Mechanical Response of <Superscript>4</Superscript>He Films Adsorbed on Graphite with a Quartz Tuning Fork

We have carried out quartz-crystal microbalance (QCM) experiments of 32 kHz quartz tuning fork for ⁴He films adsorbed on Grafoil, and have measured the temperature dependence of the resonance frequency and Q value for various areal densities. It was found that the frequency does not decrease exactly in proportion to the areal density. This means that the film still undergoes decoupling partly, although it is strongly suppressed from that of 5 MHz QCM measurements. Above the three-atom thick film, the decoupling due to the superfluidity of the overlayer is observed. In addition, we found that the competition between the superfluidity and the slippage takes place for a large oscillation amplitude. From the comparison with 5 MHz QCM measurements, it is concluded that the acceleration of substrate plays an important role in the slippage.     

Nonlinear Interfacial Friction of 4He Films Absorbed on Grafoil

No Heading We measured the slippage of ⁴He films adsorbed on Grafoil using the quartz-crystal microbalance (QCM) technique. The slippage of ⁴He films depended on the oscillating amplitude. In a large oscillating amplitude of a 5.0 MHz quartz crystal, ⁴He films underwent slipping gradually below a certain temperature. On the other hand, in a small oscillating amplitude, another additional increase appeared.PACS numbers: 67.20. +k, 81.40.Pq     

3He Effect on 2D Superfluidity in 3He–4He Mixture Films on Planar Gold

There have been a number of experiments exploring the nature of 2D superfluidity and the configuration of ³He–⁴He mixture films on various substrates. To date, a possible film-structure at T=0 is that of a simple layer model, ³He/superfluid ⁴He/solid-like ⁴He/substrate, in which the submonolayer superfluidity is strongly affected by the coverage of the ³He overlayer. Yet the mechanism is not been fully understood. In this paper, we report a QCM study at 60 MHz for the ³He effect on the superfluidity of mixture films on flat gold, mainly focusing on the anomalous depletion of the temperature dependence of the superfluid density σ _s. In the measurements, we kept the ³He coverage constant (n ₃= 0, 3.6, 7.2, 19.0, 57.2, or 92.8 μmol/m²) and then incrementally added ⁴He. We observed the evolution of the ³He effect on σ _s(T) with increasing ³He coverage; this depletion of σ _s(T) rapidly increases and then saturates near n ₃～1 layer. From the analysis of the linear-temperature region in the plot of the dissipation peak temperature T _p as a function of the superfluid ⁴He coverage n _4s and comparison with previous studies on Mylar and porous gold, we found a universal function for the strength of the ³He effect for all substrates.     

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.     

Frequency and Size Dependences of Superfluidity in?Low-Dimensional 4He Fluids

We have studied superfluidity of ⁴He fluids in two- and one-dimensional states. In the 2D state of the ⁴He films on flat substrate, superfluidity was observed in the normal fluid state above the 2D Kosterlitz-Thouless temperature at high measurement frequencies. The superfluidity in 2D also depends on the system size, e.g. pore diameter of porous glasses and grain size of powder. The 1D state was realized for ⁴He fluid nanotubes formed in 1D nanopores 1.8?C4.7 nm in diameter and about 300 nm in length. Superfluidity in the 1D state was observed by the torsional oscillator experiment. The results are qualitatively well reproduced by the Monte Carlo calculation for a classical XY spin system modeled on the present ⁴He nanotubes. Although the 1D state is in the normal fluid state at any finite low temperatures due to the 1D phonon fluctuation, the superfluid frequency shift ??f of the oscillator can be observed. Above a temperature, ??f decreases due to another kind of 1D thermal fluctuation of which excitations destroy the phase coherence in the nanotubes. The excitations depend on the tube length as well as the tube diameter.     

Competition Between the Superfluid Overlayer and the Mobile Solid Layer of 3He-4He Mixture Films on Porous Gold

In the previous quartz crystal microbalance measurements for ⁴He films adsorbed on porous gold, we have observed a competition between superfluidity and slippage: In low areal densities, the resonance frequency increases gradually below T _S due to the slippage of solid layer, while at high areal densities the slippage disappears and the superfluid onset of liquid overlayer is observed at T _C . In the crossover region, the slippage below T _S is suddenly suppressed at T _D , which is much lower than T _C . In the present work, we introduced a small amount of ³He onto ⁴He films, and studied the competition as a function of ³He areal density ρ ₃. As ρ ₃ is increased, T _C is monotonically lowered. In contrast, T _D increases up to a certain value of ρ ₃, and then turns over to decrease in parallel to T _C .     

Slippage of 4He Films Adsorbed on Grafoil

We applied the quartz-crystal microbalance (QCM) technique to ⁴He films adsorbed on grafoil. It was found that both of nonsuperfluid ⁴He films and the inert layers underneath the superfluid film slip under a certain condition at low temperatures, and that the temperature at which these films start to slip depends on the ⁴He areal density. In addition, this slippage also depended strongly on the amplitude of the quartz crystal.     

Interfacial Friction of 3He Films Adsorbed on Grafoil

We measured the interfacial friction of ³He films adsorbed on Grafoil (exfoliated graphite) using the quartz-crystal microbalance (QCM) technique, and compare present results with those of ⁴He films. In the same manner as ⁴He films, the friction decreases below a certain temperature T _S , and T _S depends on the areal density of ³He film. In two-atom and three-atom thick films, however, T _S of ³He films is lower than that of ⁴He films. Furthermore, the decrease in the friction still remains above five-atom thick films of ³He while it disappears in four-atom thick films of ⁴He and the superfluid onset is manifest.     

Low-temperature adsorption isotherms of 3He and para-H2 on grafoil and their normalization

Measurements have been made of the adsorption isotherms of ³He and of para-hydrogen (p-H₂), on bare Grafoil, the former in the temperature range 0.88–1.23 K, and the latter in the temperature range 10.0–20.0 K. For p-H₂ the quantity of material adsorbed plotted against (p/p ₀) ^T yields a single temperature-independent curve, as would follow from the potential theory for multilayer adsorption, and as emphasized by Chester et al. in 1974. The same behavior was found for ³He on Grafoil, except that deviations from a single temperature-independent curve occurred at the higher temperatures. For p-H₂ on Grafoil it is to be noted that the isotherms taken below the triple point of free, bulk p-H₂ fit the same single temperature-independent curve as do the isotherms measured at temperatures between the triple point and the boiling point. From the data, the isosteric heats of adsorption were calculated over a wide range of coverage and this provided further experimental evidence for the similarity between the uppermost layers of thick adsorbed films and the free liquid of the same substance.Supported by the National Science Foundation and the Brazilian National Council of Scientific and Technological Development (CNPq).     

Specific heat of para-hydrogen monolayers on graphite

The specific heat of para-hydrogen films has been measured from 1 to 20 K for areal densities between 0.01 and 0.055 atoms/Å ² of the partial monolayer adsorbed on grafoil. The results are compared with the specific heat of ⁴ He films at equivalent densities. It is argued that a nonideal gas regime and liquefaction are present in both systems and that solidification of thep-H ₂ films has been suppressed to below the temperature range of the experiment. Implications regarding 2D superfluidity in hydrogen monolayers are discussed briefly.     

Superfluid Transition of a 4He Thin Film Pressurized by Bulk Liquid 3He

We measured transverse acoustic impedance Z of normal fluid ³He at 46.6 MHz on a surface coated with a thin ⁴He film. The real component of the impedance, Z′, in the coated samples deviates from Z′ in the pure ³He in the low temperature region. Z′ on the coated samples is almost identical with Z′ in the pure sample at high temperature and gradually deviates below a particular temperature T _onset . T _onset  is possibly the superfluid onset temperature of the ⁴He film pressurized by the bulk liquid ³He. The gradual decrease in Z′ means that the superfluid component in ⁴He film increases gradually, which is expected from the dynamic KT transition at high frequency. The thicker is the film, the higher is the T _onset . The range of T _onset we observed was between 40 and 160 mK. This is much lower than that at the saturated vapor pressure. Suppression of T _onset achieved by the applied pressure from bulk liquid ³He was presumably caused by the dissolved ³He in the film, thickening of the inert layers and/or by the strong correlation effect. The result shows that the specularity of ³He quasiparticle scattering is strongly affected by superfluidity of the ⁴He film.     

The Quest for Bose-Einstein Condensation in Solid 4He

Ever since the seminal torsional oscillator (TO) measurements of Kim and Chan which suggested the existence of a phase transition in solid ⁴He, from normal to a ??supersolid?? state below a critical temperature T _c = 200 mK, there has been an unprecedented amount of excitement and research activity aimed at better understanding this phase. Despite much work, this remarkable phase has yet to be independently confirmed by conventional scattering techniques, such as neutron scattering. We have carried out a series of neutron scattering measurements, which we here review, aimed at observing Bose-Einstein condensation (BEC) in solid ⁴He at temperatures below T _c . In bulk liquid ⁴He, the appearance of BEC below T _?? signals the onset of superfluidity. The observation of a condensate fraction in the solid would provide an unambiguous confirmation for ??supersolidity??. Although, our measurements have not yet revealed a non-zero condensate fraction or algebraic off diagonal long-range order n ₀ in solid ⁴He down to 65 mK, i.e. n ₀=(0±0.3)%, our search for BEC and its corollaries continues with improved instrumentation.     

Surface Magnetism of 3He in Grafoil

We report the magnetic susceptibility of ³He in Grafoil filled with pure liquid³He at 27.6 bar and at temperatures down to 0.1 mK with a cw NMR method. It is composed of two contributions: from the bulk liquid and from the adsorbed layer of ³He on the Grafoil surface. The latter shows a well-known strong ferromagnetic tendency and can be fitted to a Curie–Weiss law in the high temperature region. The obtained Weiss temperature is surprisingly large compared with the previous ones.     

3He-3He and 4He-4He Cross Sections in Matter at Low Temperature

The Galitskii-Migdal-Feynman (GMF) formalism is applied to liquid ³He and (for the first time) to liquid ⁴He. The effective total, diffusion and viscosity cross sections, as well as the effective scattering length and the effective range, are calculated. For liquid ³He, it is found that S-wave scattering dominates for wave number k<0.5 Å^?1. At the Fermi momentum k _F, the effective partial cross section σ _? (and thus the total cross section σ _T) has a singularity (virtual state). This singularity may be interpreted as a signature of superfluidity or a quasi-bound state. For k>2 Å^?1, the effective total cross section is nearly constant. On the other hand, it is found in liquid ⁴He that S-wave scattering dominates for k<0.3 Å^?1, and a peak exists in σ _T arising from a peak in the effective D-wave cross section. This resonance corresponds to a quasi-bound state trapped by the ?=2 centrifugal barrier. The most prominent features of our calculations are a resonance and a Ramsauer-Townsend minimum in the matter cross section at low temperatures. This effect is absent in the ³He gas. It is, therefore, a purely many-body effect in liquid ³He. With increasing energies, the matter results approach the vacuum results. This indicates that the high-energy behavior is dominated by the self-energy contribution; the many-body effects can be neglected.     

Vibrating Quartz Crystal Studies of Wall-Film Superfluidity in Liquid 3He/4He Mixtures Near the Tricritical Concentration

We are using a thin quartz crystal immersed in the liquid, vibrating in shear modes at 24.8 and 94.0 MHz, to investigate the onset and growth of superfluidity in a thin film at the crystal surface in liquid ³He/⁴He mixtures having ³He mole fractions x near the tricritical value x=0.675. A parallel-plate capacitor in the cell monitors the phase-separation transition. Preliminary measurements of frequency shifts at x=0. 644 and x=0.705 show a relatively abrupt onset of wall-film superfluidity in the bulk normal region of the phase diagram at temperatures in good agreement with earlier studies of wall-film superfluidity by other methods.     

Magnetic susceptibility of submonolayer3He films

We calculate the magnetic susceptibility of submonolayer³He films. First, using the formulation of the equilibrium thermodynamic properties in terms of statistical quasiparticles, we obtain an expression for the magnetic susceptibility of dilute systems of particles interacting through a short-range potential, taking into account binary interactions between the particles. At high temperatures our expression reduces to the one obtained using the virial expansion truncated after the second term. Next, we apply this expression to³He in two dimensions and compare our results with the magnetic susceptibility data of submonolayer³He films adsorbed on Grafoil and on argon-coated Grafoil and previous calculations.     

Pulsed NMR study of submonolayer and multilayer 3He films adsorbed on Grafoil

The nuclear spin relaxation times T ₁ and T ₂ of submonolayer and multilayer ³He films adsorbed on Grafoil have been measured at temperatures between 1.2 and 4.2 K by a pulsed NMR technique. The T ₁ data for high-coverage films (solid and dense fluid phases) and the substrate registered phase are interpreted in terms of thermally activated vacancies. In solids the quantum exchange inherent in ³He is shown to be important at low temperatures. The data for multilayer films are discussed in the light of the particle exchange between layers and the relaxation time of each layer. The dynamical behavior of adatoms in the solid, fluid, and substrate registered phases as well as the nature of phase transitions between them are discussed on the basis of information obtained from the analysis of T ₁ and T ₂ data. The present results as a whole seem to support the phase diagram determined by specific heat measurements. In addition, the nuclear susceptibility in submonolayer films has been measured by the same technique. The effect of Fermi degeneracy was not seen in the temperature range between 1.2 and 4.2 K.     

Critical Behavior of the Liquid Gas Transition of 4He Confined in a Silica Aerogel

We have studied ⁴He confined in a 95 % porosity silica aerogel in the vicinity of the bulk liquid gas critical point. Both thermodynamic measurements and light scattering experiments were performed to probe the effect of a quenched disorder on the liquid gas transition, in relation with the Random Field Ising Model (RFIM). We find that the hysteresis between condensation and evaporation present at lower temperatures disappears at a temperature T _ch between 25 and 30 mK below the critical point. Slow relaxations are observed for temperatures slightly below T _ch , indicating that some energy barriers, but not all, can be overcome. Above T _ch , no density step is observed along the (reversible) isotherms, showing that the critical behavior of the equilibrium phase transition in presence of disorder, if it exists, is shifted to smaller temperatures, where it cannot be observed due to the impossibility to reach equilibrium. Above T _ch , light scattering exhibits a weak maximum close to the pressure where the isotherm slope is maximal. This behavior can be accounted for by a simple model incorporating the compression of ⁴He close to the silica strands.     

Nucleation of transitions in liquid 3He-4He mixtures

We present a complete set of data describing the nucleation both of superfluidity and phase separation at container walls in liquid ³He-⁴He mixtures. The appearance of superfluidity and the growth of phase-separated films are measured locally at the walls. A theoretical interpretation is given, important results of which are that the phase separation and superfluid transitions become uncoupled when the transitions are localized near the walls and that quantum fluctuations most probably strongly affect the nature of the superfluid nucleation transition at low temperature. Further, comparison of our results with data for transitions in pure ⁴He films demonstrates that a universality principle governs the transitions in both systems.Partly supported by NSF Grant No. DMR 75-21886.Laboratoire associé au CNRS.     

Structural and Superfluid Properties of the 4He Monolayer on a C28 Molecule

We have performed path-integral Monte Carlo calculations to study the adsorption of N ⁴He atoms on a single C₂₈ fullerene molecule. Radial density distributions show a layer-by-layer growth of ⁴He with the first adlayer being located at a distance of 5.3 Å from the center of C₂₈. The monolayer is found to show a commensurate structure at N=16 with each of the 16 adsorption sites on the molecular surface being occupied by one ⁴He atom. As more helium atoms are adsorbed beyond N=16, the adlayer is in a mixed state consisting of 4 localized atoms at the hexagonal faces and the other atoms delocalized over the pentagonal faces. Another structurally-ordered state is observed at N=32, where the helium layer shows the same crystalline structure with an icosahedral symmetry as observed for 32 ⁴He atoms on a C₆₀ molecule. It is found that more ⁴He atoms can be squeezed into the first layer to disrupt this icosahedral structure when enough ⁴He atoms are added in the second layer. Finally we observe the reentrant superfluid response of the monolayer with superfluidity being quenched completely at the ordered states of N=16 and 32.