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.     

Probable Observation of Quantized Vortex Lines Through Solid He Under DC Rotation

We report how one can detect quantized vortices in superfluids contained in cylindrical vessels in well-designed torsional oscillator (TO) experiments under DC rotation. We show the case of an artificial 3D superfluid (Fukuda et al. in Phys. Rev. B 71:212502, 2005) which is made of Kosterlits-Thouless 2D He film condensed on a porous glass substrate with a 3D connected surface of well-controlled pore size. We understand the TO experimental results with an extra energy dissipation peak under DC rotation by considering the circular quantized superflow around each of the vortex lines and interaction with thermally excited 2D vortices as discussed in Fukuda et al. (Phys. Rev. B 71:212502, 2005) and in Nemirovskii and Sonin (Phys. Rev. B 76: 224507, 2007). We discuss here the case of hcp solid ⁴He (see for ex. Balibar and Caupin in J. Phys., Condens. Matter 20:173201-1-19, 2008) and show the evidence of observation of the vortex lines penetration below a supersolid transition temperature (Kubota et al. in J. Low Temp. Phys. 158:572, 2010), T _c , where macroscopic phase coherence is realized. It is found at exactly the same temperature T _c , below which the hysteresis occurrs (Shimizu et ail. in arXiv:0903.1326, 2009). For hcp solid ⁴He we have reported the vortex fluid (VF) state onset temperature (Penzev et al. in Phys. Rev. Lett. 101:065301, 2008) T _o =??500 mK, by detailed drive velocity, V _ac dependence study using TO technique. The TO response of the hcp ⁴He is characterized by the energy dissipation peaked at T _p near 100 mK similar to the behavior in a KT transition. The real supersolid (SS) state occurs at T _c below T _p and much lower than T _o . Our observation of the evidence of vortex lines penetration just below T _c together with the VF state properties gives support for the idea that hcp ⁴He shares some features with the ??new type of superconductors??, where the vortex state, involving the VF as well as various vortex solid states, has been commonly discussed (Fisher et al. in Phys. Rev. B 43(1):130, 1991; Leggett in Quantum Liquids, Oxford University Press, London, 2006).     

On Flow of He II in Channels with Ends Blocked by Superleaks

We report an experimental investigation of a flow of the superfluid phase of ⁴He–He II—thermally induced by a fountain pump through vertical channels of square cross-section with ends blocked by sintered silver superleaks and its decay. We confirm the existence of a weakly temperature dependent critical velocity v _cr ^I of order 1 cm/s, which does not scale with the channel size and is therefore an intrinsic property of the self-sustained vortex tangle of vortex line density L, measured by second sound attenuation. In addition to the previously reported turbulent A-state characterized by L ^1/2=γ(T)(v?v _cr ^I ), where v is the mean superflow velocity through the channel, we have discovered a new B-state characterized by L=β(v?v _cr ^II ), where β seems only weakly temperature dependent. It poses an important question why, at higher flow velocities, the quadratic generation mechanism, so well established in thermal counterflow, ceases to work. We offer a phenomenological model assuming that in the B-state the coarse-grained superflow profile matches the classical parabolic profile, with a finite, temperature dependent slip velocity v _cr ^II of order few cm/s and that a confined viscous normal fluid flow of toroidal form is induced inside the channel due to the mutual friction force. When the fountain pump is switched off, after an initial decay, a confined quasi-viscous flow of a single-component fluid with an effective kinematic viscosity ν _eff(T) establishes, giving rise to the observed exponential decay. The values of ν _eff(T), calculated using our model from the measured decay times, are in agreement with those deduced from other experiments on decaying He II turbulence.     

Pulsed Nuclear Magnetic Resonance on 3He Adsorbed on Bare and 4He Preplated MCM-41 Using DC SQUID Detection

We report low field DC SQUID NMR measurements down to 1.5 K of ³He adsorbed in the pores of the mesoporous molecular sieve MCM-41. In the first experiment measurements were made on ³He adsorbed onto the bare pore walls of MCM-41 with coverages ranging from $n_{^{3}\mathrm{He}}=0.86n_{1}$ to full pores at $n_{^{3}\mathrm{He}}=1.79n_{1}$ , where n ₁ is the coverage for monolayer completion. A second experiment was performed with low ³He coverages ( $n_{^{3}\mathrm{He}}\sim0.01n_{1}$ ) on ⁴He preplated pores, where a crossover to a quasi-1D state is expected to occur at temperatures sufficiently below 700 mK. In both experiments relaxation times T ₁ and T ₂ ^* were measured as a function of temperature and coverage at frequencies from 80 to 240 kHz. The frequency dependence of the linewidth in the pure ³He experiment is extremely weak therefore T ₂ ^* ≈T ₂. The 1.5 K isotherm shows a small minimum in T ₂ ^* at a coverage corresponding to monolayer completion. In the experiment with ⁴He preplating there was no significant change in T ₁ or T ₂ ^* when the ³He coverage was doubled from $n_{^{3}\mathrm{He}}=0.01n_{1}$ to 0.02n ₁ at a ⁴He preplating of $n_{^{4}\mathrm{He}}=1.05n_{1}$ . This suggests that the relaxation times are dominated by single particle effects in the low density regime.     

Superfluid 3He Confined to a Single 0.6 Micron Slab Stability and Properties of the A-Like Phase Near the Weak Coupling Limit

We present the first study of the phase diagram of a thick film of superfluid ³He confined within a nanofabricated slab geometry. This cryogenic microfluidic chamber provides a well-defined environment for the superfluid, in which both the regular geometry and surface roughness may be fully characterised. The chamber is designed with a slab thickness d=0.6 μm and 3 mm thick walls to allow pressure tuning of the effective confinement between 0 and 5.5 bar. Over this range the zero temperature superfluid coherence length, ξ₀, decreases by approximately a factor of two from 77 to 40 nm. Samples have so far been cooled to 350 μK. We use nuclear magnetic resonance (NMR) to ‘finger-print’ the superfluid order parameter, with the static field applied perpendicular to the slab. To enable us to resolve high quality NMR signals from the tiny amount of superfluid ³He in the slab, we have developed a spectrometer using a two stage SQUID amplifier with unprecedented sensitivity. Simple NMR zeugmatography allows the slab signal to be unambiguously distinguished from that of a small bulk liquid region near the fill line. The measured slab transition temperature, T _c ^slab , shows a suppression proportional to ξ ₀ ² , as expected theoretically, but the absolute suppression is less than expected. Below T _c ^slab , an A-like phase is stable over a significant temperature range. A transition temperature, T _AX , is measured on warming from a so far unidentified phase, occurring at lower temperatures, into the A-phase. At the pressures investigated (3 to 5.5 bar) the transition appears to occur at an approximately fixed value of the effective confinement d/ξ(T _AX ). In this geometry we predict that the A-phase will be stable to T=0 at zero pressure.     

Simultaneous Measurements of an Ultrasound and a Torsional Oscillator for Pressurized 4He in a Nanoporous Glass

Recently, torsional oscillator (Yamamoto et al. in Phys. Rev. Lett. 93:075302, 2004) and ultrasound (Kobayashi et al. in AIP Conf. Proc. 128:797, 2007) measurements were carried out for pressurized ⁴He filled in a nanoporous glass (Gelsil), and the superfluid transition temperature T _C shows a different pressure dependence. Thus motivated, we have performed simultaneous measurements with a torsional oscillator and with ultrasound for pressurized ⁴He in Gelsil. T _C is in agreement between the two techniques at all pressures, and the superfluid component above 0.5 K shows most of the same temperature dependence. Furthermore, it was found that the χ-factor (the fraction of superfluid which remains locked to the substrate ) is independent of measuring frequency between the torsional oscillator (kHz-order) and the ultrasound (MHz-order) ranges.     

Effect of annealing temperature on magnetoresistivity, activation energy, irreversibility and upper critical field of the Cu-diffused MgB2 bulk superconductors

This study manifests the change of the pinning mechanism, superconducting and physical properties of Cu-diffused MgB₂ superconductors prepared at different annealing temperature from 650 to 850 °C by means of the magnetoresistivity measurements conducted at several applied magnetic fields in a range of 0–7 T as a function of temperature from 15 to 50 K. The onset (T _c ^onset ) and offset (T _c ^offset ) critical temperatures, activation energies (U₀), irreversibility fields (μ₀H_irr), upper critical fields (μ₀H_c2), residual resistivity ratios (R_R), cross-sectional area fractions (A_F), penetration depths (λ), coherence lengths (ξ) and electronic mean free path ( $ \ell $ ) of the samples are evaluated from the magnetoresistivity curves. Thermally activated flux creep (TAFC) model is used for the determination of the U₀ values; likewise, the μ₀H_irr and μ₀H_c2 values are obtained by resistivity criteria of 10 and 90 % normal-state resistivity, respectively. At absolute zero temperature (T = 0 K), the extrapolation of the μ₀H_irr(T) and μ₀H_c2(T) curves is used to find the μ₀H_irr(0) and μ₀H_c2(0) values of the samples. Moreover, the ξ values are deduced from the μ₀H_c2(0) values when the λ values are calculated from the Ginzburg–Landau parameter ( $ \kappa $ ). It is found that the superconducting and physical properties of the samples improve with the increment of the diffusion-annealing temperature; however, the presence of the magnetic field leading to the decrease of the flux pinning in the samples causes the reduction of these properties. Namely, the T _c ^onset and T _c ^offset values are found to increase from 38.4 to 39.3 K and 36.9 and 38.3 K with the enhancement in the diffusion-annealing temperature at zero filed. Similarly, the U₀ values increase significantly with the increase of the annealing temperature. In fact, the U₀ of 9,162 K belonging to the sample annealed at 850 °C is determined to be the maximum activation energy value. On the other hand, the minimum T _c ^onset of 30.9 K, T _c ^offset of 27.6 K and U₀ of 1,365 K at 7 T applied magnetic field are obtained for the pure sample, indicating that the sample annealed at 850 °C obtains much stronger flux pinning, better crystallinity and connectivity between grains compared to the other samples prepared. Based on these results, the superconducting and physical properties of the MgB₂ superconductors produced in this work are observed to enhance with the increase of the diffusion-annealing temperature as a result of the improvement of pinning abilities, crystallinity and connectivity between grains. The magnetic field and temperature dependence of the activation energy are also discussed.     

Possible Existence of Dense Superfluid 3He-4He Mixture in Aerogel

While studying superfluid ³He of 2.4 MPa in 97.5 %-porosity aerogel with NMR/MRI techniques, we find that the T _C is reduced when more than adequate amount of ⁴He, which covers the surface of silica strands, is introduced. For a sample, whose T _C is reduced to as low as 0.9 mK, we find that the spin diffusion coefficient in the normal phase is increased by a factor of 1.56 both in high temperature region, where ³He-³He scattering dominates, and in low temperature region, where ³He-aerogel scattering dominates. This enhancement is attributed to a modification of Landau parameter $F_{0}^{a}$ from ?0.757 to ?0.62, which is a change towards less ferromagnetic direction. The modification of microscopic quantity could be explained if small amount of ⁴He has homogeneously mixed into liquid ³He in the aerogel.     

Superfluid Phases of 3He in a Periodic Confined Geometry

Predictions and discoveries of new phases of superfluid ³He in confined geometries, as well as novel topological excitations confined to surfaces and edges of near a bounding surface of ³He, are driving the fields of superfluid ³He infused into porous media, as well as the fabrication of sub-micron to nano-scale devices for controlled studies of quantum fluids. In this report we consider superfluid ³He confined in a periodic geometry, specifically a two-dimensional lattice of square, sub-micron-scale boundaries (“posts”) with translational invariance in the third dimension. The equilibrium phase(s) are inhomogeneous and depend on the microscopic boundary conditions imposed by a periodic array of posts. We present results for the order parameter and phase diagram based on strong pair breaking at the boundaries. The ordered phases are obtained by numerically minimizing the Ginzburg-Landau free energy functional. We report results for the weak-coupling limit, appropriate at ambient pressure, as a function of temperature T, lattice spacing L, and post edge dimension, d. For all d in which a superfluid transition occurs, we find a transition from the normal state to a periodic, inhomogeneous “polar” phase with $T_{c_{1}} < T_{c}$ for bulk superfluid ³He. For fixed lattice spacing, L, there is a critical post dimension, d _c , above which only the periodic polar phase is stable. For d<d _c we find a second, low-temperature phase onsetting at $T_{c_{2}} < T_{c_{1}}$ from the polar phase to a periodic “B-like” phase. The low temperature phase is inhomogeneous, anisotropic and preserves time-reversal symmetry, but unlike the bulk B-phase has only $\mathtt{D}_{\text{4h}}^{\text{L}+\text{S}}$ point symmetry.     

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.     

Comparative study on indentation size effect, indentation cracks and superconducting properties of undoped and MgB2 doped Bi-2223 ceramics

This study examines the evaluation mechanism of MgB₂ doped Bi_1.8Pb_0.4Sr₂(MgB₂)_xCa_2.2Cu_3.0O_y (0 ≤ x ≤ 1.0) superconducting ceramics prepared by conventional solid-state reaction method via dc resistivity, X-ray diffraction analysis (XRD), scanning electron microscopy (SEM) and Vickers micro hardness (H_v) measurements. Variation of room temperature resistivity, critical transition temperatures (onset and offset), phase purity, cell parameter, texturing, grain connectivity, surface morphology, crystallinity and H _v values of the materials are deduced and compared with each other for the determination of the optimum doping level in the Bi-2223 system. It is found that all the properties given above depend strongly on the MgB₂ concentration. From dc resistivity investigations, each sample studied exhibits the superconducting behavior below their variable offset critical temperature values. The maximum onset (T _c ^onset ) and offset (T _c ^offset ) temperatures are found to be about 121.3 and 114.1 K, respectively, for the sample doped with x = 0.05. The minimum T _c ^onset of 118.6 K and T _c ^offset of 109.4 K are observed for the sample doped with x = 1.0. Similarly, XRD and SEM examinations indicate that there is an improvement in the crystal structures and surface morphologies of the superconducting materials with the increment of the MgB₂ inclusions in the Bi-2223 system up to x = 0.05 beyond which the crystallinity, grain connectivity and surface morphology start to degrade regularly and in fact reach to the worst structure appearance for the doping level of x = 1.0. Furthermore, the H_v measurement results being analyzed by Meyer’s law, proportional sample resistance (PSR), modified PSR, elastic–plastic deformation model, Hays–Kendall (HK) approach, Indentation-induced cracking model (IIC) allow us to derive the mechanical properties of the superconducting samples for the potential technological and industrial applications. According to the results obtained, HK approach, among the mechanical analysis methods, is determined as the most successful model for the samples (doped with x = 0, 0.1, 0.3, 0.5 and 1.0) exhibiting indentation size effect behavior whereas the IIC model is noted to be superior to other models for the other samples (doped with x = 0.01, 0.03 and 0.005) presenting reverse indentation size effect feature.     

The role of Lu doping on microstructural and superconducting properties of Bi2Sr2CaLuxCu2Oy superconducting system

Lutetium (Lu) added Bi₂Sr₂CaLu_xCu₂O_y superconducting samples with x = 0, 0.1, 0.3, 0.5, 0.7 and 1.0 are prepared by solid-state reaction method and annealed at 840 °C for 50 h. The heating and cooling rates of the furnace are adjusted to be 10 and 3 °C/min, respectively. For the comparison, undoped sample is subjected to the same annealing conditions. The prepared samples are characterized using X-ray powder diffraction (XRD), scanning electron microscope (SEM), energy dispersive spectroscopy (EDS), and dc resistivity (ρ?T) measurements. The volume fraction, grain size, texturing and lattice parameters are determined from the XRD measurements. The microstructure, surface morphology and element composition analysis of the samples produced are investigated by SEM and EDS measurements, respectively. Moreover, the resistivity (at room temperature), critical transition (onset and offset) temperature, variation of transition temperature and hole carrier concentration values of the samples studied are estimated from the dc resistivity measurements. According to the results obtained, the samples prepared exhibit the polycrystalline superconducting phase with less intensity of diffraction lines with the enhancement in the Lu addition due to the effect of the minor phase (Bi-2201). The lattice parameter c and volume fraction of Bi-2212 phase reduce systematically whereas the cell parameter a and minor phase fraction enhance with ascending the Lu content in the system, leading to the decrement in the superconducting properties. Scanning electron microscope measurements show that not only do the surface morphology and grain connectivity degrade but the grain sizes of the samples decrease with the increase of the Lu addition, as well. Energy dispersive spectroscopy results reveal that the Lu³⁺ ions might enter into the crystal structure by replacing Sr²⁺ ions, confirming why the superconducting properties of the pure sample are more superior to the samples doped. At the same time, dc resistivity results obtained show that the room temperature resistivity systematically increases with the enhancement of the Lu content as a result of the hole filling when the onset (T _c ^onset ) and offset (T _c ^offset ) temperatures determined from the resistivity curves decrease from 99.5 to 93.0 K and 85.0 to 60.0 K, respectively, illustrating not only the increment in the relative percentage of Bi-2201 phase formation and the reduction of the mobile carrier concentration but also the presence of impurities and weak links between the superconducting grains.     

NMR Studies of 3He Impurities in 4He in the Proposed Supersolid Phase

Preliminary results are reported for measurements of the NMR relaxation times of very dilute ³He in samples of solid ⁴He at low temperature, 0.25 K <T< 1.3 K. The results were obtained for carefully prepared samples with different ³He concentrations. The measurements of the spin-spin relaxation time, T ₂, show several interesting features. A temperature independent plateau attributed to the exchange motional narrowing is observed down to the lowest temperature studied, and the observed variation of T ₂ with ³He concentration favors the nonlinear theory suggested by Landesman. The best fit to the data is given by T ₂ ∝ x ₃ ^?1.89±0.1 rather than x ₃ ^?1 . No evidence of an exchange-phonon bottleneck for the spin-lattice relaxation is seen down to 25 mK. The vacancy activation energy is determined to be 13.5±0.3 K for a sample with x ₃=5×10^?4 and molar volume 20.9 cm³.     

Transition into the Supersolid (SS) State, Supersolid Density �� ss and?the Critical Velocity V c to Destroy the?SS State

We have reported the onset of the vortex fluid (VF) state in hcp solid ⁴He below an onset temperature T _o (Penzev et al. in Phys. Rev. Lett. 101:065301, 2008). We have also shown the transition from the VF state into the supersolid (SS) state, which is characterized by a supersolid density and macroscopic coherence, below a transition (Kubota et al. in J. Low Temp. Phys. 158:572, 2010; Shimizu et al. in arXiv:0903.1326, 2009; Yagi et al. in J. Low Temp. Phys., QFS2010, 2011) at T _c , as well as a critical velocity for the destruction of the SS state. Here we describe further confirming evidence of the phase transition into the SS state, namely, we report here some other observations than the hysteretic behavior. We find some other features which indicate a clear change of the properties in the hcp ⁴He below the same T _c as hysteretic behavior, reported in Kubota et al. (J. Low Temp. Phys. 158:572, 2010), Shimizu et al. (arXiv:0903.1326, 2009), Yagi et al. (J. Low. Temp. Phys., QFS2010, 2011). It was discovered by detailed study of the torsional oscillator (TO) drive velocity V _ac dependence of the nonlinear rotational susceptibility (NLRS) of the VF state. We discuss the features of the VF to SS transition. The large ratio between T _o and T _c may indicate large fluctuations of the system and it may give a basis for the vortex state (Fisher et al. in Phys. Rev. B 43(1):130, 1991) appearance in the hcp ⁴He, as seen in the new type of superconductors. We discuss a question related to the observation of the VF phase with specific dynamic features (Nemirovskii et al. in arXiv:0907.0330, 2009), coexisting with the SS phase and a possible new kind of phase transition coexisting with the SS phase and a possible new kind of phase transition for the VF to SS transition.     

A model for paramagnetic Fermi systems

We develop a model for paramagnetic Fermi liquids. This model has both direct and induced interactions, the latter including both density-density and current-current response. The direct interactions are chosen to reproduce the Fermi liquid parametersF ₀ ^s ,F ₀ ^a ,F ₁ ^s and to satisfy the forward scattering sum rule. TheF ₁ ^a andF ₁ ^s,a for1>1 are determined self-consistently by the induced interactions; they are checked against experimental determinations. The model is applied in detail to liquid³He, using data from spin-echo experiments, sound attenuation, and the velocities of first and zero sound. Consistency with experiments gives definite preferences for values ofm*. The model is also applied to paramagnetic metals. Arguments are given that this model should provide a basis for calculating effects of magnetic fields.     

The Decay of Forced Turbulent Coflow of He II Past a Grid

We present an experimental study of the decay of He II turbulence created mechanically, by a bellows-induced flow past a stationary grid in a 7×7 mm² superfluid wind tunnel. The temporal decay L(t) originating from various steady-states of vortex line length per unit volume, L ₀, has been observed based on measurements of the attenuation of second-sound, in the temperature range 1.17 K<T<1.95 K. Each presented decay curve is the average of up to 150 single decay events. We find that, independently of T and L ₀, within seconds past the sudden stop of the drive, all the decay curves show a universal behavior lasting up to 200 s, of the form L(t)∝(t?t ₀)^?3/2, where t ₀ is the virtual origin time. From this decay process we deduce the effective kinematic viscosity of turbulent He II. We compare our results with the bench-mark Oregon towed grid experiments and, despite our turbulence being non-homogeneous, find strong similarities.     

The High Pressure Superconductivity of CaLi2 Compound: The Thermodynamic Properties

The thermodynamic properties of the superconducting state in CaLi₂ at 60 GPa have been described in the paper. The numerical analysis has been carried out in the framework of the Eliashberg formalism. It has been shown that: (i) the critical value of the Coulomb pseudopotential is equal to 0.20, which corresponds to the value of 1795 meV for the Coulomb potential; (ii) the critical temperature (T _C ) cannot be correctly calculated by using the Allen-Dynes (AD) formula; (iii) the dimensionless ratios: $T_{C}C^{N} (T_{C} )/H^{2}_{C} (0 )$ , (C ^S (T _C )?C ^N (T _C ))/C ^N (T _C ) and 2Δ(0)/k _B T _C take the non-BCS values: 0.157, 1.78 and 3.85, respectively. The symbol C ^N represents the specific heat in the normal state, C ^S denotes the specific heat in the superconducting state, H _C (0) is the thermodynamic critical field near the temperature of zero Kelvin, and Δ(0) is the order parameter; (iv) the ratio of the electron effective mass ( $m^{\star}_{e}$ ) to the electron band mass (m _e ) assumes a high value, in the whole range of the temperature, where the superconducting state exists. The maximum of $m^{\star}_{e}/m_{e}$ is equal to 2.15 for T=T _C .     

3He Vapor Pressure near Its Critical Point

Between 0.65 K and 3.2 K, the temperature dependence of the vapor pressure P of ³He is defined by the International Temperature Scale of 1990 (ITS-90). However, the ITS-90 vapor pressure equation was not designed to be consistent with the scaling law required for the second temperature derivative of the vapor pressure in the vicinity of the liquid-vapor critical point. In this paper, two scaling-type equations are used to describe the ³He vapor pressure in the region near the critical point. The first scaling equation contains two unknown coefficients which are obtained by taking as reference the temperature $\bar{T}$ at which the product (T _c ?T)P presents a maximum ( $\bar{T}=2.56736$  K). The second scaling equation contains three unknown coefficients which are obtained by using as references $\bar{T}$ and T _up=3.2 K, the upper value of the ITS-90 interval. In both equations we take for the critical temperature and pressure the values T _c =3.31554 K and P _c =114?632.7 Pa. The proposed equations, specially the second one, are satisfactorily compared with experimental data for P and dP/dT within the temperature range (T _c ?T)/T _c ≤0.065 and with semiempirical data for d ² P/dT ² within the temperature range 0.0001≤(T _c ?T)/T _c ≤0.03.     

Superfluid State of 4He on Graphane and Graphene–Fluoride: Anisotropic Roton States

We explore the phase behavior of Helium films on two variants of graphene: graphane (graphene coated with H, denoted GH) and graphene–fluoride (GF). A semiempirical interaction with these substrates is used in T=0 K Path Integral Ground State and finite temperature Path Integral Monte Carlo simulations. We predict that ⁴He forms anisotropic fluid states at low coverage. This behavior differs qualitatively from that on graphite because of the different surface composition, symmetry and spacing of the adsorption sites. The ⁴He ground state on both substrates is thus a self-bound anisotropic superfluid with a superfluid fraction ρ _s /ρ lower than 1 due to the corrugation of the adsorption potential. In the case of GF such corrugation is so large that ρ _s /ρ=0.6 at T=0 K and the superfluid is essentially restricted to move in a multiconnected space, along the bonds of a honeycomb lattice. We predict a superfluid transition temperature T? 0.25 (1.1) K for ⁴He on GF (GH). We have studied the elementary excitation spectrum of ⁴He on GF at equilibrium density finding a phonon–maxon–roton dispersion relation that is strongly anisotropic in the roton region. We conclude that these new platforms for adsorption studies offer the possibility of studying novel superfluid phases of quantum condensed matter.     

Sublimation study of BiBr3

Steady-state sublimation vapour pressures of anhydrous bismuth tribromide have been measured by the continuous gravimetric Knudsen-effusion method from 369.3 to 478.8 K. Additional effusion measurements have also been made from 435.4 to 478.6 K by the torsion—effusion method. Based on a correlation of Δ_sub H ₂₉₈ ⁰ and Δ_sub S ₂₉₈ ⁰ , a recommended p(T) equation has been obtained for BiBr₃(s) $$\alpha - {\rm B}i{\rm B}r_3 :log{\text{ }}p = - C\alpha /T - 12.294log{\text{ }}T + 5.79112 \times 10^{ - 3} {\text{ }}T + 47.173$$ with Cα=(Δ _subH ₂₉₈ ⁰ +20.6168)/1.9146×10^-2 $$\beta - {\rm B}i{\rm B}r_3 :log{\text{ }}p = - C\beta /T - 23.251log{\text{ }}T + 1.0492 \times 10^{ - 2} {\text{ }}T + 77.116$$ with Cβ=(Δ _subH ₂₉₈ ⁰ +46.2642)/1.9146×10^-2 where p is in Pa, T in Kelvin, Δ _sub H ₂₉₈ ⁰ in kJ mol^?1. Condensation coefficients and their temperature dependence have been derived from the effusion measurements.