Superfluidity of Pure 3He and Mixtures of 3He and 4He in Aerogel

We describe new torsional oscillator experiments on ³ He confined in 98.2% open aerogel. In one, we monitored the superfluid fraction of pure ³ He at T << T _c while we gradually changed the sample pressure. The resulting change in density alters ₀ of the superfluid ³ He relative to the distribution of the length scales (correlations) of silica in the aerogel. We observed a T = 0 normal-to-super fluid transition at a pressure of about 6.5 bar, in marked contrast to the bulk where liquid ³ He is superfluid at all pressures. In the second experiment, we measured the temperature dependence of the ³ He _s at a pressure of 21.6 bar with different amounts of ⁴ He present in the cell. Adding 2-3% ⁴ He slightly increases both T _c and _s . We found that for ⁴ He concentrations between 2% and 34%, the ³ He T _c increases by a very small amount. However, _s , which for pure ³ He in aerogel at 0.5T _c is no more than 11%, falls by another factor of 7. This behavior (constant T _c , reduced _s ) is similar to that observed in granular superconducting films where the long-range order is controlled by phase coherence between adjacent grains.     

Velocity of second sound and superfluid density near the superfluid transition in3He-4He mixtures

Using superleak condenser transducers, the velocity of second soundU ₂ has been measured near the superfluid transition temperature T in³He-⁴He mixtures with molar concentrationsX of³He of 0.0, 0.038, 0.122, 0.297, and 0.440. We have obtained the superfluid density _s/ fromU ₂ on the basis of linearized two-fluid hydrodynamics. The results for _s/ are consistent with those obtained from the oscillating disk method, as expected from two-fluid hydrodynamics. The value of _s/ at eachX could be expressed by a single power law, _s/=k, where =1-T/R, with the experimental uncertainty. It is found that the exponent is independent of concentration forX0.44 within the experimental uncertainty. This concentration independence of is in agreement with the universality concept. From the conclusion that the values of are universal forX0.44, the concentration dependence of the superfluid component _s is expressed by an empirical equation _s(X, )=²_s(0, ). It is found that corresponds to the volume fraction of⁴He in the superfluid³He-⁴He mixture. The value of is in agreement with that obtained from the measurement of the molar volume by others.This paper is based on a thesis submitted to Tokyo University of Education in partial fulfillment of the requirements for the Ph.D. degree.     

3He in 99.5% Porous Aerogel at the Normal-Superfluid Transition

We have used a torsional oscillator to measure the superfluid density and dissipation near the superfluid transition of ³ He in aerogel of 99.5% porosity. We used a new cell (constructed at Penn State) for which the aerogel was grown in the pores of a 100 m silver sinter. The cell was tested with ⁴ He and showed no signs of the second-sound resonances that have interfered with previous torsional oscillator measurements. The measurements with ³ He, presented here, were taken at pressures of 1.34 and 4.13 bars. We observed values of _s / in the T 0 limit of 0.05 and 0.14 respectively. Our measurements show an increase in the dissipation on warming through T _c . This series of measurements is ongoing and temperature sweeps at various pressures are planned.     

Torsional Oscillator Study of Thin Helium Films on Hydrogen Substrates

We have made torsional oscillator measurements of thin helium films on a Mylar surface preplated with 2 and 5 layers of H ₂ . The minimum ⁴ He coverage needed for superfluidity, or inert layer, n _o on both surfaces is found to be 6 mole/m ² . This is equivalent to 1/2 of a monolayer at bulk liquid density. The superfluid transition in coverages above n _o is similar to that found on bare Mylar, exhibiting the standard Kosterlitz-Thouless characteristics. We find no anomaly in _s or the dissipation in the film that can be identified with a second transition reported in recent third sound experiments.     

Shear viscosity of liquid4He and3He-4He mixtures,especially near the superfluid transition

High-resolution measurements of are reported for liquid⁴He and³He-⁴He mixtures at saturated vapor pressures between 1.2 and 4.2 K with particular emphasis on the superfluid transition. Here is the mass density, the shear viscosity, and in the superfluid phase both and are the contributions from the normal component of the fluid ( _n and _n ). The experiments were performed with a torsional oscillator operating at 151 Hz. The mole fraction X of³He in the mixtures ranged from 0.03 to 0.65. New data for the total density and data for _n by various authors led to the calculation of . For⁴He, the results for are compared with published ones, both in the normal and superfluid phases, and also with predictions in the normal phase both over a broad range and close to T. The behavior of and of in mixtures if presented. The sloped/dT near T and its change at the superfluid transition are found to decrease with increasing³He concentration. Measurements at one temperature of versus pressure indicate a decreasing dependence of on molar volume asX(³He) increases. Comparison of at T, the minimum of _n in the superfluid phase and the temperature of this minimum is made with previous measurements. Thermal conductivity measurements in the mixtures, carried out simultaneously with those of , revealed no difference in the recorded superfluid transition, contrary to earlier work. In the appendices, we present data from new measurements of the total density for the same mixtures used in viscosity experiments. Furthermore, we discuss the data for _n determined for⁴He and for³He-⁴He mixtures, and which are used in the analysis of the data.     

Persistent currents and critical velocities in3He-4He mixtures

Using the method of Doppler-shifted fourth sound, we have investigated the angular velocity _c1 for the onset of vorticity, the saturated critical velocity, and the dependence of _s/ onv _n –v _s for⁴He in three different pore sizes and for three different mixtures of ³ He- ⁴ Hein one of the powders used. These are the first measurements of critical velocities in ³ He- ⁴ He mixtures. We observe only a weak dependence of _c1on the pore size and within the limits of the experiment no dependence on concentrationX up toX=0.11. We find, however, that the maximumv _n –v _s attainable increases as the concentration of ³ He increases forX0.17. The observed dependence of the superfluid density onv _n –v _s is approximately two orders of magnitude stronger than predicted.     

Universality and the scaling laws in the superfluid phase transition of3He-4He mixtures

From the second-sound velocityU ₂ near the superfluid transition point, the superfluid densities in³He-⁴He mixtures, _s (X) and _s (), were deduced along the paths of constant³He concentrationX and of constant chemical potential difference of³He and⁴He. The following critical exponents of _s are determined: (a) =XX for _s (X) in the(X, T) plane,(b) X for _s (X) in the(, T) plane, and(c) for _s () in the(, T) plane. It is found that and _X change by about 4–6% relative to with increasing³He concentration up toX=0.4 and by 8–10% up toX=0.53. It seems that, belowX=0.53, universality hold for . Values of have been found to be in good agreement with the critical exponent of _s in pure⁴He under constant pressure. The values of and _X forX0.53 are also found to be consistent with the scaling relations in the (,T) plane of³He-⁴He mixture.Work performed in part while at the Electrotechnical Laboratory.     

A comment on the influence of substrates on the superfluid density of thin helium-four films atT=0

The influence of substrate potentials on the superfluid density in thin films of ⁴ He atT=0 is discussed. Estimates indicate that an observabl large reduction in _s is to be expected.     

Size effects in He II as measured by fourth sound

Fourth-sound measurements are used to determine the depletion in the superfluid density _s which occurs in the helium filled small pores of packed powders. The measurements also give the reduction in superfluid onset temperature. The pore size distribution of several samples was determined from desorption isotherms. Using this distribution and an independent pore model, calculations based on the Ginzburg-Pitaevskii ansatz with a healing length first proposed by Mamaladze are found to be in good agreement with experimental results in several cases. The superfluid onset temperature seems to be determined by the average pore size. Fourth-sound measurements as a function of temperatureT in large pore geometries accurately give _s (T –T)^2/3 in the neighborhood of the lambda temperatureT .     

Second virial coefficients in closed form for a Kihara (2m-m)-potential

In the literature second virial coefficients are calculated by series expansions or by direct numerical integration. For thermodynamic quantities such as thermodynamic functions, analytical expressions are wanted. This paper gives closed formulas for the second virial coefficient for a convex-body Kihara potential of the type U()= U ₀[( ₀/)_2m -2( ₀/) ^m ], where m can be a rational number n>3. Furthermore, a number of related problems such as dielectric virial coefficients and Buckingham-Pople integrals are reduced to the same Laplace-transformation-type technique.     

Effects of 4He substitution on low temperature heat capacities of 2D 3He adsorbed on graphite

No Heading We measured heat capacities of the second layer ³He admixed with a small amount of ⁴He (= 0.9 nm^–2) on graphite preplated with a monolayer ⁴He. The aim of this study is to elucidate possible ⁴He substitution effects on a recently proposed new quantum phase existing at densities just below that (_4/7) for the 4/7 registered phase. This phase is supposed to be the hole (zero-point vacancy) doped Mott localized phase. The substitution gives rise to an excess heat capacity (C_ex) with unusual temperature and density dependencies which is most pronounced at a slightly lower density than _4/7. The C_ex stays relatively large even at _4/7, and suddenly disappears at a slightly higher density. One possible scenario, which is consistent with the present data, is that the C_ex comes from the isotopic mixing effect existing in a narrow density range around _4/7 and that there exists an excess particle phase just above _4/7 in addition to the hole doped phase below. The result may suggest finite fluidity or unexpectedly large band widths for the isotopic impurities in the 4/7 phase.PACS numbers: 67.70.+n, 67.55.–s, 71.10.Ay.     

Equation of state of3He near its liquid-vapor critical point

We report high-resolution measurements of the pressure coefficient (P/T) for³He in both the one-phase and two-phase regions close to the critical point. These include data on 40 isochores over the intervals–0.1t+0.1 and–0.2+0.2, wheret=(T–T _c )/T _c and =(– _c )/ _c . We have determined the discontinuity (P/T) of (P/T) between the one-phase and the two-phase regions along the coexistence curve as a function of . The asymptotic behavior of (1/) (P/T) versus near the critical point gives a power law with an exponent (+–1)^–1=1.39±0.02 for0.010.2 or–1×10 ^–2t–10 ^–6 , from which we deduce =1.14±0.01, using =0.361 determined from the shape of the coexistence curve. An analysis of the discontinuity (P/T) with a correction-to-scaling term gives =1.17±0.02. The quoted errors are fromstatistics alone. Furthermore, we combine our data with heat capacity results by Brown and Meyer to calculate (/T) _c as a function oft. In the two-phase region the slope (²/T ²)_c is different from that in the one-phase region. These findings are discussed in the light of the predictions from simple scaling and more refined theories and model calculations. For the isochores 0 we form a scaling plot to test whether the data follow simple scaling, which assumes antisymmetry of – ( _c ,t) as a function of on both sides of the critical isochore. We find that indeed this plot shows that the assumption of simple scaling holds reasonably well for our data over the ranget0.1. A fit of our data to the linear model approximation is obtained for0.10 andt0.02, giving a value of =1.16±0.02. Beyond this range, deviations between the fit and the data are greater than the experimental scatter. Finally we discuss the (P/T) data analysis for ⁴ He by Kierstead. A power law plot of (1/) P/T) versus belowT _c leads to =1.13±0.10. An analysis with a correction-to-scaling term gives =1.06±0.02. In contrast to ³ He, the slopes (²/T ²)_c above and belowT _c are only marginally different.Work supported by a grant from the National Science Foundation.     

Effective Interaction and Superfluidity in Two-dimensional Liquid 3He

Effective interaction of two-dimensional liquid ³He is studied with the (selfconsistent) reaction matrix theory. The theory is found to be valid in the dilute region, _2D 0.02 Å^–2, where _2D is the areal density. In the region, the attractive interaction in the p-wave channel is the most dominant, and the system is expected to undergo a transition to a p-wave superfluid state, except for the dilue limit. The transition temperature is estimated to be of the order of mK in the clean limit. In the dilute limit, _2D 0.002 Å^–2, an s-wave superfluid state becomes more stable than a p-wave one, but the transition temperature is found to be of the order of 0.1 mK at most. Furthermore, in the reaction matrix theory, it is found that a d-wave superfluid state becomes more stable than a p-wave one at _2D 0.035 Å^–2.     

Anisotropic Electrical Transport in MgB2 Single Crystals

We report on study of transport properties of MgB₂ single crystals. The normal state resistivity has been found to be anisotropic with resistivity ratio _c / _ab =3.5. In agreement with the results of band structure calculations the normal state Hall effect measurements with H//ab-planes and H//c-axis show two type carrier behavior. Below T _c, the in-plane as well as the out-of-plane Hall resistivity, _xy and _zx , display no sign change anomaly. Furthermore, both _xy and _zx have been found to scale with corresponding longitudinal resistivity with the same exponent =1.5.     

Heat transfer in hydrocarbon fuel boiling under conditions of natural convection

Data on the heat-transfer coefficient in boiling of five jet fuels, two automotive gasolines, and a diesel fuel are presented over a wide range of regime parameters. The obtained results are described by a unified similarity equation.Notation heat-transfer coefficient, W/(m²·K) - P _s pressure, MPa - q heat flux density, W/m² - V volume, m³ - T _s temperature, K - ₁ and ₂ density of the liquid and vapor phases, kg/m³ - thermal conductivity, W/(m·K) - viscosity of the liquid, m²/sec - surface tension, N/m - C _p heat capacity, J/(kg·K) - r vaporization heat, J/kg - Nu Nusselt number - P Pecklet number.l=C _p T _{s 1}/(r₂)² serves as a governing dimension Kazan' State Techological University. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 3, pp. 438–443, May–June, 1995.     

Temperature dependence of electrical resistivity of deformed and undeformed V-rich V3Si single crystals

The electrical resistivity (T) of V-rich V₃Si single crystals (T _c-11.4 K) was measured from 4.2 to 300 K along the directions of [1 0 0] and [1 1 1] before and after plastic deformation at 1573 K. Anisotropy of (T) was observed although V₃Si has the cubic A15 structure. Plastic deformation does not affect the normal-state (T) behaviour but changes the normal-superconducting transition width T_c. At low temperatures (T _c<T 40 K), (T) varies approximately as T ⁿ where n-2.5 and this behaviour does not contradict the (0)- phase-diagram plot proposed by Gurvitch, where is the electron-phonon coupling constant and (0) is the residual resistivity.     

Studies of Both Intralayer and Interlayer Electrodynamics of Bi2Sr2CaCu2O y in the Superconducting State

We studied the intralayer and interlayer electrodynamics of the superconducting Bi ₂ Sr ₂ CaCu ₂ O _y single crystals in the microwave and millimeter wave regions. The c-axis superfluid density fraction _s ^c shows a more rapid growth than _s ^ab just below T _c and a weaker temperature dependence at low temperatures. These features suggest the anisotropic growth mechanism of _s . The temperature dependence of _ab ¹ shows a large increase below T _c with a broad peak around 20 K. However, to discuss the detailed behavior of ₁ ^c or the anisotropy of conductivity _ab ¹ / _c ¹ in the superconducting state, much more careful measurement is required in the c-axis direction.     

Superfluid density in the presence of persistent current in superfluid4He

The superfluid density _s in the presence of persistent current(v _n –v _s 0) is investigated using the Doppler-shifted fourth-sound technique. In the vortex-free Landau state, _s remains constant within our experimental resolution of two parts in 10 ⁵ . This is not inconsistent with a theoretical prediction by Khalatnikov. Where vortices are present outside the Landau region, a fractional change in _s becomes as large as 1.2%, depending on rotation velocity and temperature, and shows a relatively complex hysteresis behavior.This research is supported by NSF and ONR.     

Flux flow resistivity and upper critical field in ideal type II amorphous superconductors

Flux flow resistivity _f and upper critical fieldH _c2 of ideal type II amorphous bulk supercbnductors Zr₃Ni and Zr₃Rh on both as-quenched and thermally relaxed states have been studied. It is found that thermal annealing does not change the temperature dependence ofH _c2 in homogeneous superconductors. The temperature and field dependence of _f in all samples studied exhibits a universal scaling relation of the form _f / _n =f(h, t), where _n is the normal state resistivity, andh andt are the reduced field and reduced temperature, respectively. The results are compared with predictions of the time-dependent microscopic theories for bulk superconductors in the dirty limit. In the low-field region (HH _c2 ) the viscosity coefficient contains both the ordinary (Bardeen-Stephen, Tinkham) and anomalous (Gor'kov-Kopnin) terms. ForHH _c2 the results agree qualitatively with the theory of Imai with pair-breaking in the anomalous term. Implications of the present results are discussed.This work is sponsored by the National Science Foundation under Grant DMR-82-02624.     

Shear viscosity measurements of liquid 3He-4He mixtures above 0.5 K

Simultaneous measurements of () and of the molar volume are reported for liquid mixtures of ³He in ⁴He over the temperature range between 0.5 and 2.5 K. Here is the shear viscosity and is the mass density. In the superfluid phase, the product of the normal components, _n and _n , is measured. The mixtures with ³He molefractions 0.30 < X < 0.80 are studied with emphasis on the region near the superfluid transition T and near the phase-separation curve. Along the latter, they are compared with data by Lai and Kitchens. For X > 0.5, the viscosity singularity near T becomes a faint peak, which however fades into the temperature-dependent background viscosity as X tends to the tricritical concentration X _t. Likewise, no singularity in is apparent when T _t is approached along the phase separation branches _– and ₊. Furthermore, viscosity data are reported for ³He and compared with previous work. Finally, for dilute mixtures with 0.01 X 0.05, the results for are compared with previous data and with predictions.