The solubility of4He in3He below 0.1 K

The Zharkov-Silin Fermi Liquid theory of solutions of⁴He in non-superfluid liquid³He has been applied to the recent phase separation data of Nakamura et al. At zero pressure, the difference in binding between a⁴He atom in liquid⁴He and in liquid³He is smaller than previous estimates, and the⁴He effective mass is close to the bare mass. The volume measurements of Laheurte show that the difference in binding has a minimum near 11 atm. This implies an enhanced solubility of⁴He in³He below 0.1 K at this pressure, although there is experimental evidence that the solubility at 0 K remains zero.     

First viscosity of dilute3He-4He mixtures below 0.6 K

Starting with the Boltzmann transport equation, the first viscosity of dilute³He-⁴He mixtures for various³He concentrations x is evaluated up to around T 0.6 K by including the contribution from three-phonon processes (3PP) in the anomalous elementary excitation spectrum of liquid⁴He. Due to 3PP, the characteristic time for³He viscosity at high temperatures, i.e., T2T_F where T_F is the³He Fermi temperature, is evaluated as 5 × 10^–12/xT, which is smaller than the value estimated by Rosenbaum et al. This is interpolated with in the degenerate (quantum) region, TT_F. The obtained viscosities are in better agreement with experimental results than those of Baym and Saam, whose theory does not include 3PP. However, at very low concentrations there exists a discrepancy between the present theory and experiments, so that an alternate treatment should be considered.     

Adsorption of 4He N and 4He N 3He Clusters on Cesium

The ground-state properties of helium clusters ⁴He _N and ⁴He _N ³He, for N≤ 40, adsorbed on the surface of cesium are studied using variational and diffusion Monte Carlo calculations. Binding properties are determined using two different Cs–He interaction potentials. For the smallest clusters, self-binding on a Cs surface is stronger than in two or three dimensions. For N > 10 self-binding in three dimensions is stronger than on Cs for both types of Cs–He interaction potential considered. The obtained binding energies and structure are compared to results of recent density functional calculations. The emergence of edge states of ³He atom, localized along the contact line of ⁴He cluster with a cesium surface, is studied. First indication that ³He atom prefers to be close to the contact line appears already for the ⁴He₃ ³He cluster.     

4He in Liquid 3He below 0.1 K: Measurements of the Solubility and Prewetting Transition

We have measured the solubility of ⁴He in liquid ³He down to 0.04 K at various pressures. The solubility was obtained indirectly, from the thickness of the superfluid film in contact with unsaturated solutions. We determined the film thickness from the ratio of two parallel plate capacitors with different gaps, immersed in the unsaturated liquid. The technique is described in detail, with its advantages and drawbacks, including the effects of the edge capacitance and capillary condensation. For use in interpreting the data, the adsorption area and the van der Waals potential of the cell walls were found by measuring the thickness of ³He and ⁴He–³He films under their vapor pressure. By fitting the temperature dependence of the solubility to the predictions of Fermi liquid theory, we determined the ⁴He effective mass m*₄, the binding energy E ₄ and the partial volume v*₄, as a function of pressure. At 24 atm, a prewetting transition was observed in the ⁴He-rich film in contact with the liquid ³He. The transition, which is related to a similar phenomenon discovered by Tholen and Parpia at very low temperature, is explained by a simple model. An Appendix describes a new derivation of the thermodynamic functions of ³He-rich mixtures in Fermi liquid theory.     

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.     

Multilayer adsorption of3He and4He on zeolite from 4 K to 80 K

The adsorption isotherms of⁴He, N₂, and argon have been measured on synthetic zeolite (Linde Molecular Sieve 13X) at 78 K, and of³He and⁴He, also on zeolite 13X, in the temperature range 4 K to 20 K. The results are presented in tabular and graphical form. The N₂ isotherms, which showed characteristic step-like behavior, served to assess the specific surface area, which was 527 m² g^–1 based on a standard N₂ molecular area of 16.2 Ų. It also provided a value ofE ₁ equal to 2530 cal mole^–1. The argon isotherm at 78 K yielded a specific surface area for the zeolite 13X in fair agreement with that from the N₂ data. Nine isotherms were taken for⁴He between 4 K and 20 K and four for³He in the same temperature range. These isotherms permitted good evaluations of the isosteric heats of adsorption to be made and plotted as a function of coverage, yielding, for⁴He,Q _st =1580 j mole^–1 at zero coverage,Q _st =1030 j mole^–1 at monolayer coverage andE ₂=480 j mole^–1 at two-layer coverage. For³He, which showed everywhere smaller Q _st values. Q _st =1420 at zero coverage. By use of the Steele equation applied to⁴He, we found that the monolayer coverageV _m1 0.29 cm³ (STP) m^–2, and the second-layer coverage,V _m2 0.10 cm³ (STP) m^–2.Supported in part by a grant from the National Science Foundation and by contracts with ONR and the Department of Defense (Themis).     

NMR Relaxation times of 3He adsorbed on graphite below 4.2 K

Pulsed NMR measurements were performed at 10 and 20 MHz on thin ³He films on graphitic surfaces in the temperature range between 0.35 and 4.2 K. Most of the measurements reported here have been obtained with basal-plane oriented graphite (Grafoil) outgassed at 130 C, but in some experiments graphitized carbon black powder (Sterling FT), vacuum-baked at 1100 C, was used for comparison. The ³He coverages examined range from 0.1 to 80 monolayers on Grafoil and from 0.3 to 1.0 monolayers on Sterling FT. Measurements have also been made on ³He-⁴He films on Grafoil with one-monolayer quantity of ³He mixed with various amounts of ⁴He. The measured free-induction decay time T ₂ , the spin-echo decay time T ₂ , and the spin-lattice relaxation time T ₁suggest that the observed relaxation phenomena in ³He are largely governed by the ³He-substrate interaction. In the case of ³He on Grafoil, T ₂ is much longer than T ₂ , evidently as a result of large local magnetic field gradients and significant lateral mobility of ³He on this substrate. These results, in conjunction with a simple model of spin diffusion in restricted geometries, lead to values of the diffusion coefficient D _sof about 2.1 × 10^–5 cm²/sec at 4.2 K and 7.0 × 10^–6 cm²/sec at 1.2 K for one-monolayer coverages ; these values of D _sare indicative of a nonlocalized ³He system. To verify the model used, the restricted diffusion analysis was applied to room-temperature measurements on C₆F₆ in Grafoil ; the values of the diffusion coefficient obtained in this way are in good agreement with diffusion rates measured directly in bulk liquid C₆F₆ at room temperature. In the case of ³He on Sterling FT, the restricted diffusion analysis of the T ₂ data gives D _s\t`t2 × 10^–8 cm²/sec for 0.6 monolayer of ³He; this value of D _ssuggests a relatively localized system. The measured T ₂ is found to decrease monotonically with coverage and there is no evidence of any phase transition in ³He films for coverages up to one monolayer.Work supported in part by the National Science Foundation and a Navy Equipment Loan contract.     

Nuclear magnetic susceptibility of3He adsorbed on graphite below 4.2 K

The nuclear magnetic susceptibility of³He films adsorbed on graphite substrates was measured by means of pulsed NMR techniques at 10 and 20 MHz. Submonolayer, monolayer, and multilayer coverages were examined, as well as one monolayer of³He mixed with various amounts of⁴He. The temperature range of measurements extended from 0.35 to 4.2 K. For pure³He and for³He mixed with⁴He the nuclear magnetic susceptibility displays departures from Curie's law. The observed behavior in pure³He layers can be fitted to an ideal-Fermi-gas curve with an effective degeneracy temperature of 0.15 K. The nuclear magnetic susceptibility of³He–⁴He films is also found to fall below the values predicted by Curie's law as the temperature is lowered, but the results suggest that in this case the film is not uniform, possibly as a result of a phase separation in the film at low temperatures.Work supported in part by the National Science Foundation and a Navy Equipment Loan contract.     

The attenuation of second sound in dilute3He-4He solutions below 1 K

The attenuation of second sound in dilute solutions of³He in⁴He has been measured from the width of standing wave resonances. Results are presented here for³He molar concentrations of 1.3% and 5% in the temperature range 50 mK to 1 K at pressures of 0 and 10 atm. The results are compared with the theory of Saam, Baym, and Ebner and suggest that theoretical values of the phonon thermal conductivity lifetime are too great. Comparison is also made with recent measurements of the second-sound damping constant in very dilute solutions (X0.5%); our result shows no sign of the anomalous peak in the damping constant observed for such concentrations. The shear viscosity of the dilute solutions is also computed and found to be in agreement with the capillary flow measurements of Kuenhold, Crum, and Sarwinski.This work was supported in part by a grant from the Research Corporation.     

The velocity of second sound in dilute3He-4He solutions below 0.6°K

The velocity of second soundu ₂ in dilute solutions of³He in⁴He has been measured by a pulse, time-of-flight technique using a new type of mechanical transducer. Tables of measured values ofu ₂ as a function of temperature between 0.03 and 0.6° K are presented for³He concentrations in the range 0.14–6.3% at the saturated vapor pressure and under hydrostatic pressures of 10 and 20 atm. Estimates of the upper limit of the intrinsic attenuation of second sound have also been made and these are consistent with theory provided that the experimental values of the phonon thermal conductivity lifetime are used in place of the values calculated by Baym and Ebner.Work supported by a grant from the National Science Foundation.On leave of absence from University of Nottingham, U.K.     

Adsorption of nitrogen,argon, and neon on sintered copper and of neon on argon-coated sintered copper at low temperatures

The results of measurements of adsorption isotherms are given for nitrogen, argon, and neon on bare sintered copper and on sintered copper covered with a monolayer of argon. The temperatures employed where 77.3 K for the N₂ and argon, and 17.26, 20.22, 22.64, 25.71, and 27.00 K for the neon, and the pressure range was from 0.25 to 200 Torr. The sintered copper specimen was of mass 170 g, made with powder (Alcan Metal Powders, Inc., Druid Copper, grade MD60), which had an average particle size of 2 × 2 × 0.5 µ. The sintering was done at 650°C for 0.5 h. The bare surface area in m²/g, of the sintered copper specimen was found from the N₂ adsorption isotherms at 77.3 K. This gave =0.41 m²/g, based on a molecular area of N₂ of 13.8 Ų (solid N₂). The N₂ and argon isotherms on the bare sintered copper at 77.3 K yielded values of the monolayer coverage ofV _m =0.11 cm³(STP)/g for N₂ andV _m =0.11 cm³(STP)/g for argon. The neon results showed that at any given pressure and temperature the mass of neon adsorbed was less when the adsorption was on argon-coated copper than on bare copper. Calculations were made of the isosteric heat of adsorptionQ _st for neon, and the results are presented graphically as functions of the coverage. For neon adsorption on the bare copper,Q _st /R had a maximum value of about 390 K at a coverage of about 0.2 cm³(STP)/m², and it decreased to about 275 K at 0.5 cm³(STP)/m². For neon on the argon-coated copper,Q _st /R had a maximum value of about 320 K- at the lowest coverages and fell to about 245 K at 0.5 cm³(STP)/m². The shape of theQ _st /R curve vs. coverage for neon indicated that the argoncoated copper was more homogeneous from an adsorptive point of view than the bare copper. TheQ _st /R vs. coverage curves allowed an assessment to be made of the monolayer coveragesV _m , which were 0.38 cm³(STP)/m² for neon on the bare sintered copper and 0.34 cm ³ (STP)/m ² on the argon monolayer coated on the sintered copper. This indicated that the effective area for adsorption on the argon monolayer was 0.37 m ² /g, which was 10% less than that for the bare copper. In addition, theQ _st /R values at monolayer coverage were found to be 306 K on the bare copper and 275 K on the argon monolayer.Work supported by a contract with the Department of Defense (Themis Program) and with the Office of Naval Research and by a grant from the National Science Foundation.     

Competitive Adsorption of 3He and 4He to Carbon Nanotube Bundles

No Heading We have studied the competitive adsorption of the two helium isotopes to single-walled carbon nanotube bundles. It is observed that the presence of ⁴He suppresses subsequent ³He adsorption while the presence of ³He has little influence on the subsequent adsorption of ⁴He. These observations are generally consistent with expectations based on the difference in the masses of the isotopes.PACS numbers: 68.35.Md, 68.43.Fg, 81.07.De     

He cryostat for measurements in superfluid He below 1 K

A ³He cryostat has been constructed which allows the performance of measurements in a ⁴He bath at temperatures between 1.4 and 0.45 K with a temperature stability of ± 5 × 10⁻⁶ K at 0.82 K. Sample mounting is possible by a top-loading system.     

Melting curve and related thermodynamic properties of He3 below 1°K

Measurements of the melting curve of He³ have been made between 16.6° mK and 0.7°K. The liquid and solid molar volumes at melting have been extended from 0.33°K to below 0.03°K, and the molar volume change on melting V _m obtained. An increase in V _m from 1.20 cm³/mole at 0.33°K to 1.28 cm³/mole at 0.06°K is found, with an extrapolation to 1.27 cm³/mole atT=0. Examination of the thermodynamic consistency of the data indicates that our melting curve slopes are accurate, within experimental error, down to a temperature of 0.04°K. The demagnetization apparatus is described, with considerable attention devoted to thermometry, thermal equilibrium, and experimental techniques. Construction details of the high-sensitivity capacitive strain gauge are given.Research supported by the National Science Foundation.     

Separation of 3He from 3He-4He Mixture by means of Adsorption

No Heading A simple technique for purifying ³He from a ⁴He admixture is presented. The technique is based on different adsorption energies of ³He and ⁴He.PACS numbers: 81.20.Ym, 67.60.–g.     

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.     

Adsorption of3He on cesium

Adsorption isotherms of³He on cesium substrates have been measured in the temperature range from 0.2 K to 1.5 K. At liquid-vapor coexistence³He wets cesium at all temperatures studied. Step-like features are found in the isotherms which are similar to the prewetting transitions of⁴He on Cs substrates, but the width of these steps is ∼20 times wider for³He than for⁴He. In the case of³He on Cs, the steps are located at a chemical potential about 0.6 K below liquid-vapor coexistence. If the low temperature behavior is interpreted to be first order prewetting, the prewetting critical point temperature is 0.6±0.1 K.