Adsorption of3He and4He on copper and on argon-coated copper below 20 K

Measurements have been made of adsorption isotherms of ³ He and of ⁴ He on copper and on a monolayer of argon deposited on copper in the temperature range 6.18–18.55 K and in the pressure range 0.25 to 75 Torr. From these many isotherms, calculations have been made of the isosteric heat of adsorptionQ _st/R. In the limit of zero coverage on the argon monolayerQ _st/R=76±2 K for ³ He and 76±2 K for ⁴ He. For adsorption on the bare copper,Q _st/R is difficult to extrapolate to zero coverage, but it probably lies (for both ³ He and ⁴ He) between 135 and 165 K. At theoretical monolayer helium coverage,Q _st/R=44±2 K for ³ He on the argon monolayer and 47±2 K for ⁴ He. At theoretical monolayer helium coverage on the bare copper,Q _st/R=61±4 K for ³ He and 77±5 K for ⁴ He. The results are compared with theoretical evaluations for helium adsorbed on an argon monolayer and with some previous experimental data, and the agreement is found to be fair. All the data are summarized in tables. Finally, a review is given of evaluations, including those from this work, of the monolayer capacity of ³ He and ⁴ He on the substrates studied.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.     

Adsorption of4He,Ar, and N2 on exfoliated graphite and of4He on Ar-coated exfoliated graphite at low temperatures

The results of measurements of adsorption isotherms are given for ⁴ He, Ar, and N ₂ on bare exfoliated graphite (Grafoil) and for ⁴ He on Grafoil covered with a monolayer of argon. The temperatures employed were 77.3 K for the argon and N ₂ , and the range 4.2–18.55 K for the⁴He. The pressure range was from 0.25 to 150 Torr. The Grafoil surface area was calculated from the argon isotherm at 77.3 K, yielding a value of 19.9 m ² /g or a total surface area of 672 m ² for the 33.81 g of adsorbent used in these experiments. From the ⁴ He isotherms the isosteric heats of adsorptionQ _st /R were calculated. In the limit of zero coverage,Q _st /R on the argon monolayer was 82 K, and on the bare GrafoilQ _st /R lies between 130 and 170 K. At theoretical monolayer coverage on the argon-coated GrafoilQ _st /T=68 K. These results are compared with theoretical evaluations and with previous calorimetric data on other graphites.Work supported in part by a grant from the National Science Foundation and by contracts with DOD (Themis Program) and ONR.     

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.     

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.     

Transport properties of helium near the liquid-vapor critical point. IV. The shear viscosity of3He and4He

Shear viscosity measurements with a precision of 0.05% are reported for³He and⁴He along near-critical isochores 0.85 c <1.12, where _c is the critical density. The temperature range was –10^–4<<1, where =(T – T _c)/T _c is the reduced temperature. The experiments were carried out with a torsional oscillator operating at 158 Hz, driven at resonance in a phase-locked loop. The absolute value of the viscosity was obtained by calibration at the superfluid transition of⁴He, based on published values and from direct calculations using the free decay time constant of the oscillations. The data are analyzed in terms of a model using the recent mode-coupling (MC) expressions by Olchowy and Sengers, and where account is taken of the earth's gravity effects. The theory could be fitted very well to the experiment with a single free parameter, the cutoff wave numberq _D, which was found to be 3.0×10⁶ and 7.0×10⁶ cm^–1 for³He and⁴He, respectively. We have used for the critical exponent the MC predicted value of z=0.054, which permits a fit superior to that using z=0.064 predicted by dynamic renormalization group (DRG) theories. Detailed comparisons are made between the model calculations and data for various isochores and isotherms and good agreement is obtained. The effects of gravity are described in some detail. The predicted frequency effect in viscosity measurements is calculated for³He and is shown to be obscured by gravity effects. Using the Olchowy-Sengers formulas, we have also fitted the MC theory to the critical thermal conductivity data of³He, again withq _D as the only free parameter. This fit gaveq _D=6 × 10⁷ cm^–1, which in the ideal situation should have been the same asq _D from viscosity. We also discuss a representation of the³He viscosity data along the critical isochore by a power law and first correction-to-scaling erm. Using the viscosity and the critical conductivity data for³He, we have calculated the dynamic amplitude ratio and obtained =1.05±0.10, in agreement with predictions from MC and DRG theories. Also, agrees with data of classical fluids. Finally, a comparison is made of recent shear viscosity data for CO₂ by Bruschi and Torzo with those on He. The CO₂ data are also analyzed in terms of the MC theory, and the discrepancies are discussed. In the Appendices, we present the results of new compressibility measurements on³He along the critical isochore, as used in the MC analysis. We also present a brief analysis of the fluid hydrodynamics in the torsional oscillator leading to relations for the viscosity as a function of the measured quantities. Finally, we give a short outline of the vertical density profile calculations from the earth's gravity field for the calculations of the viscosity nearT _c.     

Nuclear magnetic relaxation of3He gas. II.3He-4He mixtures

Longitudinal relaxation timesT ₁ have been measured in³He-⁴He gas mixtures, using pulsed NMR, in the temperature range 0.6–15 K. Helium-3 number densities of the order of 10²⁴ atoms m^–3 were used. 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 precoating of solid molecular hydrogen was used to reduce the helium-substrate binding energy from 100 K on Pyrex to 13 K for³He and 15 K for⁴He. TheT ₁ data at high temperatures were similar to those observed previously in the pure³He-H₂ system. The presence of⁴He generally causedT ₁ to rise on cooling below 2 K due to the preferential adsorption of⁴He over³He at the surface. However,³He atoms that go into quasiparticle states in the superfluid helium film can be an extra source of relaxation. In uncleaned cells, relaxation probably takes place in quasiparticle states at the free surface of the superfluid film, which are bound with an energy of 5.1±0.3 K. Baking the Pyrex cells under vacuum and rf discharge cleaning the walls before sealing in the sample gas were found to increase the bulk gasT ₁ by two or three orders of magnitude. In a cleaned, sealed cell aT ₁ of 8 h was measured at 7.7 MHz and 0.8 K. In this case relaxation is probably occurring two or three helium layers away from the helium-hydrogen interface. It may be possible to observe a predicted minimum in the intrinsic dipolarT ₁ of the bulk gas by using a⁴He wall coating to suppress wall relaxation effects (which usually dominate the nuclear relaxation of the bulk gas).     

Adsorption of 4He on neon-coated exfoliated graphite

Adsorption isotherms of ⁴He on Grafoil coated with a monolayer of neon were made for the temperature range of 2–10 K and in the pressure range of 0.10–15.00 Torr, using a standard volumetric method. From these isotherms the isosteric heats of adsorption were calculated as a function of coverage. The binding energy of ⁴He on Ne was obtained from the isosteric heat for V 0, yielding a value of 39.4 K. The differential molar entropy and the internal molar energy were calculated as a function of coverage. A comparison of monolayer coverage obtained by analyzing different procedures is presented. Whenever possible the results are compared with theoretical evaluations and previous experimental data.Work supported by FINEP, CNPq, and CEPG. Part of the Cooperative Program UFRJ/Stevens Institute of Technology, sponsored by CNPq/NSF International Program.     

3He Spin Diffusion Measurements for 3He - 4He Mixture Films on Nuclepore

Preliminary ³ He spin diffusion results for ³ He - ⁴ He mixture films on Nuclepore are presented as a function of ³ He coverage for 0.1 T 0.3 K. We report measurements for a constant ⁴ He coverage of 4.41 bulk density atomic layers with ³ He coverages between 0.3 and 2.1 layers. The diffusion is observed to decrease with increasing amounts of ³ He, and some structure as a function of temperature is present.     

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.     

Excitations Beyond the Roton of Liquid 4He in Aerogel

The dynamic structure factor, S(Q, ), for wavevectors, 2.0Q3.6 Å ^–1 of liquid ⁴ He in 95% porous aerogel has been measured by inelastic neutron scattering methods. The aerogel was grown with deuterated materials and the multiple scattering involving the aerogel was negligible. S(Q, ) in the superfluid phase consists of a single peak plus broad intensity at higher energy , as in bulk superfluid ⁴ He. The single peak is identified with the phonon-roton excitation at higher Q. The weight in the peak, Z_Q , and the excitation energy dispersion curve, _Q , has the same basic wavevector dependence as in the bulk. The energy _Q is 2–3% below the bulk value at the end point and the peak is unobservable beyond Q=3 Å ^–1 within the present statistical precision. No peak is observed at T=2.3 K in normal ⁴ He suggesting, as in bulk ⁴ He, that the characteristic excitation at higher Q is associated with the superfluid phase.     

Experimental studies of the excitation spectrum of3He-4He mixtures using neutron inelastic scattering

Neutron inelastic scattering techniques have been used to study the excitation spectrum of mixtures containing 6%, 12%, and 25% of³He in⁴He at 0.75 K. The 6% mixture has also been investigated at temperatures of 0.6, 1.0, and 1.5 K. The measurements have been made in the wave-vector transfer rangeQ=0.8–2.3 Å^–1. The energy spectra observed contain two principal features, which are interpreted as scattering from (a) phonon-roton excitations arising from the⁴He, and (b) quasiparticle-quasihole excitations arising from the³He. In the dilute³He-⁴He mixture, our results indicate a³He particle-hole continuum which deviates from the quadratic form, proposed by Landau and Pomeranchuk, and which lies below the⁴He phonon-roton dispersion curve. However, we are unable to say whether or not the continuum exhibits a minimum as a function of energy, as has recently been proposed by several authors, because we were unable to resolve the scattering from the particle-hole continuum forQ1.7 Å^–1. In this region ofQ space the energy spectra are dominated by the roton excitations. We have also determined the shifts in energy and increases in linewidth of the phonon-roton excitations relative to those of pure⁴He and compared these measurements to several theoretical predictions.Work performed under a grant from the Science Research Council of Great Britain.     

3He on MgO: Nuclear magnetic relaxation properties

Using MgO powder as a substrate, the magnetic relaxation of ³He and adsorption isotherms of ³He and Kr have been measured. Relaxation data as a function of coverage were obtained at temperatures of 2.0,2.7, 3.5, and 4.2 K, and as a function of temperature at coverages of x = 0.84 and 1.0 monolayer. The Kr isotherms show steplike features whose size increases following an extended bakeout at 950 C under vacuum. This is interpreted as indicating that the MgO surface consists of a mixture of uniform and nonuniform regions. Extended heating increases the fraction of the total surface area that is uniform. The values of T ₂vs. coverage at T = 2 and 2.7 K are found to change from being roughly coverage independent to decreasing as x ^–3 at a coverage of x – 0.9, indicating a decrease in film mobility. At 3.5 and 4.2 K an approximately constant T ₂is found at all coverages with no evidence of a sudden change of mobility. The low-temperature T ₂data continue to decrease as the second layer forms, implying a low mobility for small second-layer coverages. On the basis of the relatively short values obtained for T ₁ it is concluded that a relaxation mechanism in addition to dipolar coupling is present.Supported by NSF and Research Corporation.     

Thermal Resistance of 4He Below but Very Near the Superfluid Transition

We report high-resolution measurements at saturated vapor pressure of the thermal resistivity R of superfluid ⁴He over the reduced-temperature range 3×10^–7<t1–T/T <3×10^–5 (T is the transition temperature for Q=0) and heat-current-density range 4<Q<200 W/cm². For smaller Q and t, no thermal resistance was detectable below a transition at T _c(Q)<T . For Q10 W/cm² we find that the results can be described well by R=(t/t ₀)^–2.8 K cm/W with t ₀=(Q/Q ₀)^0.904 and Q ₀=393 W/cm². Thus R has an incipient divergence at T which is, however, supplanted by T _c(Q) where R remains finite. The results imply RQ ^(m–1) with m=3.53±0.02. This differs from the original assumption m=3 of Gorter and Mellink, and from experimental results obtained well below T . However, it agrees with measurements by Leiderer and Pobell at larger currents and further below but still close to T . Our measurements could not resolve a critical heat current for the onset of resistance.     

Heat capacity study of4He desorbing from H2-plated graphite

We report measurements of the surface binding energy of⁴He adsorbed on 1.45, 2.15, or 3.15 layers of hydrogen plating graphite. The heat capacity of partial monolayer coverages of helium was measured using adiabatic heat pulse calorimetry from 0.2 to 9 K. Desorption of low surface density⁴He films was indicated above 2 K by a broad peak in the heat capacity. A model was developed to calculate the specific heat of an ideal gas in two dimensions as it desorbs into an ideal gas in three dimensions. This model was used to obtain the binding energies from our experimental data. The binding energies per atom are –39, –25.8, and –22 ± 0.5 K, respectively, for the three hydrogen platings. The 2-d compressibility of the partial solid second layer of H₂ in the 1.45 layer H₂ coverage was calculated from an increase in its melting temperature with increase of⁴He 2-d pressure.     

Dynamic form factor of liquid4He at intermediate momentum transfer

Measurements of the inelastic neutron scattering from liquid⁴He atT=1.2 K in the range of wavevector transfer 3Q12 Å^–1 have been performed to verify the oscillations in the peak position and the width of the scattering function withQ observed by Cowley and Woods and by Martelet al. We confirm these oscillations and extend the measurements to show that the oscillations in the width continue up toQ12 Å^–1 while oscillations in the peak position, which have a much smaller amplitude, could be observed with confidence up toQ8 Å^–1 only. We also present a straightforward RPA calculation of the dynamic form factorS(Q, ), beginning from the pair interatomic potential, to see how well the observedS(Q, ) can be described and to investigate the origin of the oscillations. The observedS(Q, ) is quite well reproduced and the oscillations in the width and peak position ofS(Q, ) are seen to originate from oscillations in the interaction in the RPA which we have approximated as the⁴He-⁴He scattering amplitude calculated fromv(r). While the present calculation is quite different from the model proposed previously by Martelet al., the physical origin of the oscillations inS(Q, ) is the same, namely oscillations in the⁴He-⁴He atom scattering amplitude.     

Thermal transport properties of helium near the superfluid transition. II. Dilute3He-4He mixtures in the superfluid phase

Measurements of the average thermal conductivity _exp hQ/T and of the thermal relaxation time to reach steady-state equilibrium conditions are reported in the superfluid phase for dilute mixtures of³He in⁴He. Hereh is the cell height,Q is the heat flux, andT is the temperature difference across the fluid layer. The measurements were made over the impurity range 2×10^–9<X(³He)<3×10^–2 and with heat fluxes 0.3<Q<160 µW/cm². Assuming the boundary resistanceR _b , measured forX<10^–5, to be independent ofX over the whole range ofX, a calculation is given for _exp. ForQ smaller than a well-defined critical heat fluxQ _c (X) X ^0.9, _exp is independent of Q and can be identified with the local conductivity _eff, which is found to be independent of the reduced temperature = (T–T)/T for –10^–2. Its extrapolated value at T is found to depart forX10^–3 from the prediction X ^–1 , tending instead to a weaker divergence X ^–a witha0.08. A finite conductivity asX tends to zero is not excluded by the data, however. ForQ >Q _c (X), a nonlinear regime is entered. ForX10^–6, the measurements with the available temperature resolution are limited to the nonlinear conditions, but can be extrapolated into the linear regime forX2×10^–7. The results for _exp(Q),Q _c (X), and _eff(XX) are found to be internally consistent, as shown by comparison with a theory by Behringer based on Khalatnikov's transport equations. Furthermore, the observed relaxation times (X) in the linear regime are found to be consistent forX>10^–5 with the hydrodynamic calculations using the measured _eff(X). ForX<10^–5, a faster relaxation mechanism than predicted seems to dominate. The transport properties in the nonlinear regimes are presented and unexplained observations are discussed.     

Persistent currents and critical velocities in3He-4He mixtures

Using the method of Doppler-shifted fourth sound, we have investigated the angular velocity _c1 for the onset of vorticity, the saturated critical velocity, and the dependence of _s/ onv _n –v _s for⁴He in three different pore sizes and for three different mixtures of ³ He- ⁴ Hein one of the powders used. These are the first measurements of critical velocities in ³ He- ⁴ He mixtures. We observe only a weak dependence of _c1on the pore size and within the limits of the experiment no dependence on concentrationX up toX=0.11. We find, however, that the maximumv _n –v _s attainable increases as the concentration of ³ He increases forX0.17. The observed dependence of the superfluid density onv _n –v _s is approximately two orders of magnitude stronger than predicted.     

Helium adsorption on exfoliated graphite

High precision adsorption isotherms of³He and⁴He on bare Grafoil and on Grafoil coated with a monolayer of argon have been measured in the temperature range 4–20 K, using a high resolution, pressure-sensitive capacitance gauge located at 4.2 K close to the sample chamber. This gauge obviated thermomolecular pressure effects and corrections. The isotherms yielded the following resultant data: The monolayer coverage V_m for⁴He on bare Grafoil was 0.42 cm³ (STP)/m² and for³He on bare Grafoil was 0.395 cm³ (STP)/m²: the isosteric heat of adsorptionQ _st/R of the second layer of³He on bare Grafoil was 23.5 K andQ _st/R for³He on argon-coated Grafoil for the first layers was 47.5 K. Also, the data for³He and⁴He on bare Grafoil at and just aboveV _m have been used by Novaco (see subsequent paper) for determination of the virial coefficients of the gas phase occuring in the early formation of the second layer.     

Motional states of3He and4He in the one-dimensional channels of K-L zeolite

The behavior of³He and⁴He in a one-dimensional channel (10 Å in diameter) of K-L zeolite has been studied by measuring isosteric heat of sorption and heat capacities in the temperature range 0.1–1.5 K as a function of the amount of helium adsorbed. At smaller amounts, below 40% of full channel, the He adatoms seem to be bound on the potential minima of the wall. However, at larger amounts adsorbed, between 40 and 70%, a one-dimensional translation of the excess adatoms over 40% is suggested by the results that the molar heat capacities atT1 K are about the magnitudeR/2 of a one-dimensional gas and that the heat of sorption atT=0 K is almost constant.Research Institute for Catalysis, Hokkaido University, Sapporo, Hokkaido, Japan.     

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.