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.     

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.     

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.     

Equation of state of a3He-4He mixture near its liquid-vapor critical point

Measurements of the pressure coefficient (P/T)_,x are reported for a ³ He- ⁴ He mixture with a mole fractionX=0.805 of ³ He in the neighborhood of the liquid-vapor critical point. These include data on 16 isochores taken over the density interval–0.50.5 and over the temperature range–0.1 t0.1, where =(– _c )/ _c andt=(T-T _c )/T _c ,with _c andT _c ,respectively, the critical density and temperature of the mixture. From the discontinuity of (P/T)_,x at the boundary between the two-phase and the one-phase regions we determine the dew-bubble curve nearT _c with better precision than was done in recentPVT experiments. From the extrapolation of data not approachingT _c closer than1 mK, (P/T)_,x along the critical isochore appears to be discontinuous atT _c ,while for the isochore / _c 0.92, (P/T)_,x is continuous across the dew curve. It is found that this latter isochore cuts the dew curve at its highest temperature. These observations are discussed in terms of general thermodynamic arguments and theoretical predictions of the asymptotic behavior. We calculate (P/T)_,x from the scaling equation of state proposed by Leung and Griffiths for ³ He- ⁴ He mixtures, using their numerical parameters. In spite of some systematic deviations, especially in the two-phase region, there is in general good agreement with experimental results. In particular, the shape of the measured dew-bubble curve and the apparent discontinuity of (P/T)_,x along the critical isochore show excellent agreement with theory.Work supported by a grant from the National Science Foundation. A report of this work has been presented at the Washington Meeting of the APS [Bull. Am. Phys. Soc. 20, 618 (1975)].     

Observation of Hall Scaling in MgB2 Thin Films

We have measured the Hall resistivity, _xy , and the longitudinal resistivity, _xx , in superconducting MgB₂ thin films in a mixed-state while changing the magnetic field and the current density. A Hall scaling behavior without the anomalous Hall effect was observed with a exponent of 2.0±0.1 in _xy =A _xx . This exponent is observed to be constant, i.e., independent of magnetic field, temperature, and current density.     

Thermal transport properties in the normal phase of dilute3He-4He mixtures

We present steady-state measurements of the thermal diffusion ratiok _T and of the heat conductivity for three dilute mixtures of³He in⁴He with concentrations 9×10^–3X(³He)5×10^–2 at saturated vapor pressure in the normal phase close to the superfluid transition. The data are compared with predictions by Dohm and Folk from the renormalization group (RG) theory. From auxiliary determinations of thermodynamic derivatives for these mixtures, we obtain the separation factor =–(k _T /T)×(/X) _T,P /(/T) _X,P above T over the range wherek _T is positive. Here is the mass density. From the transients of X(t) as a function of time, we obtain an estimation for the mass diffusion coefficientD and compare the results with predictions by Dohm and Folk and with results from other experiments.     

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.     

Thermal effects in high density polyethylene and low density polyethylene at high hydrostatic pressures

The temperature changes as a result of rapid hydrostatic pressure applications are reported for high density polyethylene (HDPE) and low density polyethylene (LDPE) in the reference temperature range from 298 to 423 K and in the pressure range from 13.8 to 200 MN m^–2. The adiabatic temperature changes were found to be a function of pressure and temperature. A curve fitting analysis showed that the empirical curve (/P) =ab(P)^b–1 described the experimental thermoelastic coefficients obtained from the experiments. The data were analyzed by determining the predicted thermoelastic coefficients derived from the Thomson equation (/P) = T ₀/C _p. The experimental and predicted Grüneisen parameter _T were also determined.     

Ordinary size effects and deviations from Matthiessen's rule in the resistance of fine wires

Contrary to previous statements in the literature, large deviations from Matthiessen's rule in fine wiresare to be expected on the basis of a straight-forward solution of the ordinary transport equation, assuming the relaxation-time approximation and imposing the idealized condition of diffuse scattering of electrons at the boundaries. Using Chambers' path-integral method to evaluate the current density in a wire of arbitrary cross-sectional shape, the effects of boundary scattering on the resistivity in the regimed 0.1 have been calculated for two model Fermi surface geometries. For the temperature-dependent part of the resistivity, _d (T) _d (T)– _d (0), two distinct types of behavior are found in the alternative cases: (1) for a spherical Fermi surface, _d(T) increases logarithmically with _d(0); (2) for a cylindrical Fermi surface, _d (T) increases essentially linearly with _d (0). [In each case the qualitative dependence of _d(0) on /d is, for practical purposes, linear. However, the correct value of the product in the cylindrical case is not simply given in the ordinary way by the slope of an empirical plot of _d (0) vs.d ^–1.] A comparison of theoretical results for the two simple models with the published data for indium and gallium shows that the actual temperature-dependent size effects are consistent, both qualitatively and, by a rough estimation, quantitatively, with the expected behavior.     

Third sound in3He-4He mixture films

We report third-sound studies of³He-⁴He mixture films for 0.3T1.8 K carried out in two different experimental situations. In one experiment detailed measurements of the amplitude of both the temperature and thickness variation of the film were made for pure⁴He and the results for |T/d| are in good agreement with the predictions of Bergman. Mixture studies in this apparatus were made difficult due to the presence of capillary condensation. In spite of this a number of interesting results are reported. Subsequent measurements were made in a new apparatus where capillary condensation effects could be demonstrably avoided. Helium films of 5.7 layers of⁴He were studied as a function of added amounts of³He. BelowT0.7 K the third-sound measurements are consistent with model calculations based on a bilayer film. We conclude that for 0.3T0.6 K films of the type we have studied are isotopically layered in the van der Waals field provided by the substrate.     

Effect of the elastic factor on the hydrodynamic stability of a structurally viscous medium

The effect of relaxation phenomena on the hydrodynamic stability of the plane gradient flow of a structurally viscous medium is investigated using linear theory.Notation _ij stress tensor deviator - U_i components of the velocity vector - x_i coordinates - t time - P pressure - =₀L/^*V plasticity parameter - _o limiting shear stress - andc dimensionless wave number and the perturbation frequency - Re=VL/* Reynolds number - density - F_ij deformation rate tensor Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 35, No. 5, pp. 868–871, November, 1978.     

Viscosity of steam in the critical region

The shear viscosity of fluids exhibits an anomalous enhancement in the close vicinity of the critical point. A detailed experimental study of the viscosity of steam in the critical region has been reported by Rivkin and collaborators. A reanalysis of the experimental data indicates that the behavior of the viscosity of steam near the critical point is similar to that observed for other fluids near the critical point. An interpolating equation for the viscosity of water and steam is presented that incorporates the critical viscosity enhancement.Nomenclature a critical region equation of state parameter - a _k coefficients in equation for ₀ - a _ij coefficients in equation for ¯ - b critical region equation of state parameter - c _p specific heat at constant pressure - c _v specific heat at constant volume - k critical region equation of state parameter - k _B Boltzmann constant - P pressure - P _r 22.115 MPa - P ^* P/P _r - P _c critical pressure - P _i coefficients in critical region equation of state - R~P (P-P _c )/P _c - q parameter in equation for critical viscosity enhancement - r parametric variable in critical region equation of state - T temperature in K (IPTS-48) - T _r 647.27 K - T ^* T/T _r - T _c critical temperature - T (T–T _c )/T _c - V volume - critical exponent of specific heat - critical exponent of coexistence curve - critical exponent of compressibility - critical exponent of chemical potential at T=T _c - dynamic viscosity - ₀ lim ₀ - ¯ normal viscosity - critical viscosity enhancement - ¯ thermal conductivity - normal thermal conductivity - critical thermal conductivity enhancement - parametric variable in critical region equation of state - correlation length - ₀ correlation length amplitude above T _c at = _c - critical exponent of correlation length - density - _r 317.763 kg/m³ - ^* / _r - _c critical density - (– _c )/ _c - _p estimated error of pressure - _T estimated error of temperature - estimated error of viscosity - exponent of critical viscosity enhancement - _t (/P) _T symmetrized compressibility - _T ^* _T P _r / _r ² - _{t t} P _c / _c ²     

Behaviour of amorphous poly(ethylene terephthalate) annealed at T<T g by thermally stimulated currents

Thermally stimulated current (TSC) discharges in open circuit of amorphous poly(ethylene terephthalate) (PET) corona-charged electrets show a heteropolar relaxation at 87 °C, ₁ between and peaks. This relaxation tends to become homopolar when the sample is annealed at temperatures below the glass transition temperature. This is due to the formation of a trapped charge density on the surface of the material that originates, during the TSC discharge, a current that counteracts the one that results in ₁ This trapping effect, which initially is null, increases with annealing due to the rise in resistivity. On the other hand, TSC discharges in short-circuited annealed samples result in a heteropolar peak, ^*, that corresponds to ₁ The area of ^* increases with the annealing time in a bounded way. This peak is related to the formation of thermal nuclei (embryos) in the bulk of the material that act as heterogeneities. This suggests that ₁ is associated with a barrier-type polarization. If the annealed sample is heated to temperatures above the glass transition temperature, the tendency to the inversion of ₁ vanishes and ^* disappears, whereas and are modified. This suggests that relaxation is related to a Maxwell-Wagner-Sillars effect.     

First-sound measurements in a 5%3He-4He mixture

Precision first-sound measurements at 17.1 kHz are presented for a 5%³He-⁴He solution. Measurements near the transition are analyzed with a modified Pippard-Buckingham-Fairbank relation using recent³He-⁴He heat-capacity measurements. The analysis takes into account the effects of gravity and dispersion. An accurate determination of (P/)_T is obtained from velocity measurements in the range 1.1–2.0 K.Work at the University of California was supported in part by the U.S. Office of Naval Research.Part of this work was performed during the author's postdoctoral year (1967) at the Physics Department of the University of California at Los Angeles.     

Hall-Effect in LuNi2B2C and YNi2B2C Borocarbides in Normal and Superconducting Mixed States

It was shown that the Hall resistivity _xy for LuNi ₂ B ₂ C and YNi ₂ B ₂ C is negative in the normal and mixed states and has no sign reversal below T _c . In the mixed state the scaling relation _{xy xx} (_xx is the longitudinal resistivity) was found for both compounds with 2.0. In the normal state a distinct nonlinearity in the _xy(H) dependence, accompanied by a large magnetoresistance, was found below 40 K only for LuNi ₂ B ₂ C. The difference in the behaviour of Lu- and Y-based borocarbides seems to be connected with the difference in the Fermi surfaces of these compounds.     

Electron transport properties of deformed potassium and a potassium-rubidium alloy from 0.08 to 4.2 K

Measurements have been performed of electrical resistivity and thermoelectric ratioG on deformed samples of potassium as well as of on a deformed 0.077 at %KRb alloy. A large anomaly in (T) forT<0.5 K is ascribed to electrons interacting with vibrating dislocations and it is shown that the data are consistent with a model of Gantmakher and Kulesko in which the scattering arises from local phonon modes associated with the dislocations. ForT>1 K, an increase in (T) is ascribed to the suppression of phonon drag by the dislocations. The latter is qualitatively confirmed by theG measurements. A maximum inG at 0.5 K is observed when dislocations are present. The two effects in (T) outlined above are so large that the change in the electron-electron scattering contribution to due to deformation cannot be precisely determined.     

Density and Viscosity of the 1-Methylnaphthalene+2,2,4,4,6,8,8-Heptamethylnonane System from 293.15 to 353.15 K at Pressures up to 100 MPa

The dynamic viscosity of the binary mixture 1-methylnaphthalene+2,2,4,4,6,8,8-heptamethylnonane was measured in the temperature range 293.15 to 353.15K (in progressive 10K steps) at pressures of 0.1, 20, 40, 60, 80, and 100MPa. The composition of the system is described by nine molar fractions (0 to 1 in 0.125 progressive steps). The density was measured at pressures from 0.1 to 60MPa in progressive 5 MPa steps. The measurements of are used to determine the excess viscosity ^E and the excess activation energy of flow G ^E as a function of pressure, temperature, and composition. Some models have been used to represent the viscosity of this binary mixture.     

Zero-point motion and superfluid helium

We propose that He II exhibits macroscopic [ _P /N O(1)] quantum zero-point motion in momentum space, i.e., that a nonzero root-mean-square superfluid velocity exists even in an equilibrium superfluid system at rest. At absolute zero, using coherent states, we relate the uncertainty _P /N in the total momentumP (per particle) to the long-range-order (LRO) part of the phase gradient correlation function, which is proposed as an order parameter. The local equilibrium equation for the superfluid velocity potential derived by Biswas and Rama Rao yields, in the strict equilibrium limit, the equation determining this order parameter in terms of fluctuation correlations that remain to be determined. The order parameter is interaction dependent, nonzero atT=0 if (0)–₀V₀>0, and can vanish at some transition temperatureT when fluctuation terms become comparable to theT=0 value. (HereV _{0 0}, and (0) are the uniform parts of the potential, density, and chemical potential with shifted zero of energy, respectively.) A characteristic length (T), diverging atT=T , appears naturally, with its defining relation reducing to a macroscopic uncertainty relation ( _P /N)(0)=/2 atT=0. With certain assumptions it is shown that atT=0, LRO in the phase gradient correlation function is incompatible with off-diagonal long-range order (ODLRO) in the (r)(r) correlation function, and with nonzero condensate function.     

Application of inert radioactive gases in the study of solids

The behaviour of different iron salts (FeSO₄.7 H₂O, FeC₂O₄.2 H₂O, Mohr's salt, and basic iron carbonate) was studied by means of the emanation method, DTA and dilatometry. The salts were heated within the temperature range of 20 to 1100 C, under identical conditions. The results obtained are compared and the process of thermal decomposition of the different salts is discussed.The activity of ferric oxide obtained by decomposition of various iron salts is estimated, and it is suggested that the low activity of the sulphate-derived ferric oxides is related to a low thermal annealing rate, while the higher activities of the other two resultant ferric oxides are similarly related to higher thermal annealing rates.     

Evolution of transient thermal processes in layer counterflow apparatuses and heat exchangers

Results are given of an analytic investigation of transient processes inside counterflow apparatuses and heat exchangers with temperature disturbance in one of the heat carriers at the entry to the apparatus.Notation =(t–t₀)/(T₀–t₀),=(T–t₀)/(T₀ s-t₀) relative temperatures - t, T temperatures of material and gas respectively - t₀, T₀ same for the initial state - Z=[ _Vm₁/c(1–w/w_g)] [–(y₀–y)/w_g] dimensionless time - m₁=1/(1+Bi/) solidity coefficient - B₁=( _FR/) Biot number - _{F V} heat-exchange coefficients referred to 1 m² surface and 1 m³ layer - R depth of heat penetration in a portion - portion heat conductivity coefficient - shape coefficient (=0 for a plate,=1 for a cylinder,=2 for a sphere) - c, C_g heat capacities of material and gas respectively - , _g volumetric masses - w, W_g flow velocities of material and gas - y distance from the point of entry to the heating heat carrier - y₀ heat-exchanger length - Y= _Vm₁y/W_gC_{g g} dimensionless coordinate - m=cw/C_g– _gW_g water equivalent ratio Deceased.Translated from Inzhenerno-Fizicheskii Zhurnal, vol. 20, No. 5, pp. 832–840, May, 1971.