Density Response and Equilibration in a Pure Fluid Near the Liquid-Vapor Critical Point: 3He

We report measurements of the local density response inside a quasi 1-D horizontal ³ He fluid layer to a step-like change T of the boundary temperature, where |T| 80 K and much smaller than |T – T_c| where T_c is the critical temperature. These experiments used a new cell design, described in the text, and were carried out along the critical isochore both above and below T_c. The observed temporal and spatial density response (t, z) and its equilibration time are described adequately by the relations developed from the thermodynamic theory of Onuki and Ferrell. We verify that over the temperature range of low stratification, where computer simulations and closed-form calculations can be compared, they are in exact agreement. The systematic differences of experimental results from predictions can be accounted for by the departure of the cell from the ideal 1-D geometry. The much larger disagreement between the experimental and predicted equilibration time scale in earlier experiments is also explained. Finally, deviations from linearity observed in the density response for steps |T| larger than 90 K are reported and the implications of such nonlinearity for the (t, z) profile and especially the effective relaxation time _eff are analyzed. We also discuss the predicted onset of convection near T_c for the conditions in our experiment. In the Appendix, the likely sources for systematic deviations in the density response function for the experimental cell from calculations in the ideal 1-D geometry are presented and their effects calculated. The so-obtained response function Z_F(, z) is compared with previously published data.     

Liquid-Vapor Coexistence in Two-Dimensional 3He-4He Mixtures

We present results from an ongoing study of the Liquid (L)-Vapor (V) coexistence boundary for single layer mixtures of ³ He and 4He adsorbed on two layers of H ₂ plating graphite. We are studying mixtures with ³ He molar fractions, x, of approximately 0.05, 0.1, 0.35, and 0.5, which we compare with previously published data for the pure isotopes. For the concentrations under study, we have approximate determinations of the L- V critical temperatures and of the low temperature density of the condensed phase.     

Second Sound Measurements Near the Tricritical Point in 3He-4He Mixtures

In this paper we discuss a pulsed second sound experiment, aimed at determining accurately the critical exponent , and the predicted logarithmic correction to scaling, for the superfluid density along a tricritical path in the ³ He- ⁴ He phase diagram. We present an accurate estimate for the limits for closest approach to the tricritical point, as set by gravitationally induced sample inhomogeneities and finite size effects, and discuss some of the complications associated with measurements close to the tricritical point.     

Fourth Sound Propagation in Superfluid 3He in Aerogel

No Heading Impurity effect on the fourth sound propagation in the superfluid ³He-aerogel system confined in a channel is discussed on the basis of a two-fluid theory in which phenomenological parameters are determined microscopically within the homogeneous scattering model.PACS numbers: 67.57.De, 67.57.Hi, 67.57.Pq.     

Sound Propagation and Transport Properties of Liquid 3He in Aerogel

Superfluid ³ He confined in aerogel offers a unique chance to study the effects of a short mean free path on the properties of a well defined superfluid Fermi liquid with anisotropic pairing. Transport coefficients and collective excitations, e.g. longitudinal sound, are expected to react sensitively to a short mean free path and to offer the possibility for testing recently developed models for quasiparticle scattering at aerogel strands. Sound experiments, together with a theoretical analysis based on Fermi liquid theory for systems with short mean free paths, should give valuable insights into the interaction between superfluid ³ He and aerogel.     

Measurements of Helium Density in Aerogel near the Liquid-Vapor Critical Point

We investigate the behavior of ⁴ He confined in silica aerogels near the bulk liquid-vapor critical point. Using a new mechanical technique to measure the density of the confined ⁴ He along isotherms, we find that the density continuously increases from a low density phase up to a dense phase as the pressure is increased up to slightly below the bulk saturated pressure. An hysteretic behavior is observed between emptying and filling, which is not uniquely due to thermal problems. We argue that, our observations are more in favor of some kind of capillary condensation than of a genuine first order phase transition.     

Pulsed Nonlinear Sound in Superfluid 4He and 4He-3He Mixtures

Sound modes in ⁴ He and ⁴ He- ³ He mixtures which arise out of the two-fluid equations are made up up a vector convective flow and scalar temperature changes. A method for modeling nonlinear pulses of sound with geometric approximations to the vector and scalar components has recently been applied towards understanding nonlinear second sound near the lambda point. ⁶ The same method may be used, in general, for modeling linear and nonlinear sounds in Helium II. We demonstrate with a model for nonlinear second sound pulses in ³ He- ⁴ He mixtures and compare the results to experimental observations.     

Experiments with 4He Heated from Above, Very Near the Lambda Point

We report on new transport phenomena observed within a column of ⁴He heated from above and close to its transition to superfluidity. In this configuration the helium sample will self-organize to a state where the temperature gradient across the column remains equal to the pressure-induced gradient of T _λ (1.273 µK/cm) even as the heat flux is varied by a factor of about a thousand. On this self-organized state we have observed a new temperature-entropy wave that propagates opposite to the direction of a steady heat flux Q. This propagating mode is due to a non-linear temperature dependence of the thermoconductance of the helium near criticality. Such a mode had been predicted to exist in this state for Q less than about 100 nW/cm². We confirm that this mode exists in this regime, however we also observe that it propagates at higher values of Q, even when the helium is pushed away from the self-organized state into the normal state.     

Resolving the Yang-Yang Dilemma in 3He Near the Critical Point

A challenging problem is to experimentally resolve the Yang-Yang dilemma for fluids-whether the critical singularity of the isochoric heat capacity is shared between the second temperature derivatives of pressure and chemical potentials. In the lattice-gas model, which serves as a well-established guidance to study fluid criticality, the divergence of the second derivative of pressure is solely responsible for the heat capacity anomaly. If it is proven that the heat capacity singularity is shared between the pressure and chemical potential derivatives, a revision of the conventional scaling theory for fluids based on the analogy between fluids and lattice-gas model will be required. Thus far, experiments on real fluids have been inconclusive, in particular, because of possible impurity effects and the intrinsic vapor-liquid asymmetry. A study of the ³He isotope gives a unique opportunity to resolve the Yang-Yang dilemma. In ³He all other impurities except ⁴He are frozen out. The almost perfect purity of the available ³He samples (typically less than 1 ppm of ⁴He in ³He) enables the elimination or quantitative study of impurity effects. Also the well-known symmetry of the ³He coexistence curve implies an absence of confluent singularities caused by liquid-gas asymmetry. In this paper we reanalyze early experimental data of near-critical ³He and show that they are internally not completely consistent. While the second derivative of chemical potential obtained from the density dependence of the two-phase isochoric heat capacity does not show a noticeable anomaly, the analysis of the same property obtained by combining the PVT and heat capacity implies the existence of the Yang-Yang anomaly. An unambiguous test of the Yang-Yang dilemma will require more accurate heat-capacity measurements closer to the critical point. To thoroughly distinguish between these alternatives one may ultimately require a microgravity experiment that will allow measurements very close to the critical point.     

Effect of 3He on Third Sound Attenuation in Thick 4He Films

We have performed measurements of third sound attenuation in thick films of superfluid ⁴He in the presence of small amounts of ³He. The attenuation due to ³He appears to depend linearly on the number density of ³He atoms in the film. We discuss the results in context of a recently proposed mechanism where the attenuation is caused by the interaction of the excitations in helium with the trapped vortices.     

Sound and transport phenomena in spin-polarized3He-4He solutions

Transport phenomena in partially spin-polarized³He-⁴He solutions are investigated. The polarization causes considerable changes in kinetic coefficients and also gives rise to new dissipative processes, such as spin thermodiffusion and second viscosity. The transport coefficients are calculated for degenerate and nondegenerate³He-⁴He solutions. The absorption of first- and second-sound waves is studied. Second-sound propagation is affected by weak dipole interactions and its velocity depends significantly on the frequency.     

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.     

Sound attenuation and3He-3He interaction in3He-4He liquid mixtures at saturated vapor pressure

The interaction potential between³He quasiparticles in³He-⁴He liquid mixtures is determined from the sound attenuation at saturated vapor pressure. Sound attenuation was measured in mixtures with³He mole fraction ranging from 0.0289 to 0.0573. The superfluid transition temperature of³He in mixtures and other properties were then estimated from the deduced interaction potential.     

Sound propagation in 3He-4He mixtures near the superfluid transition

Measurements of the acoustic attenuation and dispersion in liquid ³He-⁴He mixtures near the superfluid transition T (x) are reported. The frequency range is /2gp=1–45 MHz and the ³He mole fraction X of the mixtures is 0.007, 0.05, 0.15, and 0.36. Comparisons are made with the measurements of Buchal and Pobell for similar mixtures obtained in the kHz region, and on the whole, the consistency between the two experiments is very satisfactory. An analysis is then performed using both the kHz and MHz data. In the normal phase, where the energy dissipation is caused by order parameter fluctuations having a lifetime _F , the attenuation data can all be scaled according to the expression = (T )f(_F. Here (T )^1+y, with y being a function of the mole fraction X and _F(T–T )^–x, with x increasing weakly with X. In the superfluid phase, we attempt a similar scaling representation, which is found to be fairly successful, but where x(T\s-T ) is roughly 15% larger than x(T>T ). In the superfluid phase we also analyze the attenuation data, assuming the additivity of relaxation and fluctuation-dissipation mechanism, and discuss the relaxation times so derived. In contrast to the attenuation, the dispersion data cannot be brought satisfactorily into a scaling representation. However, at T , we find U()-U(0)^y as predicted by Kawasaki, where y is in good agreement with the values from attenuation experiments.Supported by a grant from the National Science Foundation.     

Propagation of solitary waves in a mixture of liquid3He and superfluid4He

The effect of an admixture of liquid³He on the propagation of solitary waves in superfluid⁴He is investigated. In the local density approximation, the mean field equations are reduced to the two-fluid equations describing the dynamics of the mixture of two liquids. The nonlinear perturbation approach is used to obtain a set of equations describing the density and velocity fluctuations of the homogeneous mixture at rest. The self-consistent solution of these equations is shown to be the solitary waves. Using a pseudopotential method, we perform numerical calculations to study the changes in the general properties of the waves caused by the³He impurity.     

Models for Third Sound in Thin 3He-4He Films

Third sound speeds in ³ He- ⁴ He thin films are sensitive to the transverse single-particle state occupied by the ³ He. The third sound speed in the low coverage region with the ³ He occupying the transverse ground-state can be understood quantitatively. The onset of occupation of the first excited transverse state is signaled by a high coverage feature in the third sound speed. Three third sound models for the high coverage region, differing in their assumptions about the spatial distribution of the excited states, are introduced. Using the experimental third sound data, these models can also be used to infer the fractional population of the ³ He in the first excited state as a function of coverage. It is found that the third sound analyses each predict a larger fractional population in the first excited state at monolayer completion than a recent analysis of magnetization step data taken on the same system.     

Sound attenuation in3He-4He liquid mixtures under pressure

The attenuation of sound was measured in³He-⁴He mixtures with³He concentrations ranging from 2.89 to 8.03% at pressures of 10 and 20 bar. The quasiparticle interaction potentials were then determined at each pressure by analyzing the sound attenuation data. The superfluid transition temperature of³He and other properties in the mixtures were then estimated from the interaction potentials.