Thermal transport properties of helium near the superfluid transition. II. Dilute3He-4He mixtures in the superfluid phase

Measurements of the average thermal conductivity _exp hQ/T and of the thermal relaxation time to reach steady-state equilibrium conditions are reported in the superfluid phase for dilute mixtures of³He in⁴He. Hereh is the cell height,Q is the heat flux, andT is the temperature difference across the fluid layer. The measurements were made over the impurity range 2×10^–9<X(³He)<3×10^–2 and with heat fluxes 0.3<Q<160 µW/cm². Assuming the boundary resistanceR _b , measured forX<10^–5, to be independent ofX over the whole range ofX, a calculation is given for _exp. ForQ smaller than a well-defined critical heat fluxQ _c (X) X ^0.9, _exp is independent of Q and can be identified with the local conductivity _eff, which is found to be independent of the reduced temperature = (T–T)/T for –10^–2. Its extrapolated value at T is found to depart forX10^–3 from the prediction X ^–1 , tending instead to a weaker divergence X ^–a witha0.08. A finite conductivity asX tends to zero is not excluded by the data, however. ForQ >Q _c (X), a nonlinear regime is entered. ForX10^–6, the measurements with the available temperature resolution are limited to the nonlinear conditions, but can be extrapolated into the linear regime forX2×10^–7. The results for _exp(Q),Q _c (X), and _eff(XX) are found to be internally consistent, as shown by comparison with a theory by Behringer based on Khalatnikov's transport equations. Furthermore, the observed relaxation times (X) in the linear regime are found to be consistent forX>10^–5 with the hydrodynamic calculations using the measured _eff(X). ForX<10^–5, a faster relaxation mechanism than predicted seems to dominate. The transport properties in the nonlinear regimes are presented and unexplained observations are discussed.     

Effect of SiO2 binder on the precipitation state of an AlCu4Mg1Ag/Saffil composite

The microstructure of an AlCu4Mg1Ag alloy reinforced with 15 vol % Al₂O₃-Saffil fibers was investigated by analytical transmission electron microscopy and compared to the microstructure of the unreinforced alloy. The investigation results show that the composite matrix is enriched in Si as a consequence of the interfacial reaction between the Mg from the alloy and the SiO₂ from the fiber and fiber binder. The presence of Si in the composite matrix modifies the characteristic precipitation state of the monolithic Al-alloy: in the peak aged T6-temper, the phases + S are substituted by a fine and homogeneous precipitation of plates, and a new type of rod-shaped precipitates. On overageing, these rod-shaped precipitates can be classified into two categories: precipitates containing Al, Cu, Mg, and Si (possibly a Q-phase precursor) and Si precipitates that act as nuclei for .     

A generalized scaled equation of state for n-alkanes (methane to n-nonane) in the critical region

A generalized scaled equation of state has been developed to calculate thermodynamic properties of n-alkanes from methane (CH₄) to n-nonane (C₉H₂₀) in the critical region. The equation is valid in the reduced density range 0.7 _c1.3 at T=T _c and up to 1.2T _c at = _c.     

Optimum notch configurations for the chevron-notched four-point bend specimens

The failure sequence following crack formation in a chevron-notched four-point bend specimen is examined in a parametric study using the Bluhm slice synthesis model. Premature failure resulting from crack formation forces which exceed those required to propagate a crack beyond is examined together with the critical crack length and critical crack front length. An energy based approach is used to establish factors which forecast the tendency of such premature failure due to crack formation for any selected chevron-notched geometry. A comparative study reveals that, for constant values of ₁ and ₀, the dimensionless beam compliance and stress intensity factor are essentially independent of specimen width and thickness. The chevron tip position ₀ has its primary effect on the force required to initiate a sharp crack. Small values for ₀ maximize the stable region length, however, the premature failure tendency is also high for smaller ₀ values. Improvements in premature failure resistance can be realized for larger values of ₀ with only a minor reduction in the stable region length. The stable region length is also maximized for larger chevron base positions, ₁, but the chance for premature failure is also raised. Smaller base positions improve the premature failure resistance with only minor decreases in the stable region length. Chevron geometries having a good balance of premature failure resistance, stable region length, and crack front length are 0.20 ₀0.03 and 0.70₁0.80NASA Resident Research Associate at Lewis Research Center.     

Thermodynamic properties of liquid3He-4He mixtures near the tricritical point. I. Vapor pressure measurements and their thermodynamic analysis

Sensitive vapor pressure (P _sat) measurements of ³ He- ⁴ He mixtures by means of a low-temperature strain gauge are described over the temperature range 0.5–1.5 K and the range 0.4<X<0.85, whereX is the ³ He mole fraction in the liquid phase. The vapor pressure cell is flat, with a height of only 2 mm, in order to reduce concentration gradients near the tricritical point. The pressure-sensitive device, which resolves changes of about 5×10 ^–8 atm, is described, and its advantages over a conventional manometer system are discussed. Data taken successively on mixtures of small mole fraction difference are used to locate the phase separation boundary in theT-X plane and also the lambda line from a change in (P _sat/T) _x at these transitions. The limiting slopes (dT/dX) and (dT/dX) of the phase separation curve and the lambda line in the vicinity of their junction point, the tricritical point, are presented and compared with previous work. From the vapor pressure data, the concentration susceptibility (X/) _T,P was obtained. Here = ₃ – ₄ is the chemical potential difference of the respective isotopic components ³ He and ⁴ He. It is shown that (X/) _t diverges as the tricritical point is approached along various paths in theT-X plane, and the relevant tricritical exponents are presented. The weak divergence of (X/) _T along the lambda line predicted from the postulates of Griffiths and Wheeler could not be detected and it is believed that such divergence has to occur in a temperature interval that is far too small to be resolved with present-day techniques. Furthermore, gravity effects might well prevent observation of the weak divergence. The lambda transition is well evidenced by a distinct shoulder in a plot of (X/) _T at constantX as a function ofT. This shoulder becomes smaller and gradually gets topped by a peak asX decreases from the tricritical mole fractionX _t . From a combination of vapor pressure and calorimetric data the chemical potential difference [(X, T)- _t ] is calculated between 0.78 and 1.22 K. Here _t is the value at the tricritical point. From this tabulation the critical line and its slope (d/dT) are obtained and compared with previous values based on calorimetric experiments only and with calculations based on the excess chemical potentials ₃ ^E and ₄ ^E derived from saturated vapor pressure data.Work supported by a Grant from the National Science Foundation.     

Y xBayCuzO7− δ solid solutions

Y_xBa_yCu_zO_7– ceramics forming at isobaric conditions were studied by x-ray diffraction analysis, dynamic magnetic measurements and potentiometric titration. It was established that compositions: 0.8 x 1.2 y=2, z=3; x-1, 1.8 y 2.2, z=3; x=1, y=2, 2.7 z 3.4: are in the homogeneity range of 123. It was found that compositions with nonstoichiometric cations rations have minimum T_c.     

Dielectric properties and microstructural behaviour of B-site calcium-doped barium titanate ceramics

Dielectric properties and microstructural behaviour of Ba_1–x Sr _x Ti_1–y Ca _y O_3–y ceramics, where strontium and calcium were doped on the barium and titanium sites, respectively, within the range 0x0.24 and 0y0.05, were investigated. Calcium addition decreased the tetragonality,c/a, increased the unit cell volume, and lowered the Curie temperature, which were all attributed to the occupancy of Ca²⁺ ions on titanium sites. When sintered at a low oxygen partial pressure of 10^–9 MPa, a resistivity higher than 10¹¹ cm was maintained for the formulations containing B-site calcium substitution more than 0.5 mol %. With increasing the amount of calcium addition, the Curie peak was depressed and completely broadened for the compositions with calcium addition more than 3 mol %, where the average grain size was smaller than 1 m. Co-firing with nickel electrodes in a reducing atmosphere also depressed the Curie peak and inhibited the grain growth due to the diffusion of nickel into the dielectrics.     

A scaled equation of state for real fluids in the critical region

A scaled equation of state is proposed for real fluids in the critical region which incorporates asymmetry with respect to the critical isochore. In the range of reduced densities 0.65(/ _c)1.4 and for reduced temperatures (T/T _c)1.2, the equation represents P-V-T data for steam within the experimental accuracy.     

Mixed convection boundary-layer on a vertical cylinder embedded in a saturated porous medium

Summary The mixed convection boundary layer on a vertical circular cylinder embedded in a saturated porous medium is considered. It is found that the flow depends on the parameter =R _a /P _e whereR _a andP _e are the Rayleigh number and Peclet number respectively. gives the ratio of the velocity scale for free convection to that for the forced convection. When is small the solution is, to a first approximation, obtained by a known heat conduction problem. The flow near the leading edge is considered and it is shown that a solution is possible only for ₀, ₀–1.354, and that a stable finite-difference solution away from the leading edge can be obtained only if –1; with <–1 there is a region of reversed flow near the cylinder. The finite-difference scheme is unable to give a satisfactory solution at very large distances from the leading edge, and to overcome this difficulty a simple approximate solution is developed. This solution shows that at large distances along the cyclinder, forced convection eventually becomes the dominant mechanism for heat transfer. This is also confirmed by an asymptotic solution of the full boundarylayer problem.Nomenclature a radius of cylinder - g acceleration of gravity - K permeability of the porous medium - N _u non-dimensional Nusselt number - r radial coordinate - non-dimensionalr=r/a - R _a Rayleigh number=(g T)Ka/ - P _e Peclet number=U ₀ a/ - T temperature - T _w temperature of the cylinder (constant) - T ₀ temperature of the ambient fluid (constant) - T temperature difference=T _w –T ₀ - u Darcy's law velocity in thex direction - U ₀ velocity of the outer flow - v Darcy's law velocity in ther-direction - x coordinate measuring distance along the cylinder - X non-dimensionalx,=x(aP _e )^–1 - equivalent thermal diffusivity - coefficient of thermal expansion - ratio of free to forced convection=R _a /P _e - viscosity of the convective fluid - density of the ambient fluid - non-dimensional temperature - stream function With 2 Figures     

Interface shapes in a torsionally oscillating,layered medium of viscoelastic liquids

Summary The free surface motion of a layered medium of liquids in a gravitationally stable configuration, resting on top of a layer of mercury, driven by a torsionally oscillating, cylindrical outer wall is investigated. The non-linear problem in the unknown physical domain is expressed as a series of linear problems in the rest state by means of a domain perturbation method. The flow variables and the stress are expanded into series in terms of the amplitude of the oscillation of the cylinder. The shapes in the mean of the interfaces between layers and the flow field are determined up to second order in the perturbation parameter, the amplitude of the oscillation.Nomenclature Density - Modified pressure field - Amplitude of the oscillation - Frequency of the oscillation - Interfacial value of the surface tension - Dynamic viscosity - , , Material functions - Complex viscosity - Stream function - Position vector at timet= - ₁, ₂ The first two Rivlin-Ericksen constants - Quadratic shear relaxation modulus - ,t Time - u Velocity vector - u,v,w Velocity components - S Extra stress tensor - h Interface elevation - D Stretching tensor - G Strain history tensor - A ₁ The first Rivlin-Ericksen tensor - J Mean curvature - p Pressure - t Unit tangent vector - n Unit normal vector - G Shear relaxation modulus - X Position vector in the rest stateD ₀ - r, ,z Rest state coordinates - x Position vector in the physical spaceD - R, ,Z Physical space coordinates - r ₀ Radius of the oscillating cylinder - e _r ,e ,e _z Physical basis vectors inD ₀ - e _R ,e ,e _Z Physical basis vectors inD - Indicates the jump in the enclosed quantity across an interface With 1 FigurePresented at the Xth Canadian Congress of Applied Mechanics, The University of Western Ontario, London, Ontario, Canada, June 2–7, 1985.     

Thermodynamic properties of liquid3He-4He mixtures near the tricritical point. II. Data analysis by the scaling-field method

The scaling theory for tricritical phenomena by Riedel is applied to the analysis of thermodynamic properties of liquid³He-⁴He mixtures near the tricritical point. Within this theory experimental data for the phase diagram, the³He molar concentrationX, and the concentration susceptibility (X/) _T are discussed in terms of two scaling fields that are functions of the temperatureT and the difference = ₃ – ₄ of the chemical potentials of the two helium isotopes. The quantitiesX and (X/) _T in terms of thefields T and as independent variables are obtained for the intervals –0.1<T – T _t<0.53 K and –9< – _t <0.8 J/mole, from vapor pressure and calorimetric data described in a previous paper by Goellner, Behringer, and Meyer. The transformed data are analyzed to yield the tricritical exponents, amplitudes, scaling fields, and scaling functions. The values of the tricritical exponents are found to agree with those predicted by the renormalization-group theory of Riedel and Wegner. (Logarithmic corrections are beyond the precision of the present experiment.) Relations between amplitudes are derived and tested experimentally. The (linear) scaling fields are determined by using their relationship to geometrical features of the phase diagram. The data forX and (X/) _T are found to scale in terms of these generalized scaling variables. The sizes of the tricritical scaling regions in the normal and superfluid phases are estimated; the range of apparent tricritical scaling is found to be appreciably larger in the normal-fluid phase than in the superfluid phase. The tricritical scaling function for the concentration susceptibility is compared with the analogous scaling function for the compressibility of pure³He near thecritical gas—liquid phase transition. Finally, when the critical line near the tricritical point is approached along a path of constant < _t , the experimental data are found to exhibit the onset of the crossover from tricritical to critical behavior in qualitative agreement with crossover scaling.Work supported in part by the National Science Foundation through Grant No. GH-36882 and Grant No. GH-32007, and by a grant of the Army Research Office (Durham).     

Evidence for collective excitations in superconducting tin whiskers

Based on the assumption that a phase-slip center in a clean quasi-one-dimensional superconductor excites a collective oscillation, the time-averaged value of the electrochemical potential of quasiparticles is calculated. At larger distances from the phase-slip center, swings below (or above) the electrochemical potential _p of the Cooper pairs. This makes it possible to understand the unexpected results of previous measurements.     

Heat transfer and the combustion temperature of coke particles in a fluidized bed

The temperature of carbon particles undergoing combustion in a fluidized bed is measured. Heat-transfer laws are ascertained.Notation a diffusivity of air - c heat capacity of air - D diffusion coefficient of oxygen in air - d₀, d initial and running diameters of carbon sphere - d_i diameter of inert particles - k rate constant for carbon monoxide combustion - q calorific value of carbon oxidation to CO₂ - T temperature difference between burning particle and fluidized bed - X, X_n oxygen concentration in the fluidized bed and on the surface of the burning particle - Z, Z_n running concentration of carbon monoxide and concentration on the surface of the burning particle - heat-transfer coefficient between fluidized bed and burning particle - _m maximum heat-transfer coefficient between fluidized bed and a stationary body submerged in the bed - masstransfer coefficient between fluidized bed and burning particle - thermal conductivity of air - kinematic viscosity of air - ₀, gr, ₄ density of oxygen, air, and inert material - relative thickness of burning gas layer - relative thickness of diffusion boundary layer Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 42, No. 1, pp. 21–27, January, 1982.     

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.     

Diffraction studies of β″-magnesium sialon

The compositions of high magnesium content -magnesium sialon crystals within the 3M/4X plane of the Mg-Si-Al-O-N system indicate some form of metal atom ordering wihtin the structure. Although it is not possible using X-ray diffraction to detect weak additional reflections arising from the ordering between magnesium, aluminium, and silicon atoms, such weak reflections are revealed on electron diffraction photographs for a phase, resulting in a tripling of the hexagonal latticec-dimension. These show to have a structure very similar to rhombohedral willemite (Zn₂SiO₄), with the (Mg, Al) metal atoms ordered with respect to the silicon atoms in a 21 ratio. However, there are some additional weak diffraction spots with indices not obeying the rhombohedral condition of –h+k+l=3n. It is proposed that the structure of this is identical to that of willemite and the extra spots are a result of some form of twinning, which implies the existence of ordered microdomains.     

Thermal Expansion and Isothermal Compressibility of TlIn1 – xNdxSe2 (0 ≤ x≤ 0.08) Crystals

The thermal expansion coefficient () and isothermal compressibility ( _T ) of TlIn_{1 – x} Nd _x Se₂(0 x 0.08) crystals were measured between 77 and 400 K. In the range 77–160 K, both and _T increase with temperature, the increase in being much steeper. At higher temperatures, and _T change very little. The observed composition dependences of and _T are interpreted in terms of energy-band structure.     

High-accuracy bench mark solutions to natural convection in a square cavity

A fourth-order high-accuracy finite difference method is presented for the bouyancy-driven flow in a square cavity with differentially heated vertical walls. The two bench mark solutions against which other solutions can be compared were obtained. The present solution is seemed to be accurate up to fifth decimal. The proposed scheme is stable and convergent for high Rayleigh number, and will be applicable to general problems involving flow and heat transfer, especially in three dimensions.List of symbols a thermal diffusivity - g gravitational acceleration - h mesh length in the x-direction - k time step - L side length of cavity - Pr Prandtl number - Ra Rayleigh number = gTL ³/a - t time - T _c, T _h surface temperatures (see Fig. 1a) - T temperature - T temperature difference = T _h - T _c - u, v velocity in the x and y directions, respectively - x, y coordinates - x, y mesh lengths in the x- and y-directions, respectively Greek symbols volumetric expansion coefficient - kinematic viscosity - stream function - vorticity     

Breakup of an anomolously viscous liquid film in a centrifugal force field

An equation is obtained for the breakup radius with consideration of tipping moments and Laplacian pressure forces acting on the liquid ridge at the critical point.Notation K, n rhenological constants - density - surface tension - r current cup radius - R maximum cup radius - r_c critical radius for film breakup - ¯r=¯r=r/R dimensionless current radius - ¯r_c=r_c/R dimensionless critical radius - ₀, _c actual and critical film thicknesses - current thickness - R_r ridge radius - h₀ ridge height - h current ridge height - ₀ limiting wetting angle - current angle of tangent to ridge surface - angle between axis of rotation and tangent to cup surface - angular velocity of rotation - q volume liquid flow rate - v₁ and v meridional and tangential velocities - =4vv _lm/r,=4v_m/r dimensionless velocities - M moments of surface and centrifugal forces - M_v moment from velocity head - p_r pressure within ridge - P_vm pressure from velocity head - p_m, p_pm pressures from centrifugal force components tangent and normal to cup surface - deviation range of breakup radius from calculated value - ¯r_max, ¯r_min limiting deviations of breakup radius - _c angle of tangent to curve _c/°₀=f(¯r) at critical point - t random oscillation of ratio _c/_c Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 1, pp. 51–56, July, 1980.     

Standard Gibbs' energies of formation of BaCuO2, Y2Cu2O5 and Y2BaCuO5

The Gibbs' energies of formation of BaCuO₂, Y₂Cu₂O₅ and Y₂BaCuO₅ from component oxides have been measured using solid state galvanic cells incorporating CaF₂ as the solid electrolyte under pure oxygen at a pressure of 1.01×10⁵ Pa BaO + CuO BaCuO₂ G _f,ox ^o (± 0.3) (kJ mol^–1)=–63.4–0.0525T(K) Y₂O₃ + 2CuO Y₂Cu₂O₂ G _f,ox ^o (± 0.3) (kJ mol^–1)=18.47–0.0219T(K) Y₂O₃ + BaO + CuO Y₂BaCuO₅ G _f,ox ^o (± 0.7) (kJ mol^–1)=–72.5–0.0793T(K) Because the superconducting compound YBa₂Cu₃O_7– coexists with any two of the phases CuO, BaCuO₂ and Y₂BaCuO₅, the data on BaCuO₂ and Y₂BaCuO₅ obtained in this study provide the basis for the evaluation of the Gibbs' energy of formation of the 1-2-3 compound at high temperatures.     

Defects on TiBiTe2 single crystals

Single crystals of rhombohedral TiBiTe₂ examined by transmission electron microscopy consist of large areas separated by {100}- and {110}-type twins. By measuring the rhombohedral angle from the splitting of diffraction patterns in the twin areas, we calculated the residual strain which remained after the transformation O_h D _3d, ranging from 1.2 to 12.2 %. Dislocations with Burgers vector (a/2) 1¯10 were mobile and the main slip system was (111) 1¯10. Planar defects with complex - fringe contrast were also observed.