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.     

Investigation of the lifetime of longitudinal phonons at GHz frequencies in liquid and solid4He

The attenuation of longitudinal 1-GHz phonons was measured as a function of temperature in liquid ⁴ He at svp and at 23 bar as well as in hcp ⁴ He at 36 bar. The lifetime of the phonons which were generated by stimulated Brillouin scattering was determined optically by a probing light pulse. The results in liquid ⁴ He are discussed in terms of relaxation processes in the phonon and roton gas and are in good agreement with existing work. The attenuation in hcp ⁴ He, which approximately shows aT ⁴ temperature dependence, is attributed to three-phonon processes with longitudinal thermal phonons. A quantitative comparison with Landau-Rumer theory gives satisfactory agreement with the data. No effect of phonon dispersion on sound attenuation is found down to 0.8 K.     

Narrow-Angle Beams of Strongly Interacting Phonons

We demonstrate that narrow-angle phonon pulses of low energy phonons in liquid ⁴ He are strongly interacting and rapidly come into equilibrium within a narrow cone in momentum space. The effect of collimation on such a system is to strongly reduce the axial phonon flux. This gives a method of separating high and low energy phonons.     

NMR study of the solidification and melting of3He in porous glasses

TheP-T phase diagrams of the liquid-solid phase transition of³He in three porous glasses with different pore sizes have been determined from spin-lattice relaxation measurements in the temperature range 0.5–4.2 K. The onset of solidification of³He in the pores occurs at excess pressure over the bulk phase transition. The excess pressure depends on the pore size. A model of the phase transition in small pores which takes into account the contribution of the surface energy to the free energy is described and compared with experimental results. TheT ₁ relaxation mechanism of³He in the pores is found to be due to the surface relaxation when³He is in the liquid phase and due to the relaxation of bulk solid³He when it is in the solid phase.     

Relaxation of Anisotropic Systems of Quasi-particles in Superfluid Helium

We investigate the relaxation of boundless and anisotropic quasiparticle systems, in liquid ⁴He, with given initial values of momentum and energy densities. The evolution is governed by the dispersion curve which determines the interactions between quasi-particles. The first stage of the relaxation is the rapid creation of a quasistationary low-energy phonon system. This system transforms to another quasistationary system which contains high-energy phonons as well as low energy-phonons. Finally the system evolves to a stationary system of phonons and rotons. The temperature T and the drift velocity u are found for the closed quasi-particle system during its relaxation. This allows us to study the quasi-particle energy and the angular distribution of momentum, and the thermodynamic functions of the quasi-particles system, at each of stage of its evolution.      

Theory of heat transfer between phonons and quasiparticles in dilute solutions of3He in4He

A calculation of the heat transfer rate between phonons and quasiparticles in solutions of³He in⁴He is described. The phonon-quasiparticle interaction of Baym and Ebner is used, and two processes contributing to the heat transfer are considered. One process is phonon absorption and emission with the excess momentum distributed among the quasiparticles by quasiparticle-quasiparticle interactions. The other is quasielastic scattering of the phonons by quasiparticles. Numerical results are presented for 0.1% and 0.5% solutions. The calculated heat transfer rate for the 0.1% solution is in agreement with the one reported experiment atT40 mK, but is too small at higher temperatures (50T60 mK).     

Phonon reflection at a silicon-3He interface

The reflection of heat pulses at an interface between the (111) surface of silicon and liquid ³He has been measured for heat pulse temperatures from 1.4 to 9K. The measurements were made with the silicon-helium temperature equal to 0.4 or 1.8K. The detectors were cadmium or aluminum superconducting bolometers. Longitudinal and transverse phonons incident nearly perpendicularly on the surface had reflection coefficients of 1 and 0.8, respectively, independent of pulse temperature. Transverse phonons incident at a large angle and diffusely reflected had reflection coefficients dropping from 0.7 at 1.5K to 0.4 at 9K. The results are in broad agreement with previous measurements on solid-⁴He interfaces obtained from heat pulse and monochromatic phonon experiments.Equipment grants and financial support provided by the National Research Council of Canada and the School of Graduate Studies and Research.     

Possible 3He Boltzmann Gas Formed on Three-Dimensional Nanopores Preplated with 4He

We have measured the heat capacity of ³He adsorbed on three-dimensionally connected nanopores, 2.7 nm in diameter, preplated with about 1.3 atomic layers of ⁴He. At low coverages of ³He, the ³He heat capacity is roughly constant at the measured temperatures between 0.1 and 1 K. Its molar heat capacity is on the order of the gas constant R, between 1.1R and 1.8R. This suggests a Boltzmann gas state of the adsorbed ³He. At high coverages, the heat capacity is likely approaching linear in T at low temperatures, which suggests a degenerate state at further lower temperatures.     

The Universality of Energy Spectrum of Phonon and Vacancy Excitations in Solid Helium

The most careful measurements on the specific heat C(T) and dP/dT (P is the pressure, T is the temperature) are analysed using a model where the thermodynamic properties of ³He and ⁴He crystals are described by a sum of phonon and vacancy contributions. The analysis, in which the Debye model of phonons and the Hetherington model for wide-band vacancies are used, yields a universal molar volume depence for the Debye temperature Θ _D and the vacancy activation energy Q _V , and constant values for the Grüneisen parameters in the molar volume range of 14–24 cm³/mol. The Θ _D values are found to be in good agreement with the data obtained from the elastic moduli measurements and with Horner’s theoretical calculations. The Q _V values are in good agreement with the X-ray measurements on the temperature dependences of ³He and ⁴He crystal lattice parameters analysed in terms of the Hetherington model.     

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.     

Inelastic Neutron Scattering Studies of First Order Phase Transitions in bcc Solid 4He

We report inelastic neutron scattering studies of the [110] transverse phonon branches of bcc ⁴He near the bcc-hcp transitions on the solid-liquid coexistence line and near the melting transition. The question behind the experiment was whether these transitions in a quantum solid are in any way different from what one observes in usual materials. In contrast to large softening of the T₁ branch seen near the bcc-hcp transition in group IV metals, we found that the transverse phonons in bcc ⁴He do not soften at all. Altough visual studies of the crystals near the transition are consistent with a martensitic transformation, neutron scattering indicates that the transition in solid ⁴He is different than in metals. Thus, the mechanism of the bcc-hcp transition remains an open question. Similar study done near the melting transition indicates that none of the phonons measured in the present experiment is affected by melting, which rules out a mechanical instability of the bulk as a mechanism of melting. Finally, in addition to the phonons, we observed a new feature at q=0 and at an energy transfer of 1.23meV which we attribute to neutron scattering by point defects. Similarly to the phonons, this feature did not change near any of the phase transitions.     

Interpretation of Temperature-Dependent Resistivity of La–Pb–MnO3: Role of Electron–Phonon Interaction

The present paper deals with the theoretical investigation of temperature-dependent resistivity of the perovskite manganites La_0.78Pb_0.22MnO_3-δ within the framework of the classical electron–phonon model of resistivity, i.e., the Bloch–Gruneisen model. Due to inherent acoustic (low-frequency) phonons (ω_ac) as well as high-frequency optical phonons (ω_op), the contributions to the electron–phonon resistivity have first been estimated. At low temperatures the acoustic phonons of the oxygen-breathing mode yield a relatively larger contribution to the resistivity as compared to the contribution of optical phonons. Furthermore, the nature of phonons changes around T = 215 K exhibiting a crossover from an acoustic to optical phonon regime with elevated temperature. The contribution to resistivity estimated by considering both phonons, i.e., ω_ac and ω_op, when subtracted from experimental data, infers a T^4.5 temperature dependence over most of the temperature range. Deduced T^4.5 temperature dependence of ρ_diff = [ρ_exp − {ρ₀ + ρ_e-ph( = ρ_ac + ρ_op)}] is justified in terms of electron–magnon scattering within the double exchange (DE) process. Within the proposed scheme, the present numerical analysis of temperature dependent resistivity shows similar results as those revealed by experiments     

Quantum evaporation of 4He

Quantum evaporation is the process in which an excitation is annihilated at the free surface and an atom is ejected. With liquid ⁴He the excitation is a phonon or a R ⁺ or R ^– roton. The conditions necessary to observe this phenomenon are discussed and the various experiments that demonstrate the conservation of energy and parallel component of momentum are reviewed. It is shown that phonons, with energy >10K, and rotons have long lifetimes, tending to as T 0. These excitations can be injected into liquid He and collimated into beams so that angular and scattering measurements can be performed.     

Adsorption Potentials and Film Growths of 4He in Nanometer Pores of FSM-16 (2.8 nm) and HMM-2 (2.7 nm)

No Heading To find the one- and the three-dimensionalities for the superfluid onset of the ⁴He films formed in nanopores, we have been studying ⁴He adsorbed on FSM-16 and HMM-2 that have pores of almost the same diameter, 2.8 and 2.7 nm, but ID and 3D connections of the pores, respectively. For these two substrates, the adsorption potential profile and layer-by-layer growth of ⁴He films were observed by the precise measurement of the vapor pressure for adsorption. The isothermal compressibility _T, the film thickness d, and the isosteric heat q_st of adsorption are derived from the vapor pressure. _T and d indicate that ⁴He adatoms form uniform layers up the second layer on both substrates. Almost the same q_st for both substrates suggest that the adsorption potential is the same between these SiO₂-based substrates. These results suggest that FSM-16 and HMM-2 are ideal substrates to use in investigating the dimensionality of the superfluid onset.PACS numbers: 67.40.–w, 67.70.+n     

Fluid States of Helium Adsorbed in Nanopores

We have studied helium adsorbed in new nanopores which have regular structures from nano-cage to three-dimensionally (3D) connected pores. Adsorption potential and layer formation of the adsorbed helium are observed by the vapor pressure for the adsorption. New paradigms of zero-D and 1D helium fluids are realized in nano-cages and nano-channels, respectively. The superfluid onsets (transitions) in the 1D and 3D nanopores show obvious dependence on the pore connections. The superfluid in the 3D pores has properties similar to the Bose-Einstein condensation of the 3D Bose atomic gas. The films of the ³He gas formed in the ⁴He preplated nanopores show the dimensional crossover depending on the pore connection: from the 2D Boltzmann gas to a 1D or 3D gas state with decreasing temperature. This gas changes to the degenerate state in each dimension at the lower temperatures. Extremely high frequency measurements of the helium adatoms on flat substrate determined the superfluid vortex parameters of the ⁴He films, and revealed a slippage (decoupling) of the helium adatoms in the non-superfluid state.     

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.     

Nuclear Spin-Kinetics of 3He in Carbonizates with Various Porosity

In the present work the NMR relaxation of the gaseous ³He inside carbonizate pores was investigated at temperature 1.5 K. The carbonizates synthesized from fructose and wood of the tropical tree astronium were used. The dependences of the ³He relaxation rates T ₁ and T ₂ on the gas pressure and the amount of the ³He atoms adsorbed on the surface of pore walls were measured. The analysis of obtained results reveals the existence of the ³He phases inside carbonizate—adsorbed solid layers, liquid and gas.     

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.     

Contribution of Phonon Drag to the Knudsen Effect in the Superfluid Mixtures of Helium Isotopes

Contribution of phonon drag to the Knudsen effect in ³ He- ⁴ He mixtures is studied. A set of the model kinetic equations for ³ He-quasiparticles and phonons is solved. The effect of non-equilibrium in the phonon system on the formation of the steady state of ³ He- ⁴ He mixture in restricted geometry is investigated.     

Phonon Interactions in an Anisotropic Phonon System Leading to a Suprathermal Distribution in Liquid 4He

The relaxation rates of high energy phonons are calculated for a highly anisotropic phonon system which can be realised by phonon pulses in liquid ⁴He. We find that the creation rate for these phonons is very much greater than the decay rate over almost all of the momentum range. As a consequence, we have the unusual behaviour of the distribution function, for the high energy phonons, not being the Bose–Einstein distribution function. From our results we expect that the distribution function will be very much greater than the Bose–Einstein one and also to have a quite different momentum dependence. The analytic expressions which are derived, enable us to explain the physical reasons for a suprathermal distribution of high energy phonons which are predicted to occur in highly anisotropic phonon systems.