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.     

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.     

Path integral monte carlo simulations of thin4He films on a H2 surface

Atomatically thin⁴He films of up to three monolayers on molecular hydrogen (1,1,1) surfaces are studied at T = 0.5 K, using path integral Monte Carlo. We compute the binding energy of⁴He to the H₂ substrate as a function of⁴He coverage and obtain evidence of the prewetting transition. Density profiles perpendicular to the⁴He-H₂ interface are obtained, as well as the zero point motion and effective mass of⁴He parallel to the substrate surface. The superfluid density of⁴He vs. coverage is calculated, and the intermediate scattering function is computed, from which we estimate the speed of third sound. Finally, we calculate the vorticity-vorticity correlation function.     

Vortex Diffusivity and Core Diameter of 2D Superfluid in 4He Films on Gold and H2 Substrates

The two-dimensional (2D) ⁴He fluid films show the Kosterlitz-Thouless (KT) transition where pairing and unpairing of the 2D vortices play an important role. However, the vortex properties (the diffusion constant D, the core diameter a ₀) have not been precisely obtained for various conditions. Here, we accurately determined the parameter D/a ₀ ² by the high frequency dependence of the superfluid onset up to 180 MHz for the submonolayer ⁴He fluid films adsorbed on gold and H₂ (3.3 layers) preplated on gold, respectively. The superfluid onset coverage changes from 1.6 (gold) to 0.5 layers (H₂), which clearly indicates the large difference of the adsorption potential. The parameter D/a ₀ ² , on the other hand, has the same value for the coverages with the same KT temperature T _KT. This suggests that the vortex diffusions on both substrates have the largest value D～?/m in the quantum limit. The core diameter a ₀ was estimated to be the same magnitude as the de Broglie wavelength at T _KT between 0.1 and 0.9 K.     

QCM Measurements of Superfluid Response in 4He Films up to 180 MHz

At finite frequencies, a dynamic Kosterlitz–Thouless (KT) theory predicts a frequency dependence of the superfluid transition in ⁴He films on planar surfaces. We report results of QCM measurements to study the superfluid response on planar gold surfaces for very high frequencies up to 180 MHz in the temperature range of 0.6–1.0 K. As the frequency is increased, we observed the expected KT behavior that the superfluid transition shifts to a higher temperature from the static transition temperature T _KT and the transition temperature region broadens. The frequency dependence of the dissipation peak temperature at the transition agrees with a simple equation of the frequency dependence based on the dynamic KT theory. The microscopic parameter for the dynamic transition, the ratio of the diffusion constant to the square of the vortex core radius D/r ₀ ², is estimated to be on the order of 10¹⁰ s⁻¹.     

Hydrogen adsorption on alkali metal surfaces: Wetting,prewetting and triple-point wetting

We report the results of a quartz microbalance study of the multilayer adsorption of H₂ and D₂ on sodium and on rubidium. On sodium H₂ and D₂ display the well known phenomenon of triple-point wetting. Interestingly low temperature adsorption isotherms of H₂ on the evaporated Na surface show sharp layering transitions. On rubidium a weaker substrate H₂ and D₂ undergo a wetting transition in the liquid phase followed by sharp presetting transitions away from liquid-vapor coexistence. The prewetting phase diagram of H₂ on Rb has been quantitatively mapped out.     

The thermal conductivity of and convective onset in liquid3He at saturated vapor pressure above 1.3 K

This paper presents thermal conductivity data for liquid³He taken at saturated vapor pressure (s.v.p.), and also the critical Rayleigh number at which convection begins. The temperature in this experiment ranged from 1.3 K to 3.2 K. We compare the thermal conductivity results with those of earlier experimenters, and find they agree well. The convective onset measurements are the first reported for³He, and we find the critical Rayleigh number Ra_c = 1500 ± 105, which is similar to the experimental values reported for⁴He. References are provided for the thermodynamic properties necessary for calculating the Rayleigh number Ra at s.v.p.     

Phase transitions in the growth of4He films

Using a microscopic, variational approach we examine the growth of⁴He absorbed to graphite and alkali substrates. We find that superfluid layers are formed and their behavior as a function of coverage is closely related to the one of a purely two-dimensional superfluid. The growth of a new layer undergoes a phase transition from a cluster formation into the connected superfluid when the coverage is increased. Based on the important connection to the two-dimensional fluid we propose a microscopic theory of quantum vortices in⁴He films at zero temperature, in which single vortices are treated as quasiparticles. We calculate the energy needed to create the single vortex, vortex inertial mass, microscopic interaction between vortices and binding energy of the vortex-antivortex pair as a function of density. We predict that at the⁴He superfluid density less than about 0.037 Å^–2 the binding energy of the pair becomes negative, indicating a phase transition into a new state where vortex-antivortex pairs are spontaneously created.     

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).     

Equation of State of He-H2 and He-D2 Dense Fluid Mixtures at High Pressures and Temperatures

The fluid variational theory is used to calculate the Hugoniot equation of state (EOS) of He, D₂, He + H₂, and He + D₂ fluid mixtures with different He:H₂ and He:D₂ compositions at high pressures and temperatures. He, H₂, and D₂ are the lightest elements. Therefore, the quantum effect is included via a first-order quantum correction in the framework of the Wigner-Kirkwood expansion. An examination of the reliability of the above computations is performed by comparing experiments and calculations, in which the calculation procedure used for He and D₂ is adopted also for He + D₂ and He + H₂, since no experimental data for the mixtures are available to conduct these comparisons. Good agreement in both comparisons is found. This result may be seen as an indirect verification of the calculation procedures used here, at least, in the pressure and temperature domains covered by the experimental data for He and D₂ used for comparisons, which is nearly up to 40 GPa and 10⁵ K. Also, the equation of state of He + H₂ fluid mixtures with different compositions is predicted over a wide range of temperatures and pressures.     

Specific heat of normal and superfluid3He

Extensive measurements of the heat capacity of liquid ³ He in the normal and superfluid phases are reported. The experiments range from 0.8 to 10 mK and cover pressures from 0 to 32.5 bar in zero magnetic field. The phase diagram of ³ He, based on the platinum NMR temperature scale, is presented. In the normal liquid at low pressures and near the superfluid transitionT _c an excess specific heat is found. The effective massm* of³He is at all pressures about 30% smaller than the values reported earlier. The calculated Fermi liquid parameters F₀ and F₁ are reduced asm*/m, while the spin alignment factor (1 + Z₀/4)^–1 is enhanced from 3.1–3.8 to 4.3–5.3, depending on pressure. The specific heat discontinuity C/C atT _c is forP = 0 close to the BCS value 1.43, whereas at 32.5 bar C/C is 1.90±0.03 in the B phase and 2.04±0.03 in the A phase, revealing distinctly the pressure dependence of strong coupling effects. The temperature dependence of the specific heat in the B phase agrees with a model calculation of Serene and Rainer. The latent heatL at the AB transition is 1.14±0.02 µJ/mole forP = 32.5 bar and decreases quickly as the polycritical point is approached; at 23.0 bar,L = 0.03 ± 0.02 µJ/mole.Work supported by the Academy of Finland.     

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.     

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.     

Calorimetric Study of CeRu2Ge2 Under Continuously Swept Hydrostatic Pressure up to 8 GPa

We have implemented AC calorimetric measurements in diamond anvil pressure cells. The range of pressure (0–20 GPa), the excellent hydrostatic conditions of solid ⁴He used as the pressure transmitting medium associated with the possibility of continuously tuning the pressure at low temperature makes this experiment ideally suited for investigating phase diagrams under pressure and in particular for studying the thermodynamics of correlated metals around a Quantum Critical Point (QCP) where magnetic order is suppressed at absolute zero temperature. We present here results on the heavy fermion compound CeRu₂Ge₂ up to 8 GPa and down to 2 K. The specific heat anomalies associated with the different magnetic phase transitions are clearly resolved, allowing a precise determination of the magnetic phase diagram. On approaching the QCP close to 7 GPa, we observe a striking broadening of the antiferromagnetic transition associated with an anomalous behavior of the signal phase which could correspond to a change in the nature of this transition.     

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.     

State of the4He film at monolayer completion

We calculate the density of⁴ He at which a monolayer completes when adsorbed at zero temperature on a hypothetical substrate (characterized by the potential well depthD and the gas-surface dispersion coefficientC ₃). In the case of an alkali metal substrate, the monolayer is fluid; otherwise, it is a two-dimensional solid, except for H₂, which is a borderline case. We discuss the prospects for monolayer superfluidity.     

Structure in thin superfluid helium films

Precision measurements of third sound in atomically thin⁴He films on Ne, Ar, and CO₂ substrates reveal a periodic structure not corresponding to whole layers. Treating the He film as an incompressible, continuous fluid, the data indicate that the chemical potential has a contribution proportional to l^–6, where l is the He coverage in layers, which is modulated at intervals of 0.62±0.04 layers and which weakens the van der Waals potential. Alternatively the data indicates the existence in the film of a damped smectic density wave with a 0.54±0.40 layer periodicity.     

Possible Phase Transition at Low mK Temperatures in Liquid Helium Mixture Films Adsorbed on Graphite

We report heat capacity and magnetisation measurements of ³He adsorbed on the surface of graphite plated with three atomic layers of ⁴He. For ³He coverages n ₃>4 nm^?2 the heat capacity corresponds to a 2D Fermi fluid. The inferred hydrodynamic mass of the ³He quasiparticles is 1.38±0.05 m₃. The ³He effective mass ratio increases with coverage to 2.4 at n ₃=4 nm^?2, due to Fermi liquid interactions. The heat capacity isotherm exhibits a steplike increase centred on n ₃=4.5 nm^?2, similar to that previously observed on four layers of ⁴He. This is associated with the population of the first excited Andreev surface bound state. However, in the present case, as n ₃ is increased through the step a pronounced anomalous feature develops in the temperature dependence of the heat capacity, around 10 mK. Below 5 mK the heat capacity is approximately linear in temperature. With n ₃=7 nm^?2, we find that this behaviour is very sensitive to small changes in the ⁴He third layer coverage, around the completed third layer. Measurements of the ³He magnetisation,, by continuous wave NMR methods, find a significant increase with decreasing temperature below around 20 mK. Together the data suggest that a phase transition takes place in the film at low mK temperatures.     

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.     

Boundary Effects in Superfluid Films

We have studied the superfluid density and the specific heat of the x − y model on latticesL×L×H withL≫H (i.e. on lattices representing a film geometry) using the Cluster Monte Carlo method. In theH-direction we applied staggered boundary conditions so that the order parameter on the top and bottom layers is zero, whereas periodic boundary conditions were applied in theL-directions. We find that the system exhibits a Kosterlitz-Thouless phase transition at theH-dependent temperatureT _c ^2D below the critical temperature T_gl of the bulk system. However, right at the critical temperature the ratio of the areal superfluid density to the critical temperature isH-dependent in the range of film thicknesses considered here. We do not find satisfactory finite-size scaling of the superfluid density with respect toH for the sizes ofH studied. However, our numerical results can be collapsed onto a single curve by introducing an effective thicknessH _eff=H+D (whereD is a constant) into the corresponding scaling relations. We argue that the effective thickness depends on the type of boundary conditions. Scaling of the specific heat does not require an effective thickness (within error bars) and we find good agreement between the scaling functionf ₁ calculated from our Monte Carlo results,f ₁ calculated by renormalization group methods, and the experimentally determined functionf ₁.