Heat transport in dilute mixtures of3He in superfluid4He

We report new measurements of the effective thermal conductivity K_eff and relaxation time τ in dilute mixtures of³He in superfluid⁴He, with molar concentrationsX≤10⁻³. The temperature range extended fromT≈1.4 K toT _λ. Both K_cff and τ are found to agree with theoretical predictions, in contrast to previous experiments where significant differences were observed. A new thermal conductivity cell design was used which almost completely eliminates extraneous volumes and surfaces, and the earlier results are explained in relation to these design changes.     

NMR Studies of 3He Droplets in Dilute 3He-4He Solid Solutions

We have performed measurements of the temperature dependence of the nuclear spin-lattice relaxation times (T ₁) for a wide range of ³He concentrations for dilute mixtures of ³He in solid ⁴He. The temperatures for phase separation are determined for ³He concentrations 500<x ₃<2000 ppm for a molar volume V _M =20.7 cm³. We report the temperature dependence of the nuclear spin-lattice relaxation times for ³He in the droplets formed after phase separation at low temperatures. The temperature dependence suggests that the interface ³He atoms responsible for the relaxation are degenerate, not solid-like.     

Nuclear magnetic relaxation of3He gas. II.3He-4He mixtures

Longitudinal relaxation timesT ₁ have been measured in³He-⁴He gas mixtures, using pulsed NMR, in the temperature range 0.6–15 K. Helium-3 number densities of the order of 10²⁴ atoms m^–3 were used. Relaxation takes place on or near the walls of the Pyrex sample cells and measurements ofT ₁ give information about the surface phases. A cryogenic precoating of solid molecular hydrogen was used to reduce the helium-substrate binding energy from 100 K on Pyrex to 13 K for³He and 15 K for⁴He. TheT ₁ data at high temperatures were similar to those observed previously in the pure³He-H₂ system. The presence of⁴He generally causedT ₁ to rise on cooling below 2 K due to the preferential adsorption of⁴He over³He at the surface. However,³He atoms that go into quasiparticle states in the superfluid helium film can be an extra source of relaxation. In uncleaned cells, relaxation probably takes place in quasiparticle states at the free surface of the superfluid film, which are bound with an energy of 5.1±0.3 K. Baking the Pyrex cells under vacuum and rf discharge cleaning the walls before sealing in the sample gas were found to increase the bulk gasT ₁ by two or three orders of magnitude. In a cleaned, sealed cell aT ₁ of 8 h was measured at 7.7 MHz and 0.8 K. In this case relaxation is probably occurring two or three helium layers away from the helium-hydrogen interface. It may be possible to observe a predicted minimum in the intrinsic dipolarT ₁ of the bulk gas by using a⁴He wall coating to suppress wall relaxation effects (which usually dominate the nuclear relaxation of the bulk gas).     

Towards Superfluidity of 3He Diluted by 4He

Search for the superfluid state of dilute ³He dissolved to ⁴He is one of the major remaining problems of low temperature physics. We describe our two experiments designed to pursue the lowest achieved temperature in such mixtures essentially below the values reported before.     

AC Thermal Conductivity Measurements in Dilute Mixtures of 3He in Superfluid 4He

In Part III of a three-part study, we report measurements of the thermal response, T(), of ³ He-superfluid- ⁴ He mixtures to an ac heat flux, Q(t)=Q₀e^it. These data are for dilute concentrations, X, and they show the presence of three separate thermal resistances. One of these is the bulk-fluid resistance predicted by Khalatnikov and associated with the effective conductivity, _eff . Results for this component of the resistance are in quantitative agreement with the Khalatnikov predictions. With parallel work by Murphy and Meyer, these experiments resolve a long-standing conflict between theory and experiment. One of the remaining resistances is the ordinary boundary resistance R_b. The third resistance, R ₀ , is independent of the fluid layer height, d. This resistance is presumably the same as that seen in earlier dc measurements. Both the temperature and concentration dependences of this anomalous resistance differ from that of either R _fluid or R_b. It has been ascribed recently by Murphy and Meyer to effects associated with the narrow gaps usually present in cryogenic thermal conductivity experiments. We use an ad hoc model as a convenient way to parameterize the extra thermal resistance. The present studies have been carried out with an apparatus which permits us to vary d continuously and in situ from zero to 3 mm. This feature and the ac technique are important for separating the various components of the thermal resistance. In two preceeding studies, we considered related aspects of the ac thermal response of liquid helium. Part I addresses the response of normal liquid helium. Part II, provides the theoretical backdrop for the present experimental study.     

Relaxation times and mass diffusion in superfluid dilute3He-4He mixtures

Relaxation times are reported from the transients observed during thermal conductivity _eff and thermal diffusionk _T ^* measurements in superfluid mixtures of³He in⁴He with a layer thickness of 1.81 mm. The experiments extend from 1.7 K toT and over a³He concentration range 10^–6X<5×10^–2. The agreement between the measured and the predicted from the two-fluid thermohydrodynamic equations is satisfactory forX>10^–3 but deteriorates for smaller³He concentrations. This situation is similar to that for _eff andk _T ^* results and indicates that the transport properties in very dilute mixtures with layers of finite thickness are not well understood. ForX>10^–3, the mass diffusion coefficientD _iso for isolated³He in⁴He has been determined from and from _eff measurements. There is an inconsistency by a constant numerical factor between these determinations. This problem might be related to the observations that in the superfluid phase, the relaxation times for different cell heightsh do not scale withh ². FromD _iso derived via the _eff data, the³He impurity-roton scattering cross section is determined. Comparisons with previous work are made.     

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.     

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.     

4He Adsorption and Superfluid Transition on C60

We present adsorption isotherm data of⁴He on C₆₀ for 1.50 K<T<1.68 K determined by measurements of the frequency of quartz crystal microbalances (QCM’s) coated with C₆₀ films. We find a Kosterlitz-Thouless transition with a jump in the areal superfluid density close to predictions. By comparing the adsorbed⁴He on two QCM’s we derive an upper limit for the amount of⁴He intercalated into C₆₀ at low temperature of 0.05⁴He atoms per C₆₀ molecule. The low coverage portion of the adsorption data shows an apparent excess adsorption of⁴He onto the C₆₀.     

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.     

3He Impurity Effects on the Growth Kinetics of 4He Crystals

We report the growth kinetics of the⁴He crystals with a small amount of³He impurities around 0.8 K. The growth resistance was measured using the response of the charged interface with respect to an externally applied voltage. In 5 ppm and 10 ppm³He mixtures, it is found that (1) the relaxation process can be expressed as an exponential behavior, (2) the growth resistance becomes larger compared to pure⁴He and does not have a strong³He concentration dependence, and (3) the temperature dependence of the growth resistance is much the same as pure⁴He. We discuss several possible explanations of the present experiment.     

NMR,optical, and plastic flow experiments in bcc3He —4 He mixture crystals — in pursuit of a vacancy fluid

We describe experiments on the properties of bcc³He —⁴ He solid mixtures on the melting curve between 0.5K and 1.9K. In this paper we focus on effects related to the presence of thermal vacancies. First, we used NMR to image the³He distribution within the solid in equilibrium with the superfluid, as well as its T₁ and t₂. The most surprising result was that above about 1K, vacancy related motion of³He atoms in the solid becomes faster than in the liquid. To check the macroscopic aspects of this motion, we used the vibrating wire technique to look at plastic flow of the bcc solid phase, by moving the wire through the crystal. The temperature dependence of the plastic flow velocity indicates that the vacancy population in the bcc solid behaves like a viscous fluid. The extent to which the vacancy population causes the solid to have liquid like properties is best demonstrated through optical observations of the distillation of³He atoms out of the crystal, which takes place via formation of fluid bubbles within the solid, which then percolate into the liquid, creating a vivid impression of boiling.     

Phase separation of3He-4He mixture in aerogel

Torsional oscillator measurements of ³ He- ⁴ He mixtures confined in aerogel show evidence of a well defined phase separation region. This region is detached from the superfluid transition line, opening up a region of miscible superfluid mixture at high ³ He concentration.     

Thermal resistance between liquid3He and copper potassium tutton salt

The thermal resistance between liquid³He and copper potassium tutton salt (CPS) has been measured through its magnetic ordering temperature (T _c=29.6 mK). The thermal resistanceR for pure³He has a broad minimum near 60 mK and increases continuously throughT _cwith decreasing temperature, except for a dip atT _c. BelowT _c,R is proportional toT ^–1.5. Effects of⁴He coating have been studied by stepwise addition of⁴He into liquid³He. The thermal resistance increased drastically for the liquid containing 150 ppm⁴He and more for 95%⁴He. By sudden depressurization of the liquid³He containing 480 ppm⁴He, a considerable decrease ofR was observed. SinceR for pure³He was much smaller than the calculated Kapitza resistance, the present experimental results indicate the existence of surface magnetic coupling between liquid³He and CPS.     

Temperature and Concentration Relaxation in Phase-separated Superfluid 3He–4He Mixtures

The kinetics of the temperature and concentration variations in the superfluid ³He–⁴He mixtures with initial concentration of 9.8% ³He, and heated from below, was studied experimentally under the pressure of 0.38 bar over a temperature range of 150–400 mK. It is found that in contrast to homogeneous liquids, the temperature and concentration relaxation in phase-separated mixtures can be described by a superposition of two exponential processes in which the time constants of temperature and concentration variations coincide. If the initial mixture was homogeneous and phase separation was triggered by a heat flow, the temperature and concentration vary non-monotonically and exhibit anomalous features at the moment of phase separation. In this case the phase transition starts in the metastable superfluid, formed out of a quite supersaturated mixture where the nucleation of the new phase may be caused by quantized vortices. The results are analyzed in terms of two possible mechanisms of relaxation–the acoustic mechanism with the second sound velocity and the diffusive one connected with dissipative flows of impurity and thermal excitations. It is shown that the measured relaxation times agree with a prediction of the theory.      

Spin Pumping Effect in Superfluid 3He A1

A fountain effect is a common phenomenon in both ³He and ⁴He superfluids. Unique to superfluid ³He is the magnetic fountain effect, which has been used to determine the spin direction of the condensate in ³He A₁ phase. Here we present a pressure driven fountain effect in A₁ phase. The experimental cell is composed of a large reservoir connected to a small detector chamber through superleak channels of width of 20 μm. One wall of the detector chamber houses a movable circular 6 μm thick membrane which serves as a sensitive capacitive pressure sensor and also acts as a spin pump. In A₁ phase, a DC voltage applied on the capacitor induces a simultaneous mass and spin superfluid current into the small chamber. After equilibration, removal of the DC voltage causes a sudden pressure drop followed by a slow relaxation. The sudden drop is a consequence of reversed superfluid flow through the superleak. The observed decay times during the slow relaxation agree with those obtained in magnetically induced spin flow experiment. These observations show that the slow relaxation stems from spin relaxation in the absence of applied field gradient.     

The dielectric formalism for3He-4He mixtures

The microscopic theory of³He-⁴He mixtures with a Bose condensate is formulated in terms of the dielectric formalism. By expressing all correlation functions in terms of proper, irreducible contributions, one sets the stage for approximate calculations that will be consistent with various exact sum rules and Ward identities, just as in the case of pure⁴He. The present analysis includes a symmetry-breaking term that allows us to deal with the continuity equations properly, and is valid at finite temperature. As a specific application, we express the normal fluid density _N in terms of the static⁴He current-current correlation function. We also give the first formal proof that in the presence of a moving condensate, the³He atoms make no direct contribution to the superfluid flow.     

Simulations of a Thermal Conductivity Cell Filled with Normal 4He and Dilute Mixtures of 3He in Superfluid 4He

We have simulated the thermal response of a cylindrical thermal conductivity cell filled with liquid helium to AC and DC heat fluxes. The conductivity cell in these simulations is realistic in that it includes sidewalls and gaps, which cannot be treated analytically or in a one-dimensional simulation. Our simulations are to able to account quantitatively for the apparent departure of the effective thermal conductivity, _eff , of dilute mixtures of ³ He in superfluid ⁴ He from theoretical predictions. We have recently demonstrated experimentally that this departure is due to the presence of gaps in previous thermal conductivity cells. These simulations also show that the additional phase lag in the response of normal ⁴ He to an AC heat flux, measured by Olafsen and Behringer, is due to gaps in the heated plate.     

Visual Observation of a Sound-Induced Bubble in Liquid 3He–4He Mixtures

We report visual observation of a sound-induced bubble in superfluid ³He–⁴He liquid mixtures using a high-speed camera at a rate of 1 msec/frame. The experiments were performed in the ³He dilute phase of phase-separated mixtures at 300 mK. The resonant frequency of the piezoelectric transducer was 9.36 MHz and the diameter of the active electrode was about 4 mm. When an acoustic wave pulse of sufficient magnitude was applied to the dilute phase from the transducer under saturated vapor pressure, a single bubble was nucleated on the active area. The bubble expanded almost spherically on the transducer, as it reached maximum size, it started shrinking, detached from the transducer, and collapsed. We also investigated the motion of the bubble in mixtures with a ³He concentration of 25% at 750 mK. In this case, the bubble grew elliptically on the transducer and detached from it without much change in shape.     

The magnetic susceptibility of dilute mixtures of3He in liquid4He

The relative changes in the low-temperature susceptibility of a number of dilute mixtures of³He in liquid⁴He at various pressures are reported and analyzed. Under elevated pressures, the solubility of³He in⁴He increases and the effects of the interaction between³He quasiparticles clearly become larger. However, no evidence of a BCS pairing transition was found in direct measurements of susceptibility and nuclear resonance frequency down to the temperature 1.5 mK in saturated solutions with a pressure of 21 bar.Guggenheim Fellow on leave from Cornell University, Ithaca, New York.