Statics and dynamics in binary mixtures near the liquid-vapor critical line

Static and dynamic properties are investigated near the liquid-vapor critical line in fluid binary mixtures. Simple expressions are given for thermodynamic derivatives and transport coefficients in terms of parameters characterizing the coexistence surface in thep-T- space, where is the chemical potential difference. It becomes possible to understand special crossover phenomena occurring when fluids are nearly azeotropic or when the concentration dependence of the critical temperatureT _c (X) [or the critical pressurep _c (X)] is weak. The results are used to explain recent data on³He-⁴He mixtures that apparently contradict previous theories. As a by-product, general relations are found for correlation functions of dynamic variables and thermodynamic derivatives in fluid mixtures.     

Universal behavior of3He-4He mixture films near the Kosterlitz-Thouless transition

We report measurements of the convective thermal conductance of³He-⁴He mixture films near the Kosterlitz-Thouless transition. The thickness of our⁴He films is 14.7 and 19.1 Å above the inert layer and the³He concentration ranged from 0.033 to almost 2%. The thermal response is tested for the critical behavior as observed in pure films, and it is found to be preserved in the mixture films case. However, the parametersb, D/a ² andT _c exhibit a strong dependence on the concentration. The mixture film conductance at fixedT-T _c is found to decrease upon addition of³He implying a decrease in the 2D correlation length. Mixture films thus exhibit 2D behavior over a narrower temperature range than pure films. Further, for temperaturesT _c , the largest measurable conductance decreases sharply with the addition of³He. We attribute this behavior to a³He-⁴He scattering mechanism and a³He induced free-vortex density.     

Critical and tricritical dynamics in3He-4He mixtures

A new formalism is presented to study the critical and tricritical dynamics of³He-⁴He mixtures near the superfluid transition for arbitrary concentration. In this fluid two conserved variables, the molar concentrationX and the entropys, are twofold coupled to a complex order parameter ψ first in the dynamic equations reversibly and second in the free energy dissipatively. However, at an intermediate concentrationX=X _D (which is 0.37 at the saturated vapor pressure) a linear combination ofX ands is found to be asymptotically decoupled from ψ both reversibly and dissipatively. There, dynamic renormalization group equations reduce to those of pure⁴He (or those of the F model) and some dynamic properties are common to those of pure⁴He. For example, atX≈X _D , the gradient ?(T?T _λ ) under heat flow goes to zero without³He mass flow, whereT _λ is the critical temperature, dependent onX, and the thermodiffusion ratio loses the singularity with the critical exponent α. Our dynamic renormalization group equations take into account the above two nonlinear couplings and can be used for any concentrations. Furthermore, using a linear response scheme, general relations are obtained among the kinetic coefficients. As a result the thermal conductivity on the λ line is found to be exactly proportional toX ^?1 at smallX. The coefficient in front ofX ^?1 can be expressed in terms of the diffusion constant of an isolated³He molecule in⁴He.     

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.     

Bound states of3He in3He-4He mixture films

³He atoms dissolved in super fluid⁴He may form aimers (³He)₂ in twodimensional (2D) geometries. We study dimer formation in films of dilute³He-⁴He mixture. After designing a schematic³He-⁴He interaction potential we calculate the dimer binding energy for various substrates. It is shown that³He impurity states localized near the substrate give rise to the largest magnitudes of the binding energies.Unité de Recherche des Universités Paris XI et Paris VI associée au CNRS.     

Free energy and specific heat of critical films

Based on the field-theoretical renormalization group theory forO(N) symmetric systems in 4 — dimensions the free energy of critical films confined between two parallel plates at distanceL is analyzed. For temperatures aboveT _c,bulk the universal scaling functions are presented and discussed. At bulk criticality the scaling functions reduce to the universal Casimir amplitudes. Using these field-theoretical results quantitative predictions on the specific heat of⁴He films and films of³He-⁴He mixtures close to the onset of superfluidity are made. Wetting of a substrate by⁴He or³He-⁴He mixtures close to the — transition is studied in detail and thus the full scaling function is probed.     

Development of a thermodynamic model for a cold cycle 3He-4He dilution refrigerator

A thermodynamic model of a ³He-⁴He cold cycle dilution refrigerator with no actively-driven mechanical components is developed and investigated. The refrigerator employs a reversible superfluid magnetic pump, passive check valves, a phase separation chamber, and a series of recuperative heat exchangers to continuously circulate ³He-⁴He and maintain a ³He concentration gradient across the mixing chamber. The model predicts cooling power and mixing chamber temperature for a range of design and operating parameters, allowing an evaluation of feasibility for potential ³He-⁴He cold cycle dilution refrigerator prototype designs. Model simulations for a prototype refrigerator design are presented.     

Thermodynamic Properties of Liquid 3He-4He Mixtures Between 0–10 bar below 1.5 K

The thermodynamic properties of liquid ³He-⁴He mixtures at pressures of up to 10 bar and temperatures below 1.5 K are determined. The calculations are based on previously determined thermodynamic properties of ³He-⁴He mixtures at saturated (zero) pressure, and available experimental measurements of the molar volume, which are used to determine an expression for the molar volume. Since available experimental data for mixtures at higher pressures are restricted to low temperatures (below about 0.7 K), the calculated molar volumes at high pressure and high temperature are largely based on pure ³He and pure ⁴He data.     

Thermal equilibration of fluids near the liquid-vapor critical point:3He and3He-4He mixtures

We study the temperature-equilibration process of fluids at constant volume in a thermal conductivity cell, where an initial temperature gradient relaxes to zero. The calculation is performed in the linear approximation for a pure fluid and a binary mixture. Near the critical point of the pure fluid, the adiabatic heating process, which takes place at constant volumeV, causes equilibration to proceed four times faster whenC _P /C _V 1 than for the process at constant pressureP. For the mixtures, the relaxation rate enhancement at constantV compared with constantP is restricted to a temperature region where the coupling between temperature and mass diffusion is small. The predictions are compared with experimental results for³He and for two³He-⁴He mixtures along their critical isochores. Finally, we discuss the thermal relaxation in the two-phase (liquid-gas) and one-phase (gas) regimes at the critical density, as measured with a conductivity and a calorimetry cell. The contrasting behavior for³He and a³He-⁴He mixture in these two regimes and under these different constraints is pointed out and discussed.     

Distillation of Nuclear Polarization of 3He-4He Mixtures in Very High Magnetic Fields

We have used the method of fractional distillation to produce an enhanced nuclear polarization of a saturated ³ He- ⁴ He mixture. For the experimental study reported in this paper, we have developed an all plastic distillation setup, which allows high ³ He circulation rates at low temperatures (18 mol/s at 150 mK) up to the highest magnetic fields (22.5 T). The magnetization has been measured with a torque magnetometer. The nuclear magnetic relaxation time T₁ of the ³ He- ⁴ He mixture was found to increase with the square of the magnetic field, indicating that T₁ is dominated by surface relaxation. As a consequence, the enhancement of the magnetization due to the distillation process, which is amongst others proportional toT₁ , increased also with the square of the magnetic field. At the highest field at 140 mK, a polarization of 8% of the ³ He- ⁴ He mixture has been obtained, 1.6 times the equilibrium value. Various ways to improve the set-up are discussed.     

Quasi-2D Flows of 3He – 4He Mixtures

Transport in degenerate ³ He- ⁴ He mixtures in quasi-2D flow channels is discussed. The quasiparticle mean free path combines particle-wall and particle-particle collisions including the interference between them. The temperature, concentration, and polarization dependences of the transport coefficients allow easy extraction of the correlation parameters of random surface roughness from transport data.     

Instability of vortex lines in the presence of axial normal fluid flow

We show that a normal mode analysis of the complete Hall two-fluid equations in rotating He II yields a critical velocity for axial normal fluid flow which is identical to the critical velocity derived in an earlier paper from the superfluid equation alone. We also present a simplified derivation of the critical velocity based on consideration of the forces acting on an isolated vortex line. The analysis is extended to ³ He- ⁴ He solutions and it is shown that rather small impurity concentrations can greatly increase the critical heat current in axial thermal counterflow.     

Thermodynamic Properties of Liquid 3He-4He Mixtures Between 0.15 K and 1.8 K

Thermodynamic property relations for liquid ³He-⁴He mixtures at saturated pressure based on experimental measurements of the specific heat are determined. The relations are valid over the entire concentration range and for temperatures from 0.15 K to 1.8 K. Thermodynamic properties are first determined in the two-phase region, and then extended to the single-phase He-II and He-I regions. The results are in good agreement with some other ³He-⁴He mixture property data, though the scarcity of experimental data in large parts of the region of interest precludes a more thorough comparison. We derive some thermodynamic quantities that may be useful to the analysis of heat exchangers and throttles with superfluid ³He-⁴He flows. We also discuss how these properties can be extended to higher pressures.     

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.     

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.     

The solid-liquid surface tension at a helium/cesium interface

The existence of a wetting transition for helium adsorbed on cesium provides an experimental opportunity to investigate the solid-liquid surface tension. We have extracted the temperature dependence of the solid-liquid surface tension at the⁴He/Cs interface from our earlier measurements of the wetting temperature of pure⁴He on thin layers of cesium overlaying gold. More recently we have measured the wetting temperature as a function of the³He concentration for³He-⁴He mixtures. An analysis of these experiments paralleling Andreev's investigation of the free surface reveals³He bound states at the helium/cesium interface.This work was supported by NSF grant DMR-9223775.     

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.     

Magnetic behavior of weak links in bulk superconducting YBa2Cu3O7−x: Ag composite

The magnetization of a polycrystalline composite YBa₂Cu₃O_7?x :Ag_0.1 in the superconducting state is measured in the presence of a small a.c. magnetic field. With increase in field amplitude, the magnetizationM(t) changes its shape from nearly sinusoidal to square-wave like and then to a two-peak structure. A similar behavior of the magnetizationM(t), calculated from the critical-state model with intergranular critical currentJ _c =αc[μ(H ₀ +¦H¦)]^?1 is obtained. A very good fit is found between the theoretical and experimental results, and the parameters of the model are estimated.