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.     

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.     

Rayleigh linewidth in4He near the gas-liquid critical point

Spectra of Rayleigh-scattered light in⁴He near the gas-liquid critical point have been measured, using a photon correlation method. Fitting the obtained relaxation times to Kawasaki's expression with background modification, we have obtained along the critical isochore the correlation length =(3.6±0.78)^{–0.534±0.046} Å and the high-frequency shear viscosity *=21.5±3.6 µP. * has been revealed to be in good agreement with the regular part of the viscosity _r=21±2µP. The singular part of the thermal diffusivity has been determined to beD _Ts =(4.9±2.7)×10^{–5–0.543±0.046} cm²/sec along the critical isochore.     

Effective Interaction and Superfluidity in Two-dimensional Liquid 3He

Effective interaction of two-dimensional liquid ³He is studied with the (selfconsistent) reaction matrix theory. The theory is found to be valid in the dilute region, _2D 0.02 Å^–2, where _2D is the areal density. In the region, the attractive interaction in the p-wave channel is the most dominant, and the system is expected to undergo a transition to a p-wave superfluid state, except for the dilue limit. The transition temperature is estimated to be of the order of mK in the clean limit. In the dilute limit, _2D 0.002 Å^–2, an s-wave superfluid state becomes more stable than a p-wave one, but the transition temperature is found to be of the order of 0.1 mK at most. Furthermore, in the reaction matrix theory, it is found that a d-wave superfluid state becomes more stable than a p-wave one at _2D 0.035 Å^–2.     

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.     

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.     

Critical light scattering in4He near the gas-liquid critical point

Scattered intensities of light were measured near the gas-liquid critical point of ⁴ He at scattering angles of 30, 60, and 90° as functions of the reduced temperature =|T–T _c |/T _c along the critical isochore (T>T _c ) and the coexistence curve (T>T _c ). The temperature range was 3×10 ^–5 <<1.5×10 ^–2 . Critical exponents and coefficients describing divergence of the generalized susceptibility and the correlation length are obtained as (T>T _c )=1.31±0.02, v(T>T _c )=0.66±0.02, ₀ (T>T _c )=4.2±0.6 Å, (T>T _c )=1.32±0.02, v(T>T _c )=0.68±0.02, _± (T>T _c )=2.6±0.7 Å, =0.06±0.06(T>T _c ), 0.05±0.05(T>T _c ), and ₀(T>T _c )/x_± (T>T _c )=3.6±0.4. It is pointed out that the quantal nature of ⁴ He has remarkable influence on the critical behavior of ⁴ He in the above-mentioned temperature region.     

Continuing Specific Heat Measurements of 3He in 3He - 4He Mixture Films

Additional data from our on-going experiments for the heat capacity of ³ He in ³ He- ⁴ He mixture films on a Nuclepore substrate are reported over the temperature range 90T165 mK, for ³ He coverages between 0.05 and 1.4 bulk-density atomic lagers, on a ⁴ He film of thickness 4.33 bulk-density atomic lagers. This is a two-dimensional Fermi liquid system, in which we can change the ³ He coverage and thus tune the Fermi temperature.     

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.     

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.     

Heat Capacities of Monolayer 3He Fluids Floated on A Superfluid 4He Thin Film

We have measured heat capacities of monolayer ³ He floated on a superfluid ⁴ He thin film (three atomic layers) adsorbed on graphite at low temperatures. The ³ He films behave as degenerate 2D Fermi fluids with m* 1.3m ₃, where m* is the quasiparticle effective mass and m ₃ is the bare mass of ³ He, in the whole temperature range we studied (1 T 80 mK). No anomalous behavior suggesting puddling nor other phase transitions is observed. In contrast to our previous measurements for pure ³ He films without the underlying ⁴ He film, the temperature independent heat-capacity contribution is not observed. This can be explained by the second-layer localized spins trapped on substrate heterogeneities being replaced by nonmagnetic ⁴ He.     

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.     

Specific Heat Measurements of 3He in 3He-4He Mixture Films

Preliminary data for the heat capacity of ³ He in ³ He- ⁴ He mixture films on a Nuclepore substrate are reported over the temperature range 90T165 mK, for ³ He coverages between 0.05 and 1.7 bulk-density atomic layers, and a ⁴ He film thickness of 4.33 bulk-density atomic layers. In this two-dimensional Fermi liquid system, a step structure appears in the specific heat as a function of ³ He coverage, similar to the step previously observed in the magnetization.     

NMR Studies on 3He-3He and 3He-4He tunneling motions in solid 3He-4He mixtures

Helium-3 nuclear spin relaxation times T ₁, T ₂, and T ₁have been measured for ³He-⁴He solid mixtures at the exchange plateau region (~0.5K). The ³He concentrations X ₃of the samples were 7.2, 2.9, 1.8, 1.4, 0.67, 0.65, and 0.22%, and their molar volumes varied between 19.9 and 20.9cm³/mole in hcp phase. The spectral density function J() for dipolar field fluctuations was determined in the low-frequency branch from T ₁measurements and in the high-frequency branch from conventional T ₁measurements. It was found that J() is given by J() = cJ()|_3–4 + (1–c)J()|_3–3, where J()|_3–4 is the spectral density function due to the ³He-⁴He tunneling motions, and J()|_3–3 is that due to the ³He-³He tunneling motions. Using the Torrey theory, the correlation frequency of the ³He-⁴He tunneling motions was evaluated from T ₁data, and was found to be in good agreement with Landesman 's theory.Supported in part by the Japan Society for the Promotion of Science through a grant to Y.H.     

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.     

Effects of 4He substitution on low temperature heat capacities of 2D 3He adsorbed on graphite

No Heading We measured heat capacities of the second layer ³He admixed with a small amount of ⁴He (= 0.9 nm^–2) on graphite preplated with a monolayer ⁴He. The aim of this study is to elucidate possible ⁴He substitution effects on a recently proposed new quantum phase existing at densities just below that (_4/7) for the 4/7 registered phase. This phase is supposed to be the hole (zero-point vacancy) doped Mott localized phase. The substitution gives rise to an excess heat capacity (C_ex) with unusual temperature and density dependencies which is most pronounced at a slightly lower density than _4/7. The C_ex stays relatively large even at _4/7, and suddenly disappears at a slightly higher density. One possible scenario, which is consistent with the present data, is that the C_ex comes from the isotopic mixing effect existing in a narrow density range around _4/7 and that there exists an excess particle phase just above _4/7 in addition to the hole doped phase below. The result may suggest finite fluidity or unexpectedly large band widths for the isotopic impurities in the 4/7 phase.PACS numbers: 67.70.+n, 67.55.–s, 71.10.Ay.     

Excitations and Their Temperature Dependence in Superfluid 4He Beyond the Roton

The temperature dependence of the dynamic structure factor S(Q,) for superfluid ⁴ He has been measured by inelastic neutron scattering for wave vectors between 2.3 and 2.6 Å ^–l. S(Q,) has two peaks: one sharp peak at low energies whose dispersion flattens out and whose strength decreases with increasing Q, and one broader peak at higher energies with a stronger dispersion. The first peak disappears gradually with increasing temperature, while only part of the second peak vanishes at T . This indicates the existence of a third broad contribution, related to atoms above the Bose condensate. The two-peak structure can be interpreted in terms of a Bose-condensate induced coupling of the two-particle spectrum to the one-particle spectrum. The overall temperature dependence is consistent with the density-quasiparticle picture.     

Spin diffusion and magnetization studies of3He in3He-4He mixture films

The longitudinal spin diffusion coefficient and magnetization of a submonolayer coverage of ³ He, n ₃ =0.0066 Å^–2, in a thin adsorbed ⁴ He film has been measured as a function of temperature0.024 K T0.5 K and ⁴ He coverage0.21 Å ^–2 n ₄ 0.32 Å ^–2.     

Preparation and electrical properties of ITO thin films by dip-coating process

Indium tin oxide (ITO) thin films were prepared on quartz glass substrates by a dip-coating process. The starting solution was prepared by mixing indium chloride dissolved in acetylacetone and tin chloride dissolved in ethanol. The ITO thin films containing 0 20 mol% SnO₂ were successfully prepared by heat-treatment at above 400 °C. Chemical stability of sol were investigated by using a FTIR spectrometer. The electrical resistivity of the thin films decreased with increasing heat-treatment temperature, that is carrier concentration increased, and mobility decreased with increasing SnO₂ content. The ITO thin films containing 12 mol% SnO₂ showed the minimum resistivity of =1.2 × 10^–3 ( cm). It also showed high carrier concentration of N=1.2 × 10²⁰(cm^–3) and mobility _H=7.0(cm² V^–1 s^–1).