

NMR study of 3He bubbles in phase-separated solid 3He –4He mixtures

³ He droplets embedded in a solid ⁴ He matrix have been studied by NMR and pressure measurements. One feature of the experiment is that the mixture crystals, of ³ He concentration 1%, are grown under constant pressure conditions to minimise the formation of defects. A number of sample pressures below 34 bar have been studied. Isotopic phase separation and the melting of the bubbles are clearly observed. Measurements of T₁ , T₂ and magnetisation give detailed information on the structure of the droplets. At an initial sample pressure of 28.3 bar preliminary measurements of the T₁ of the liquid bubbles show a temperature dependence of the form (A+ B/T²)^–1. This indicates that the expected relaxation in the liquid is augmented by a constant contribution, probably from the surface of the droplets.     

Measurements of the Superfluid Joule–Thomson Refrigerator Using High Concentration 3He–4He Mixtures

The superfluid Joule–Thomson refrigerator (SJTR) uses a liquid superfluid ³He–⁴He mixture to provide cooling below 1 K. Performance measurements of the SJTR using 5% and 11% ³He concentration mixtures are reported. High concentration operation shows higher cooling powers at high temperature. Ultimate temperatures are seen to increase with increasing concentration due to a pinching of the temperature defect in the recuperative heat exchanger. This pinching effect is due to the variation of the heat capacity of the ³He–⁴He mixture with temperature and concentration and is discussed in detail and design changes are suggested to mitigate it.     

Visualization of Bubble Nucleation in Boiling 3He

The heat transfer properties of ³He bubbles in the nucleate boiling state have been investigated in liquid ³He below 1.0 K by using the shadowgraph method. The temperature difference between the copper surface and liquid ³He temperature was also measured as a function of heat flux in steady state. The size and number of bubbles departing from the surface in a specific time were compared using photograph recorded by a high-speed video camera at various heat flux and liquid ³He temperature of 0.5, 0.7 and 1.0 K.     

The Wall Potential in the Pores of Vycor Glass Experienced by 3He Quasiparticles in a Dilute 3He-4He Solution

We have studied the Fermi fluid, ³He in ³He-⁴He solution, confined within the narrow channels of Vycor glass. Continuous wave NMR signals were observed in two almost identical coils, one containing bulk solution and the other the solution in Vycor glass. Three different solutions (0.1, 1.6, and 6%) have been studied over the temperature range 3mK to above 1K. The measurements relate to two exclusion effects of ³He from Vycor glass. One concerns potential energy, and we demonstrate the partial exclusion of ³He independent of concentration as the temperature is lowered from high temperatures down to around 200mK, thus giving an experimental measure of the van der Waals forces between the wall and the helium. The second effect is the additional quantum exclusion which arises from the influence of quantum wire confinement on the kinetic energy, as the temperature is progressively lowered below 50mK in the very dilute (0.1%) solution.     

Melting Pressure Thermometry of the Saturated Helium Mixture at Millikelvin Temperatures

The melting pressure of a ³ He–⁴He mixture has a very simple quadratic temperature dependence below some tens of mK, determined by the entropy of the ³ He component in the liquid mixture. For undersaturated mixtures, the melting pressure also depends on the ³ He concentration x, which may vary in the course of the experiment as ⁴ He transfers between the liquid and the solid phases. On the other hand, if the mixture is saturated, the system is in a univariant state with a melting pressure that depends uniquely on temperature and, thus, offers a thermometric standard. However, the univariant state includes a pure liquid ³ He phase, which complicates the temperature dependence around its superfluid transition temperature T_c. In this paper, we analyze the melting pressure of the saturated mixture in simple terms and find an expression that is in good agreement with our experimental data, and is applicable across T_c down to very low temperatures. The obtained derivatives of the melting pressure with respect to the square of temperature are 0.92 Pa·mK⁻² above T_c and 1.52 Pa·mK⁻² in the zero-temperature limit. An erratum to this article can be found at     

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.     

Hysteretic Response of Torsionally Oscillated Solid 4He and Its Dependence on 3He Impurity Concentration

Measurements on hysteretic response of compound torsional oscillator containing annular-shaped solid ⁴He samples were carried out by varying the oscillator drive amplitude starting from high to low and then back up to the initial high value. Hysteresis in the oscillator frequency and amplitudes were observed only below an onset temperature. The hysteresis onset temperature (T _H ) did not depend on the oscillator frequency, width of the sample annulus, annealing and refreezing after melting. A systematic increase in T _H was observed as the ³He impurity concentration in solid ⁴He samples was increased. The dependence of T _H on ³He impurity concentration followed approximately that of the dissipation peak temperatures. Possible relationships of the observed hysteresis phenomena with models of solid ⁴He dynamics based on freezing of a vortex liquid and dislocation motion are discussed.     

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.     

Thermodynamic properties of4He. II. The bcc phase and theP-T and V-T phase diagrams below 2 K

The constant-volume heat capacity of ⁴He has been measured at molar volumes from 20.45 to 29.71 cm³/mole in the temperature range from 0.3 to 4 K. The entropy has been obtained as a function of volume and temperature by extrapolation of the data to 0 K. The P-T equilibrium curves below 2 K were obtained from the volume dependence of the entropy in the two-phase regions. The V-T curves were obtained above 1.25 K by observation of heat capacity discontinuities at the phase boundaries and below 1.25 K from the equilibrium pressure-temperature data and the properties of the pure phases. The minimum in the melting pressure occurs at 0.774 K and is 8.04 × 10^–3 atm below the 0 K value. The corresponding maxima in the molar volumes of the solid and liquid were also determined. In the bcc phase (S/V) _T and (C _v /V) _T are everywhere positive. Both the temperature and volume dependence of the heat capacity are similar to those of bcc ³He, in the very limited ranges of volume and temperature in which the phase could be studied. An unexpected rise in heat capacity in the 20 mK interval below the melting temperature was observed.Work supported by the U.S. Energy Research and Development Administration.     

Morphology and Growth Kinetics of 3He Crystals Below 1 mK

The shapes as well as the growth and melting properties of bcc-³He single crystals have been investigated with a low temperature Fabry-Pérot interferometer. Eleven types of facets were clearly identified during slow crystal growth at the temperature of 0.55 mK, where the solid is in the antiferromagnetically ordered u2d2 phase. The growth rates of the individual facets have been measured and the results indicate significant growth anisotropy. The observed linear dependence of the growth velocity on the driving force shows that facets grow due to the presence of screw dislocations, while the step velocity is limited by the spin wave velocity due to the strong interaction of the moving step with magnons in the solid. The measured growth rates of the facets and the assumed growth mechanism gave us the unique opportunity to obtain the step free energies for ten different types of facets observed during a single growth sequence. The dependence of the free energy of the step on the step height is compared with predictions of the weak- and strong-coupling models. Our results suggest that ³He crystals have rather strong coupling of the liquid/solid interface to the crystal lattice and that the step-step interactions are of elastic origin.     

Nucleation of 4He Crystal at Melting Pressure by Acoustic Waves

No Heading When an acoustic wave pulse of several msec was applied to superfluid ⁴He at melting pressure, ⁴He crystal was nucleated on the transducer and rapidly disappeared after the pulse. We measured thresholds of the acoustic wave power which induced a nucleation in the temperature range between 0.09 K and 1 K. The treshold of the nucleation exhibited no temperature dependence below 0.3 K. The nucleation was not induced above 0.6 K even if the injected acoustic pulse was strong. 0.6 K is close to the inversion temperature at which the direction of the force by acoustic wave was inverted on the solid-liquid interface of ⁴He [Phys. Rev. Lett. 90, 075301 (2003)]. Our observation indicates that the effect of acoustic radiation pressure contributes to the heterogeneous nucleation by acoustic waves.PACS numbers: 67.80.–s, 68.08.–p, 81.10.–h, 43.25.Qp.     

Direct measurements of thermal vacancies in BCC4He

X-ray lattice parameters of bcc⁴He crystals in contact with superfluid⁴He were measured with 300 ppm accuracy in the temperature range 1.494–1.711 K, corresponding to solid molar volumes between 20.88 and 21.09 cm³. Thermal vacancy concentrations in the solid at melting were estimated from a comparison of these lattice parameters with bulk solid molar volumes from the literature. Independently, temperature-dependent x-ray lattice parameter measurements on a bcc sample, held at constant macroscopic volume from 1.700 to 1.735 K, were referenced to the same solid sample (at 20.90 cm³) in the hcp phase near 0.8 K, where thermal vacancy content is small. The value of the free energy of formation for vacancies in bcc⁴He obtained from these measurements isf=9±1 K. The relationship between this value and indirect inferences about vacancy formation from ion mobility and NMR experiments is discussed. Comparisons are made between vacancy properties in bcc⁴He and in the more extensively studied bcc phase of³He. There are many parallels between the two systems. But a puzzling apparent difference between the vacancy relaxation energies in the two solids is pointed out.     

Onset of Convection in Superfluid 3He-4He Mixture Heated from Below

The thermal instability of ³He-⁴He mixtures caused by heating the liquid from below has been studied experimentally. The temperature gradients were measured which appeared in the mixture with initial concentration 9.8% of ³He below 0.5 K in the presence of different heat flows from the heater at the cell bottom. At a certain critical heat flow the effective thermal conductivity of the liquid was observed to increase sharply which was naturally attributed to the convective heat transfer. It is shown that the thermal convection develops at high temperature gradients. In this case the Rayleigh numbers exceed many orders of magnitude those for heating from above. Thus the convective instability develops in a system in which the light liquid is at the top and where no prerequisite for instability is seemingly available. The resugts obtained are analyzed in terms of the theory of convective instability in binary mixtures. It is suggested that the phase separation, of superfluid mixtures caused by a heat flow could be a destabilizing factor initiating convection. The vortex formation in superfluid helium and the related turbulent flows appearing at high temperature gradients can be another factor favourable for instability of the liquid.     

The preferential adsorption of 4He from 3He-4He mixtures onto Vycor glass

The preferential adsorption of ⁴He from liquid ³He-⁴He mixtures onto Vycor glass has been measured over a wide concentration range between 1 and 3 K. Over most of this temperature range the preferential adsorption extends beyond the second atomic layer, with a preferential binding energy of about 3.5 K/mole. Near 1 K and below, the thickness of the ⁴He layer increases rapidly as a precursor to the bulk liquid phase separation.