Quartz Oscillator Study of Monolayer 4He and 3He - 4He Mixture Films Adsorbed on Solid H2

The superfluid transition in submonolayer and monolayer ⁴ He films and ³ He - ⁴ He mixture films on solid H ₂ has been studied using a quartz crystal microbalance technique. Kosterlitz-Thouless (KT) transitions were observed in submonolayer ⁴ He films with density greater than 0.062 ± 0.002 Å ^–2 . We determine a binding energy of ⁴ He to 0.241 Å ^–2 H ₂ of –15.7 K in the. presence of 1 monolayer of ⁴ He. At several ⁴ He coverages, a range of submonolayer ³ He coverages was studied (n ₃ 0.0567 Å ^–2 ). With each increase in the ³ He coverage, the KT transition temperature decreased. For the higher coverage mixture films studied (n ₄ 0.0726 Å ^–2 ) we observed an apparent second decoupling of the film from the quartz oscillator frequency in addition to the KT transition. We have studied the. coverage dependence of this new feature.     

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).     

Spin diffusion in 3He-4He solutions under pressure

We have measured the spin diffusion coefficient D for ³He-⁴He solutions of nominal ³He concentration x = 1.3% and 5.0% at pressures of ~0, 10 and 20 atm, and an x=8.5% solution at 4, 10 and 20 atm. The results are interpreted in terms of the Bardeen-Baym-Pines theory for ³He-⁴He solutions, and curves for the effective ³He-³He interaction V(k) are presented. We find no evidence for a minimum in V(k) at nonzero k. Weak coupling BCS pairing transition temperatures calculated from the V(k) lie in the range 10^–6–10^–7 K.Research supported in part by Research Corporation.     

Surface tension of liquid3He and4He near the liquid-gas critical point

The surface tension of liquid³He and⁴He was measured near the gas-liquid critical points in the reduced temperature range 3×10^–4–1, where t (T _c –T)/T _c . The critical exponents were found to be ₃=1.289±0.015 for³He and ₄=1.306±0.017 for⁴He. These values are very close to those for classical liquids, and are consistent with the value of 1.28 predicted by Widom, but are apparently different from the exponents previously obtained for liquid helium isotopes, which are near unity. The critical coefficients show good agreement with the quantum-corrected corresponding states theory for the Lennard-Jones 6–12 potential discussed by Young. The interface thickness is deduced from Widom's theory to bed=d ₀t^–v withd ₃₀=0.14±0.03nm and v₃=0.57±0.04 for³He, andd ₄₀=0.37±0.07 nm and v₄=0.58±0.01 for⁴He.     

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.     

Ground-state properties of a3He impurity in liquid4He monolayers

We present the results of ground-state energies, radial distribution functions, liquid structure functions and effective interactions for a³He impurity in a⁴He background in two dimensions. The hypernetted-chain scheme for the system described by a Jastrow-type wavefunction is used, taking into account the triplet correlations and elementary diagrams up to fifth order. Solving the Euler-Lagrange equations for the two-body distribution functions, which contain triplet correlation and elementary diagrams, improves the results considerably. Furthermore, as a³He impurity is inserted into the⁴He background, the ground-state energy increases, but the equilibrium density decreases from 0.0350 Å^–2 to 0.0336 Å^–2. The radial distribution function is broadened, while its maximum is lowered and shifted to the right (the direction of increasing radial distance) due to its larger zero-point energy, with therefore less localization of the³He particle. The results are compared with Monte Carlo results and other studies.     

Effects of3He impurities on the4He solid-liquid interface

Using crystallization waves we have measured the interfacial stiffness, , and the temperature dependence of the growth resistance, (Km)^–1, of the⁴He solid-liquid interface in the presence of³He impurities. For the purest⁴He sample, (Km)^–1 is consistent at the lowest temperatures with the assumption that the growth velocity is limited by the scattering of ballistic phonons from the moving interface. At higher concentrations of³He, we observe that (Km)^–1 increases exponentially with temperature below 0.25 K. We observe that decreases with increasing³He concentration.     

Equilibrium phase diagram and kinetics of isotopical phase separation of 3%3He in HCP4He mixture

The isotopical phase separation in a weak solid mixture of³He in⁴He is investigated by 250 kHz pulsed NMR under a pressure of 3.7 MPa in the temperature range 100 – 240 mK. The equilibrium concentrations of³ He in HCP phase are found to be in a good agreement with classical regular solution theory for phases with different crystal structures. The time constant of decay at steplike cooldown along the separation line are shown to monotonously decrease. The linear dependence of the time on the concentration may point towards an important role of quantum diffusion.     

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.     

Ground state of two-dimensional liquid 4He

The ground-state energy and liquid structure function of two-dimensional liquid ⁴He are calculated in the density range 0.028–0.075 Å^–2, using the Lennard-Jones 6–12 potential. The optimal Jastrow function is first determined by a self-consistent paired-phonon calculation and then the contributions of three-body factors the wave function are calculated. Tables of values are given at several densities for the radial distribution function, Jastrow function, and liquid structure function.Research supported by National Science Foundation Grants DMR 74-01237 A01 and DMR 78-09226.     

Distribution of 3He–4He Mixtures in a Bi-Porous System

We have investigated the distribution of ³He–⁴He mixtures in a system comprised of two porous materials: aerogel and silver sinter. The particle number density, and thus the ³He–⁴He concentration, was measured directly in the aerogel sample. We discuss both the observed history dependence for the low temperature equilibrium ⁴He fraction in aerogel and the temperature evolution of the ⁴He fraction.     

Apparent new phase of monolayer3He and4He films adsorbed on Grafoil as determined from heat capacity measurements

Heat capacity measurements in monolayer³He and⁴He films adsorbed on Grafoil at densities higher than the one corresponding to the substrate lattice registered phase show a series of sharp, narrow peaks at 1 K for densities between 0.072 and 0.077Å ^–2. The exact nature of the transition cannot be determined from this measurement alone, but several possibilities are discussed. It has been determined that the melting line of two-dimensional solid films starts atn=0.078Å ^–2 for both isotopes. Extensive heat capacity measurements at and above this density are presented for³He, and some new measurements for⁴He are shown to complement measurements reported elsewhere. The solid³He measurements are compared to predictions of recent models for melting in two dimensions.Work supported by National Science Foundation Grant # DMR72-03003A04.     

Nuclear magnetic relaxation of3He gas. I. Pure3He

Longitudinal relaxation timesT ₁ have been measured in³He gas, using pulsed NMR, for number densities between 3 × 10²³ and 6 × 10²⁵ spins m^–3 and temperatures between 0.6 and 15 K. Relaxation takes place on or near the walls of the Pyrex sample cells and measurements ofT ₁ give information about the surface phases. A cryogenic wall coating of solid molecular hydrogen was found to delay the formation of a³He monolayer on cooling, andT ₁ measurements were consistent with a binding energy of 13 K for a³He atom to a hydrogen surface. At temperatures below 2 K a completed³He monolayer forms on the H₂ coating. No variation of the areal density of monolayer completion with bulk number density at fixed temperature could be observed and the completed³He monolayer is thought to be a dense fluid. Baking the Pyrex sample cells under vacuum and using an rf discharge in³He gas to clean the walls before sealing in the sample gas were found to increase the observed T₁'s by up to three orders of magnitude. Once a³He monolayer has formed on the H₂ surface in these cleaned, sealed cells, the dipolar interaction between adsorbed spins is thought to be the dominant source of longitudinal relaxation. The data are consistent with a dipolar relaxation model with a correlation time of 2 × 10^–9 sec. This time is long compared to the value of 10^–11 or 10^–12 sec in the 3D fluid. This suggests that if the surface phase is a 2D fluid and the dipolar mechanism is indeed the dominant one, then the atoms in the 2D fluid are less mobile than in three dimensions. This is consistent with recent susceptibility measurements.     

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     

High-Resolution Measurements of the Coexistence Curve Very Near the 3He Liquid–Gas Critical Point

The shape of the liquid–gas coexistence curve of ³He very near the critical point temperature T _c was measured in the range –5× 10^–3c–1<–1.5 × 10^–6 using the quasistatic thermogram method. This study was performed in the Earth6s gravitational field using two cells of very different heights (0.5 and 48 mm). The measured coexistence curve near the critical point was strongly affected by the gravitational field. Away from the critical point, we compare the coexistence curve obtained using the thermogram method with earlier work by Pittman et al. The recently developed crossover parametric model of the equation-of-state is used to take gravity effects into account. The shape of the measured coexistence curve very near the critical point is remarkably symmetric about the critical density. Our results close to the critical point are consistent with the slope of the rectilinear diameter obtained by Pitman et al. from measurement farther away from T _c. The deviation from a law of rectilinear diameter predicted by revised scaling and the Yang–Yang anomaly were not observed in ³He within the 0.1% accuracy in our measurements.     

Concentration dependence ofD,T 1, andT 2 for dilute solutions of3He in solid4He

Measurements of the spin diffusion coefficientD and NMR relaxation timesT ₁ andT ₂ are reported for dilute solutions of³He in solid⁴He at two molar volumes, 20.95 and 20.7 cm³. The weakly interacting impuriton model, for whichD ^–1 is proportional to impurity concentration, is observed only at fractional impurity concentrationx ₃ below 3 × 10^–4. Forx ₃ around 10^–3,T ₁ andT ₂ are controlled by the formation and breakup of³He₂ molecules.     

The Fermi Liquid theory of4He in3He

The Zharkov-Silin Fermi Liquid theory of solutions of⁴He in normal (non-superfluid) liquid³He is reviewed and slightly extended. The theory is expected to be valid only below 0.1 K, and it predicts that there should be a hundred-fold increase in the diffusion coefficient as the temperature is lowered into this region. The limited range of validity explains the apparent disagreement between the recent very low temperature measurements of the phase separation line by Nakamura et al. and extrapolations from higher temperatures. In the low temperature experiments the⁴He concentration X₄ is so small that there is no macroscopic phase separation, only a gradual thickening of the⁴He-rich film on the walls. We confirm that the phase separation temperature T_ps(X₄) estimated from the thickening is close to the values which would be observed in an ideal experiment with a macroscopic phase. Fits to T_ps(X₄) including the new data show that the⁴He effective mass m ₄ ^* is close to, and may be equal to, the bare mass m₄. The difference in binding at zero pressure between⁴He in liquid⁴He and in liquid³He is (E₄₄–EE₄₃)/k_B=(0.21+0.03/–0.01)) K. Using the volume measurements of Laheurte to calculate the pressure dependence of E₄₃ indicates that the difference in binding has a minimum of (0.0±0.2) K near 11 atm. This implies that the solubility of⁴He in³He is enhanced in this region of pressure. The behavior of the spinodal line at low temperature, and the possibility of observing Bose condensation in a metastable solution of⁴He in liquid³He are also discussed.     

Viscosity and Mean Free Path of Very Diluted Solutions of 3He in 4He

We have measured the laminar friction of various diluted ³ He- ⁴ He mixtures, of natural ⁴ He and of isotopically pure ⁴ He on an oscillating sphere below 1 K. For ³ He concentrations x ₃ ranging from 10 ^–2 to 10 ^–4 we find a reduction of the drag above 0.5 K when compared to the pure liquid and a large enhancement below, which is almost independent of x ₃ . At low concentrations 5·10 ^–5 >x ₃ 5·10 ^–7 the drag becomes proportional to x ₃ which implies a transition from a hydrodynamic to a ballistic regime. This is confirmed by deducing the mean free path of the ³ He atoms from the data. The temperature dependence of the drag in the ballistic regime, however, is found to be proportional to T and therefore different from the expected T ^1/2 behaviour.     

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.     

Observation of Anomalously Low Momentum Transfer in the Low Energy Scattering of Large 4He Droplets From 4He and 3He Atoms

The momentum transferred to large superfluid ⁴ He droplets in low energy ( 4–10 K) scattering from ⁴ He and ³ He atoms was determined from time of flight measurements after the droplets have passed through a low temperature (T = 1.7–4.2 K) scattering box filled with the gas of either He isotope. The results are compared with ³ He droplets scattered from either ⁴ He or ³ He gas for which all of the incident momentum is transferred, as expected for classical capture of the scattering gas atoms. In the case of the ⁴ He droplets a smaller momentum transfer is found amounting to 65% for ⁴ He atoms and 45% for ³ He atoms but only at the lowest collision energies. These results are consistent with transmission of some of the atoms through the droplets.