The temperature and pressure dependence of the normal fraction of superfluid3He-B

Measurements have been made of the normal fluid fraction of superfluid³He-B at eight different pressures between 0 and 29.2 bar. The minimum temperatures were such that _n / was reduced to less than 0.5%. The experiments, carried out independently at Cornell and Texas A&M Universities, used similar Andronikashvilli-type torsional oscillators. The results are qualitatively similar, but show significant differences due to the use of different temperature standards. Both sets of results are presented in tabular form. The inconsistencies in the temperature scales preclude the examination of the results for possible strong coupling effects.     

Spin hydrodynamic equations with external disturbances and suitable Green's functions for superfluid3He-B. New onsager relations

The spin hydrodynamic equations for superfluid³He-B have been obtained for the case of external, time-dependent fields. On the basis of a microscopic approach, expressions are found for additional terms in equations containing these fields. Considering the linear response of the system to the switching on of external fields, formulas are found for suitable Green's functions (magnetization-magnetization, rotation-rotation, magnetization-rotation, rotation-magnetization). The rotation-rotation Green's function has the 1/q ² singularity characteristic of superfluid systems. Connections between Green's functions lead to relations among kinetic coefficients v, ₁, and ₂. It is also shown that there is a conserved quantityQ ^(B) = div v _s ^(B) that describes sources or magnetic type charges (monopoles) of the superfluid velocity v _s ^(B) . Comparison with the phenomenological approach suggests thatQ ^(B) is proportional to a pseudoscalar giving the projection of the spin density onto the vector describing the axis of rotation.     

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)].     

Dynamic Measurements of Thermal Transport Coefficients and Boundary Resistance. II.Model for 3He-Superfluid 4He Mixtures

This is the second of a three-part study of the ac response of liquid helium. We derive the temperature response function, T(), of a ³ He-superfluid ⁴ He mixture from the equations of superfluid hydrodynamics in the presence of two interfacial boundary resistances,R_b.Specifically, we consider the response T(), across a fluid layer of thickness,d, to an ac heat flux,Q(t) = Q_o exp(it).T() depends on the effective thermal conductivity, _eff , Griffin's diffusion coefficient, _o (i.e. the thermal diffusivity of ³ He impurities, D_iso in the low ³ He concentration limit) and the thermal boundary resistance, 2R_b. This analysis provides the basis for experiments to determine these parameters. Although past experiments to measure these properties have been carried out using dc and transient techniques, an ac technique offers significant noise reduction over these techniques. By sweeping the frequency, it is possible for an experimenter to clearly identify different components of the system response to the heat flux. For instance, if t is the slowest fluid thermal response time, conventional Kapitza boundary effects dominate at frequencies, 1. These calculations reveal an interesting analogy to the Piston Effect for near-critical classical fluids. In Part I of this work, we used normal liquid ⁴ He as a testing ground for developing models of ac heat transport. In Part III of this work, we will present results in which we apply this technique to measurements on dilute mixtures of ³ He in superfluid ⁴ He.     

Conductivity of the Wigner Solid on the Free Surface of Superfluid 3He-B

We have measured the conductivity of the 2D electron crystal (the Wigner solid) trapped on the free surface of superfluid ³ He-B down to 230 K. The resistance R(T) greatly decreases as temperature T decreases, obeying Arrhenius' law, R(T) exp (–(T)/k _B T), with (T) which we assign to the superfluid energy gap. This reveals that the scattering of ³ He quasiparticles by the WS determines the transport. As the input voltage increases, an anomalous behavior dominates the resistance just below the superfluid transition. The WS provides a new experimental method for probing both the bulk and free surface of superfluid ³ He.     

Nonmonotonic Temperature Dependence of the Thermal Hall Angle of a YBa2Cu3O6.95 Single Crystal

We have performed high-resolution measurements of the magnetic field (0 TB9 T) and temperature (10 KT<140 K) dependence of the longitudinal and transverse Hall thermal conductivity of a twinned YBa₂Cu₃O_6.95 single crystal. We have used and compared two recently published methods to extract the thermal Hall angle _H(T, B). Our results indicate that cot(_H) varies quite accurately as T⁴ in the intermediate temperature range 0.3c. It shows a well defined minimum at T_m20 K which resembles that observed in the c-axis microwave conductivity. The electronic part of the longitudinal and the transverse thermal conductivity show the scaling behavior for transport properties predicted for d-wave superconductors in the temperature range 18 KT30 K.     

Vibrating-wire measurements in vacuum,liquid3He and liquid3He-4He mixtures

In order to overcome the 200µK - barrier in the refrigeration of liquid ³ He- ⁴ He mixtures we have constructed an experimental cell using only pure materials to minimize possible origins for heat leaks into the liquid. With this arrangement we were able to cool a saturated6.8%- mixture to a temperature of 150µK. A vibrating wire which was immersed in pure ³ He floating on top of the phase-separated mixture was used as a thermometer. This wire was calibrated in a second experiment with pure ³ He only in the cell. In superfluid ³ He-B at T0.15 mK the damping of the wire due to the quasiparticles becomes very small, and we observe typical characteristics of the vacuum damping of the wire which was extensively examined before filling any liquid into the cell.     

Measurement of the g-shift in superfluid3he-B

We have measured the g-shift in superfluid³He-B as a function of temperature above 0.5 mK at a pressure of 1.03 bar, and a frequency of 3.87 MHz. We compare our results with predictions of the quasi-classical and Ginzburg-Landau theories, and present values of the Fermi-liquid parameter F ₂ ^a and the -parameter ₃₄₅.     

Thermal Conductivity of Sm3S4 System with Mixed Valence Sm Ions

The thermal conductivity () and electrical resistivity () of mixed-valence compound Sm₃S₄ have been measured in the temperature range 5 to 300 K. The present results and those presented previously [1] for the thermal conductivity between 80 to 850 K are interpreted in terms of the temperature-dependent fluctuating valence of Sm ions. Sm₃S₄ crystallizes in the cubic Th₃P₄ structure, and the cations with different valences occupy equivalent lattice sites. Divalent and trivalent Sm ions are randomly distributed in the ratio of 1:2 over all possible crystallographic cation positions (Sm²⁺ ₂Sm³⁺ ₂S^2– ₄). The behavior of the Sm₃S₄ lattice thermal conductivity _ph is extraordinary since valences of Sm ions are fluctuating (Sm³⁺Sm²⁺) with a temperature dependent frequency. In the interval 20 to 50 K (low hopping frequencies), _ph of Sm₃S₄ varies as _ph T ^–1 (it is similar to materials with static distribution of cations with different valences): at 95 to 300 K (average hopping frequencies 10⁷ to 10¹¹ Hz), _ph changes as _ph T ^–0.3 (it is similar to materials with defects). Defects in Sm₃S₄ appear because of local strains in the lattice by the electrons hopping from Sm²⁺ ions (with big ionic radii) to Sm³⁺ ions (with small ionic radii) and back (Sm²⁺Sm³⁺), at T>300 K (high hopping frequencies), _ph becomes similar to materials with homogenous mixed valence states [1].     

Longitudinal magnetic relaxation in superfluid 3He

Longitudinal magnetic relaxation in both ³He-A and ³He-B is studied in a variety of magnetic fields and three different geometries. Relaxation as described by Leggett and Takagi is observed for particular geometries in both ³He-A and ³He-B within a very limited range of magnetic field and temperature near T _c. Under certain other conditions the longitudinal magnetization in ³He-A does not relax monotonically in time. Relaxation in ³He-B very near the critical temperature is shown to be remarkably different following nominal 90 and 180 pulses. Other observations using RF pulses with a time-dependent frequency provide evidence for a negative frequency shift in ³He-B at large tipping angles in certain geometries.Supported by the U.S. Department of Energy under contract number EY-76-S-03-0034, P.A. 143.     

Spin dynamics of superfluid3He-B in a slab geometry

The spin dynamics and the spin relaxation mechanisms of the superfluid³He-B were studied by using the NMR method in a slab geometry, where the superfluid3He-B was confined between narrow parallel plates with a gap smaller than the healing length of then-texture and the magnetic field was applied parallel to the plates. The relaxation parameter in the Leggett-Takagi (LT) equations was determined from a line width measurement of the transverse CW NMR. By using the pulsed NMR method, spin dynamics were studied in the nonlinear region. The observed spin dynamics were in good agreement with a numerical calculation of the LT equations together with the relaxation parameter determined by the CW NMR. When the tipping angle became larger than a certain critical value, the superfluid³He-B entered the Brinkman-Smith (BS) state. In this case, we observed the slow relaxation process in the BS state and then the rapid recovery process from the BS state to the initial non-Leggett configuration. The slow process in the BS state was attributed to the surface relaxation mechanism due to the torque from the surface-field energy.     

On a nonlinear stefan problem arising in the continuous casting of steel

Summary The continuous casting process employed in the steel industry is a many faceted big industrial problem which has given rise to many sub-problems. Here, we examine the problem involving the determination of the solid-liquid steel interface and we develop and extend a previously proposed model, which incorporates heat transfer through two layers of solid and liquid mould powder and the interface between the solid powder and the mould wall. The problem simplifies to the classical Stefan problem except that the condition on the boundary is nonlinear. Integral formulation procedures are used to establish the normalized pseudo steady state temperature as an upper bound to the normalized actual temperature. The pseudo steady state approximation yields an upper bound on the interface position, which an independent numerical enthalpy scheme confirms to be an extremely accurate approximation for the parameter values occurring in practice. The present work is important since it provides a simple method for the prediction of the solid-liquid steel interface and a bounding procedure which can be used to validate other estimates.List of symbols D flux thickness atz ^*=0 - H enthalpy - L latent heat of steel - M the half thickness of the cast steel - Q heat flux - R interface thermal contact resistance - S _m ^* melting temperature of steel - T ^* temperature - T normalized temperature - T _m ^* melting temperature of mould powder - T ^* temperature of cooling water - T _w ^* temperature on mould wall - T _u ^* temperature of solid flux on its interface with mould wall - T ₀ ^* temperature on casting surfaceT ^*(0,z ^*) - U casting speed - X ^*(z ^*) physical coordinate of the steel phase change boundary - X(z) non-dimensional coordinate of the steel phase change boundary - c specific heat of steel - h(z ^*) thickness of liquid flux layer - k thermal conductivity of steel - ks thermal conductivity of solid flux layer - k _l thermal conductivity of liquid flux layer - m surface heat transfer coefficient - s(z ^*) thickness of solid flux layer - t time - , , positive constants given by (3.2) - constant given by (3.5) - coefficient of linear thermal expansion of steel - angle shown in Figure 2 - positive constant defined by (M-D)/2 - (z) positive parameter - (z ^*) amount of contraction of steel - density - (z) positive parameter used in (5.7) and (5.8)     

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     

Investigation of the thermal and electrical transport properties of niobium and niobium films at temperatures between 9 and 50 K

The thermal conductivity and the electrical conductivity of niobium crystals and niobium films have been investigated in the normal state from 9 to 50 K. The deviations from the Matthiessen rule, w=/T+T², have been studied in detail for the thermal case. The investigation shows a slight dependence of the electron-phonon scattering coefficient upon the impurity content of the sample. With the specific electrical residual resistivity ₀ as the measure for the impurity content, the following correlation can be formulated: =1.2×10^-2[₀/-cm)]^0.04, being obtained in cm/W K. Above 20 K an additional scattering mechanism occurs. The temperature dependence of the additional resistance W between 20 and 50 K is proportional to T ^5.5 ··· T ⁴. Possible causes of this phenomenon are discussed. For the discussion, all the data available in the literature on the thermal conductivity of niobium in this temperature region are used.     

Temperature field in a plate containing a system of heat sources

The temperature field is determined in a circular plate with a system of thin extrinsic heat sources.Notation T temperature in the plate with the inclusions - r polar radius - polar angle - time - (r,) coefficient of thermal conductivity - (r,) heat transfer coefficient - C(r,) volume heat capacity - W(r,, ) specific intensity of the heat sources - half thickness of the plate - (x) Dirac's delta function - ¯T finite Fourier cosine transform of the temperature - p parameter for this transformation - T Laplace transform of the temperature - s its parameter - Iv(x) Bessel function with imaginary argument of order - K _v (x) the MacDonald function of order - and dimensionless temperature - Po Pomerantz number - Bi Biot number - Fo Fourier's number - dimensionless polar radius - b₁ ^* dimensionless radius of the circle on which the inclusions are placed - R^* dimensionless radius of the plate Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 3, pp. 495–502, March, 1981.     

Half-solitons in superfluid3He-A: Novel π/2-quanta of phase slippage

Core structures of nontopological solitons between inequivalent vacua in superfluid³He-A are considered. We analyze the symmetries of these A-A interfaces, and compute their hard-core structures in the Ginzburg-Landau regime. We discuss both domain walls where the orbital anisotropy l-vector is flipped (l–l), and those with the same l(x=–) and l(x=+) asymptotics. In particular, we find new classes of A-A boundaries: these novel /2-solitons, which can occur in the absence of a change in the asymptotic l-vector field, constitute the elementary quanta of phase slippage in superfluid³He-A. We ascribe these half-solitons to a new topological scenario for the flaring-out of vorticity in the extended (k, r)-space. Edges of such walls serve to provide vortices with 1/4 quantum of circulation in³He-A. In analogy with the B-B domain walls in superfluid³He-B, solitons of pure phase slippage by —with a normal core—prove unstable in³He-A; they either fission into a pair of ordinary l-solitons—domain walls with superfluid cores both flipping the orbital anisotropy axis (i.e., l–ll), or form a bound pair of walls, each of which constitutes an l-soliton with a phase shift of /2. Our investigation of the superfluid A-A vacuum interfaces may prove useful in a broader context since the A-A boundaries exemplify the possible domain walls relevant for the Higgs-field solitons (cosmic domain walls) within the Weinberg-Salam model.     

Coupling of order parameter collective modes to spin density in3He-B

We derive a general expression for the dynamic spin susceptibility of³He-B which is valid for all magnetic fields. The coupling of real and imaginary modes by particle-hole asymmetry is taken into account. Then we calculate the contribution of the mode at frequency =2 – 1/4 ( is the effective Larmor frequency) to the transverse susceptibility. The spectral weight of this mode in magnetic resonance absorption is proportional to (/)^1/2 (–)², where and are particle-hole asymmetry parameters. From the experimental coupling strength of the real squashing mode to sound we estimate (–)²10^–4. The dynamic susceptibility satisfies the sum rules of Leggett. Finally we point out the difficulties in calculating the transverse NMR frequency of³He-B. These difficulties arise from theS _z =0 Cooper pairs and from the coupling ofJ _z =±1 modes forJ=1 andJ=2.     

Ortho-para conversion in hydrogen bubbles in copper

The low-temperature heat release in copper due to ortho-para conversion in hydrogen bubbles is investigated. Deviations from a model of free solid hydrogen are observed: a more intense heat release atT10 K and a rapid (10 h) heat release after cooling to 1.3 K. The experimental results can be explained by the assumption of autocatalytic conversion in the bulk and the catalytic influence of the bubble surface.     

Nonlinear asymptotic theory of hypersonic flow past a circular cone

Summary The hypersonic small-disturbance theory is reexamined in this study. A systematic and rigorous approach is proposed to obtain the nonlinear asymptotic equation from the Taylor-Maccoll equation for hypersonic flow past a circular cone. Using this approach, consideration is made of a general asymptotic expansion of the unified supersonic-hypersonic similarity parameter together with the stretched coordinate. Moreover, the successive approximate solutions of the nonlinear hypersonic smalldisturbance equation are solved by iteration. Both of these approximations provide a closed-form solution, which is suitable for the analysis of various related flow problems. Besides the velocity components, the shock location and other thermodynamic properties are presented. Comparisons are also made of the zeroth-order with first-order approximations for shock location and pressure coefficient on the cone surface, respectively. The latter (including the nonlinear effects) demonstrates better correlation with exact solution than the zeroth-order approximation. This approach offers further insight into the fundamental features of hypersonic small-disturbance theory.Notation a speed of sound - H unified supersonic-hypersonic similarity parameter, - K hypersonic similarity parameter, M - M freestream Mach number - P pressure - T temperature - S entropy - u, v radial, polar velocities - V freestream velocity - shock angle - cone angle - density - density ratio, /() - ratio of specific heats - polar angle - stretched polar angle, / - (), (), () gage functions     

First viscosity of dilute3He-4He mixtures below 0.6 K

Starting with the Boltzmann transport equation, the first viscosity of dilute³He-⁴He mixtures for various³He concentrations x is evaluated up to around T 0.6 K by including the contribution from three-phonon processes (3PP) in the anomalous elementary excitation spectrum of liquid⁴He. Due to 3PP, the characteristic time for³He viscosity at high temperatures, i.e., T2T_F where T_F is the³He Fermi temperature, is evaluated as 5 × 10^–12/xT, which is smaller than the value estimated by Rosenbaum et al. This is interpolated with in the degenerate (quantum) region, TT_F. The obtained viscosities are in better agreement with experimental results than those of Baym and Saam, whose theory does not include 3PP. However, at very low concentrations there exists a discrepancy between the present theory and experiments, so that an alternate treatment should be considered.