Phase Diagram of 4He Film in 3D Nanopores of ZTC

In the study to examine effects of three-dimensional (3D) film connectivity on superfluid ⁴He film in the pore network, we have measured heat capacities of ⁴He film adsorbed in zeolite templated carbon (ZTC), which is an assembly of graphene fragments and has network of 1.2 nm pore with the 3D period of 1.4 nm, shorter than those of nanoporous materials studied so far. From the heat of desorption, the ⁴He film adsorbed in ZTC was observed to be formed up to about 1.4 atomic layers. Heat capacities of the ⁴He film are rather similar to those on SiO₂-based porous materials than those on graphite, except for large heat capacities of monolayer ⁴He film. At low coverages, the heat capacity rapidly decreases below a temperature T _L, suggesting a localized state of ⁴He at T<T _L. The T _L almost monotonically lowers with increasing the coverage. Heat capacity isotherms show maxima around 1.1 layers, which suggests quantum degenerate fluid (Bose fluid) above the coverage. From these results, the phase diagram of ⁴He film adsorbed in ZTC has been determined.     

Slippage of Nonsuperfluid 4He Films on Ag

We measured the mechanical response of nonsuperfluid ⁴ He films adsorbed on a Ag substrate using the quartz-crystal microbalance technique. In ⁴ He coverages from 0.06 to 0.1 atoms/Å ² , we observed that the resonance frequency increases at low temperatures accompanied by a decease in Q-value. This behavior suggests that nonsuperfluid ⁴ He films undergo partial slipping relative to the Ag substrate.     

Influence of 4He Preplating on 3He Fluid Formed in One-Dimensional 28 Å-Pores

No Heading A degenerate Fermi fluid has been realized recently for ³He films adsorbed in one-dimensional (1D) pores 28 Å in diameter, preplated with ⁴He layers. In order to study the influence of the ⁴He preplating on the ³He Fermi fluids, heat capacity was measured down to 4 mK for two preplated ⁴He films of different thickness. At low temperatures, no substantial difference was found between the two cases. On the other hand, a large difference appeared above about 150 mK. The large ³He heat capacity for the thick ⁴He preplating suggests thermal excitation of the ³He atoms to the excited energy levels of the Andreev states in the ⁴He fluid layers.PACS numbers: 67.70 +n. 67.55 Cx.     

Specific heat of monolayer films of3He-4He mixtures adsorbed on Grafoil between 0.04 and 4.2 K

The specific heat of mixtures of ³He and ⁴He adsorbed on Grafoil has been measured at four partial monolayer coverages corresponding to areal densities of 0.0279, 0.0419, 0.0485, and 0.066 »^–2 for 0.04 < T < 4.2 K. The ³He concentration in the mixtures was x ₃ = 0, 0.050, 0.091, 0.201, 0.485, 0.650, 0.908, and 0.999. A feature in the specific heat not seen in measurements with the pure isotopes is found for the two intermediate coverages at about 0.4 K. The measurements are analyzed at the higher temperatures using a theoretical virial expansion for two-dimensional gaseous mixtures. The entropy of mixing calculated by numerical integration of the specific heat curves shows that at 4 K the two isotopes are mixed. While mixing effects develop at temperatures below 1 K, the evidence for phase separation as in bulk mixtures is inconclusive.Work supported by the National Science Foundation, Grant DMR-72-03003A03.     

The Heat Capacity of 4He Monolayers Adsorbed on Evaporated Gold

The specific heat of ⁴He condensed on an evaporated gold surface has been measured for coverages between 0.007 and 0.096 Å^?2 and temperatures between 0.4 and 3.0 K. There are at least two types of physisorption site on the gold surface with binding energies ?83 ± 7 and ?94 ± 7 K. For coverages below 0.06 Å^?2 (～0.5 monolayers), the ⁴He is a two-dimensional classical gas at sufficiently high temperatures. At lower temperatures and higher coverages, the ⁴He forms condensed phases, including liquids, solids commensurate with the gold lattice, and incommensurate solids. The phase diagram of ⁴He/evaporated gold is similar to that for ⁴He/graphite, but the phase boundaries are shifted and not well defined, nor is the diagram as rich in structure.     

Calorimetric Study of the Desorption and Phases of 3He And 4He Adsorbed on Two Layers of H2-plated Graphite Above 0.2K

We have conducted new heat capacity studies of films of ³ He and ⁴ He adsorbed on 2.15 layers of hydrogen plating exfoliated graphite for temperatures T > 0.2K and coverages (n) over the entire first layer and beginning of the second layer. Low-density ³ He films show two-dimensional Fermi fluid behavior with no liquid-vapor condensation below 0.9K. We have mapped the n-T melting tine and estimated monolayer completion density using heat capacity isotherms. By fitting ³ He films' desorption specific heats to a theoretical model, we have calculated the ³ He binding energy (21.3K to 21. 7K) and compare it to a previous measurement for ⁴ He films on the same substrate (25.1K to 25.5K).     

Strongly Correlated Two Dimensional Fluid 3He

A two dimensional system of strongly correlated fermions can be realised by a fluid monolayer of ³ He adsorbed on an atomically flat surface. We report extensive measurements of the heat capacity, c, of ³ He adsorbed on graphite plated with two layers of hydrogen deuteride (HD) over a closely spaced grid of coverages in the temperature range l-80mK. The quasiparticle effective mass ratio, inferred from the linear temperature coefficient of the heat capacity, increases from near unity at low densities and appears to diverge approaching localisation. The maximum value of m*/m we are able to unambiguously extract from the data is 13 at a density 5 nm ^–2. At this density c/T is temperature independent only below 5mK. The behaviour of m*/m and F ₀ ^a , inferred from magnetization data, are consistent with the model of almost-localised fermions. We can track the evolution of strong finite temperature deviations from Fermi liquid behaviour as the density of the film and hence m*/m are increased. At sufficiently low temperature this correction is of T ² form going over to a large TlnT deviation for T > 0.05 T _F *, as predicted for 2D spin fluctuations. Thus in this system non-Fermi liquid behaviour extends to very low temperatures in the strongly correlated, large m */m, limit.     

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.     

Influence of Adsorption Potential on 3He Fluid States Formed on 4He-Preplated Substrates

No Heading From heat capacity measurements for ³He adsorbed on ⁴He-preplated mesopore in substrates, FSM-16, HMM-2, and Hectorite, we found fluid states of the ³He adatoms. At very dilute ³He densities, however, it strongly depends on the substrate whether the adatoms are in a localized or a fluid state. The molar heat capacity of a two-dimensional gas or a degenerate Fermi fluid appears above densities n_c = 0, 0, and 2 mol/m² for FSM-16, HMM-2, and Hectorite, respectively. The critical coverages n_c are extremely small or zero for the former two SiO₂-based substrates. On the other hand, n_c for Hectorite is large. Since Hectorite has strong adsorption sites due to the electric-dipole field gradients around ions located on the substrate surface, these potentials are likely to affect the localization of the dilute ³He adsorbed even on the ⁴He film.PACS numbers: 67.55.Cx, 67.70+n, 71.30+h     

4He Fluid in Extremely Narrow 1D Channels 1.5?nm in?Diameter

To examine whether one-dimensional (1D) helium quantum fluid is realized in narrower channels than those studied previously, we have measured heat capacities of ⁴He adsorbed in nanoporous material FSM with straight 1D channels 1.5 nm in diameter. From the heat of desorption for adsorbed ⁴He, the coverage n _f, up to which ⁴He film grows in the channels, is determined to be 15.4 ??mol/m² using the Frenkel-Halsey-Hill model. At coverages sufficiently below n _f, the temperature dependence of the ⁴He heat capacity has a shoulder, above which adsorbed ⁴He is delocalized from the substrate. On the other hand, the depression of the heat capacity indicating quantum effects has not been observed up to n _f, which suggests that ⁴He film in the channels remains amorphous-like normal fluid. Just above n _f, the quantum effect is observed in ⁴He adatoms on the grain surface of FSM powder, which indicates that 1.5 nm channels are slightly below the limit required to realize quantum effect in the inside ⁴He fluid.     

Specific heat of adsorbed films of3He,4He,and isotopic helium mixtures near monolayer coverages

Specific heat results are presented for near-monolayer films of³He,⁴He, and isotopic He mixtures adsorbed on Vycor porous glass in the temperature range between 1 and 4°K. In the case of the pure He monolayers and submonolayers, the specific heats depend only onT ² , like a two-dimensional Debye elastic medium. A film of slightly greater than monolayer coverage needs an additional temperature-independent term. Monolayer coverages of mixtures are difficult to define, but all coverages used, some of which are submonolayer, need bothT ² andT-independent terms. The constant term may arise from atoms in the second layer forming a classical noninteracting system, which in the mixture case would indicate selective adsorption of⁴He in preference to³He at the substrate wall, in agreement with previous adsorption experiments on the same substrate.Work supported in part by the U.S. Atomic Energy Commission.     

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.     

Observation of Superfluid 4He Adsorbed in One-Dimensional Mesopores

To study one-dimensional (1D) quantum liquid of ⁴ He, we measured the heat capacity and performed a torsional oscillator experiment for ⁴ He adsorbed on a new mesoporous substrate whose adsorption area consists of walls of straight one-dimensional 18Å diameter tunnels. The presence of adsorbed quantum liquid was examined by the isotope effect on the heat capacity for ³ He and ⁴ He adatoms. Above a coverage n _o , the heat capacity isotherms are completely different because of the Fermi and the Bose fluids, respectively. In the torsional oscillator experiment we observed superfluid ⁴ He above n _o . The fraction of the superfluid decoupled from the motion of the substrate is 0.13, which is the same order as 0.18 for packed Pt fine powder and 0.24 for 80 Å-porous glasses. The result indicates that the superfluid state exists in the one-dimensional ⁴ He adatoms formed in the 18 Å diameter pores.     

Solidification of the third helium layer on graphite

No Heading We report heat capacity and magnetization measurements of ³He adsorbed on graphite pre-plated by a solid bilayer of ⁴He. The first ³He layer adsorbed on this composite substrate remains fluid up to and beyond layer promotion. However it is observed to solidify significantly before the second ³He layer is completed. Remarkably, at fluid coverages on the verge of solidification, we observe a distinctive heat capacity and magnetisation maximum, which occurs at progressively lower temperatures as the coverage is increased. Possible magnetic instabilities in the fluid and analogues with heavy fermion systems are discussed.PACS numbers: 67.70 n+n, 67.80. Jd     

The High Temperature Phase Diagram of Single-Layer 3He-4He Mixtures

We present resugts of an extensive investigation with heat capacity measurements of the first layer phases of ³He-⁴He mixtures adsorbed on graphite preplated with two layers of H₂, for a wide range of coverages, and for temperatures between 0.2 K and 2.0 K. We observe the evolution of the twodimensional liquid(L)-vapor(V) coexistence region as a function of the ³He molar fraction(x). The L-V critical points, starting with 0.9 K at x=0, move to lower temperatures and the density of the self-bound liquid decreases as x increases, pointing towards a limiting value of x for L-V coexistence, in agreement with theoretical expectations. At densities higher than those producing L-V coexistence, we observe the onset of transitions to a phase present in the mixtures but apparently absent in the pure isotopic cases. Possible interpretations of the data will be discussed.     

Self-consistent measurement of the adsorption of He on Cu,CO2, Ar,and Ne

The chemical potentials as a function of He coverage have been determined from He adsorption isotherms measured at 1.72 K for the following thick substrates: Ne, Ar, and CO₂-plated Cu, and bare Cu. The adsorption isotherm data were analyzed self-consistently using the modified Brunauer-Emmett-Teller method for low coverages and the Frenkel-Halsey-Hill vapor pressure relation at high coverages. The analysis establishes the surface area, chemical potential constant, =–d ³, and capacity increases and heats of adsorption of the first and second monolayers of He for each adsorbent. The measured chemical potentials follow the expected inverse-cube law for coverages greater than 2.5 layers, but differ substantially for smaller coverages. We use results of the isotherm analysis to interpret measurements of third sound velocities, and to make precision measurements of the He inert (nonsuperfluid) layer coverages on these substrates     

Vapor Pressure and Heat Capacity Measurement of 3He Adsorbed on 18Å-Pores

We have measured the vapor pressure (0.84 K 3 He adsorbed on pores 18 Å in diameter. The results of the vapor pressure measurement indicate that ³ He film grows up to the second layer. In the first layer, the heat capacity of ³ He shows the same temperature and coverage dependence as ⁴ He, indicating a solid phase. Above a little higher coverage than second layer promotion, heat capacity isotherms for ³ He at several hundred mK increase with coverage while those for ⁴ He decrease. This large heat capacity of ³ He is the nuclear spin heat capacity of the second layer fluid ³ He.     

3He Transverse Excited State Occupation in Thin 3He-4He Films

The discovery that ³ He was occupying transverse excited states at submonolayer coverages in ³ He-⁴ He mixture films on a Nuclepore substrate, was a surprise. In this note we discuss the relationship between theory and experiment in attempting to understand the physics of this behavior. We first discuss various single-atom-limit calculations of the level spacing between the ground-state and first excited state. We then introduce a free, quasi-particle picture for analyzing experimental magnetization step data and compare those results with the single-atom-limit calculations. The experiments clearly show excited state occupation at submonolayer coverages in contradistinction with the calculations. We then briefly discuss a microscopic, semi-phenomenological theory which, in agreement with experiment, yields ³ He occupation of the first excited state at submonolayer coverages. The mechanism is a model ³ He-³ He effective interaction due to one ripplon exchange. This effective interaction is density dependent and very long ranged. It strongly modifies the small-k properties of the ³ He self-energy and, in particular, causes the ground-state to first excited state level spacing to decrease with increasing ³ He areal density.     

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.     

Low Temperature Heat-Capacities of Liquid 3He Thin Films

We have measured the heat capacity of ³ He thin films adsorbed on graphite at an areal density of 15.0 nm ^–2 down to as low as 100 K. The second-layer ³ He behaves as a degenerate 2D Fermi fluid in the whole temperature range we studied. We observed no anomalous behavior in the heat capacity near 3 mK in contradiction to the recent report by other workers. This indicates that possible superfluid transitions would be below 100 K. Instead, a small and temperature-independent contribution to the heat capacity was observed, which we attribute to nuclear-spin degrees of freedom in glassy solid ³ He trapped in substrate heterogeneities.