Thermophysical properties data on molten semiconductors

Thermophysical properties of molten semiconductors are reviewed. Published data for viscosity, thermal conductivity, surface tension, and other properties are presented. Several measurement methods often used for molten semiconductors are described. Recommended values of thermophysical properties are tabulated for Si, Ge, GaAs, InP, InSb, GaSb, and other compounds. This review shows that further measurements of thermophysical properties of GaAs and InP in the molten state are required. It is also indicated that a very limited amount of data on emissivity is available. Space experiments relating to thermophysical property measurements are described briefly.Nomenclature Density - C _p Specific heat - Kinematic viscosity - Dynamic viscosity= - Thermal diffusivity - Thermal conductivity=C_p - Volumetric thermal expansion coefficient - Surface tension - d/dT Temperature coefficient of surface tension - g Gravitational acceleration - T Temperature - T Temperature difference - L Characteristic dimension     

A flat jet in a granular bed of finite height

The distribution of gas flows in the vicinity of the jet is discussed and the conditions of disruption of the static equilibrium of the bed, the formation and growth of a cavity, and the jet breakthrough of the bed are investigated qualitatively.Notation a, b functions calculated in [11] - C, C constants in (7) - F derivative of the complex potential - f function in (6) - G function defined in (19) - H dimensionless height of bed - h height of cavity - k coefficient introduced in (15) - p, po pressure inside bed and in cavity - p dimensionless pressure drop - Q, q dimensional and dimensionless jet flow rates - q₁, q₂ critical values - T dimensionless height of cavity - T₀, T₁ T₁, T₂ characteristic values of T - u,v filtration velocities - u, u_* initial filtration velocity in the bed and minimum fluidization velocity - u_o velocity scale introduced in (14) - u * velocity scale introduced in (14) - u* velocity of fictitious flow defined in (15) - U complex velocity - Z=X+iY, z=x+iy dimensionless coordinates - z=x+iy dimensional coordinates - coefficient of hydraulic resistance - parameter from (5) - specific weight of particles' material - porosity - =+i coordinates in the plane obtained from z=x+iy as a result a of conformai transformation - _m value of giving a minimum of the function G - f complex and real flow potentials - angle of internal friction - stream function - angle of inclination of boundaries of the region of plastic flow to the vertical Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 5, pp. 804–812, November, 1979.     

Stress-induced hydrogen movement and the partial molal volume of hydrogen in AISI 4340 steel

Stress-induced movement of hydrogen to the high tensile region in AISI 4340 steel was measured at room temperature and 202 °C. A neodymium hydrogen detection method was used to determine the location and concentration of hydrogen. The AISI 4340 stress rings with local hydrogen content up to 0.69 ppm and loaded to 16.87, × 103 kg cm-2 did not fail, whereas a stress ring with 0.73 ppm did fail for the test condition cited. The predicted hydrogen concentration versus fracture time curves at constant tensile stress indicated a good agreement with the stress ring test data.The partial molal volume of hydrogen, ¯H, was calculated to be 2.47 cm3 per g-atom for AISI 4340 steel, which was greater than the reported value for alpha iron at 2.0 cm3 per g-atom. Knowing the value ¯H and the hydrogen content for equation RT In C/Co = ¯H/3 the increase of hydrogen concentration by a given applied stress can be calculated.     

Solution of thermal conductivity problems with boundary condition of the third kind and arbitrary coordinate and time dependence of the biot number

An analytical solution of the thermal conductivity problem with boundary conditions of the third kind and arbitrary coordinate and time dependence of the Biot number is found in the form of a converging series of quadratures.Notation , z dimensionless coordinates - dimensionless temperature - Q dimensionless volume heat-liberation density per unit time - Fo=/² Fourier number - Bi₁(, Fo)=(, Fo) · / Biot number - thermal diffusivity coefficient - plate thickness - time - (, Fo) heat-liberation coefficient - thermal conductivity coefficient - i summation index - Jo zero order Bessel function of the first kind Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 536–540, September, 1981.     

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.     

The crystal growth and thermoelectric properties of chromium disilicide

Single crystals of chromium disilicide about 8 mm in diameter and 35 mm long were grown using the floating zone technique. Measurements of electrical resistivity , Hall coefficient R and thermoelectric power were carried out in the temperature range from 85 to 1100 K. The values of and showed the anisotropy over the temperature range studied. The ratios parallel and perpendicular to the c-axis were / =1.9 and /=1.7 respectively, at room temperature. It was found to be a degenerate semiconductor having the hole concentration of 6.3×10²⁰ cm^–3 below 600 K. The effective masses of holes parallel and perpendicular to the c-axis determined from the thermoelectric power and the hole concentration near room temperature were estimated to be five and three times as large as a free electron mass, respectively. The calculation on the values of and was made using those effective masses. These values showed good agreement with the observed values in the temperature range from 150 to 1100 K.     

The variation of the index of refraction in a vortex tube

Three models of a vortex tube (isentropic, isothermal, and isochoric) are considered as optical inhomogeneities. Expressions relating the index of refraction to the coordinate are obtained. The possibility of obtaining Schlieren pictures of such flows is discussed.Notation a speed of sound - n index of refraction - p pressure - r radius - T absolute temperature - v linear velocity - angular deflection of the beam - x adiabatic exponent - density - angular velocity - ¯v, ¯p etc. dimensionless parameters - v₀, ₀ values at the core bounboundary - p, etc. stagnation values - n_c index of refraction at center of vortex     

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.     

Underpinning of a simple blunt flaw fracture initiation relation

With the cohesive process zone representation of the micro-mechanistic processes that are associated with fracture as a basis, the author is involved in a wide-ranging research programme, the objective being to extend the fracture mechanics methodology for sharp cracks to blunt flaws, so as to take credit for the blunt flaw geometry. In earlier work, a Mode I fracture initiation relation has been derived, subject to the restriction that the process zone size s is small compared with the flaw depth (length) and any characteristic dimension other than the flaw root radius . The relation gives the critical elastic flaw-tip peak stress _pcr, and has been derived using a two-extremes procedure, whereby the separate, and indeed exact, solutions for small and large s/ values are blended together to give an all-embracing relation that is valid for all s/ values. _pcr is expressed in terms of the process zone material parameters and geometrical parameters but, for a wide range of flaw geometry parameters, _pcr essentially depends on only one geometrical parameter . This paper provides underpinning for the general thrust of the two-extremes procedure by appealing to exact results for the complete spectrum of s/ values from analyses of appropriate Mode III models. Results obtained by applying the two-extremes procedure are shown to be in very good agreement with the exact results.     

Heat transfer of cylindrical bodies when a system of round jets flows over them

An experimental installation for the study of the heat transfer of cylindrical bodies in interaction with multijet streams is described. The test data are generalized in criterial dependences with allowance for the range of variation of the heights of rise of the cylinders above the jet grids.Notation D, d diameters of cylinders and of openings of jet grid, m - R radius of jet grid, m - h, h=h/d absolute and relative heights of rise of cylinder above jet grid - S₁, S₂ longitudinal and transverse distances between rows of openings in jet grid, m - w average discharge velocity of jets, m/sec - , average and local coefficients of heat transfer, W/m²·deg - , coefficients of thermal conductivity and kinematic viscosity, W/m·deg, m²/sec - Nu_d=d/ Nusselt number - Re_d=wd/ Reynolds number Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 5, pp. 773–776, November, 1979.     

Stress relaxation in hot-drawn low density polyethylene

The tensile stress relaxation behaviour of hot-drawn low density polyethylene, (LDPE), has been investigated at room temperature at various draw ratios. The drawing was performed at 85° C. The main result was an increase in relaxation rate in the draw direction, especially at low draw ratios when compared to the relaxation behaviour of the isotropic material. This is attributed to a lowering of the internal stress. The position of the relaxation curves along the log time axis was also changed as a result of the drawing, corresponding to a shift to shorter times. The activation volume, , varied with the initial effective stress ₀ ^* according to ₀ ^* 10kT, where ₀ ^* =₀ — _i, is the difference between the applied initial stress, ₀, and the internal stress _i. This result supports earlier findings relating to similarities in the stress relaxation behaviour of different solids.     

Varistor characteristics in PTCR-type (Ba,Sr)TiO3 ceramics prepared by single-step firing in air

This paper deals with donor, acceptor-codoped (Ba_0.4Sr_.6)TiO₃ ceramics with distinct varistor characteristics at room temperature, which were prepared by single-step firing in air. The materials, with the Curie point at around –90 °C, exhibited a large PTCR (positive temperature coefficient of resistivity) effect of more than seven orders of magnitude in the temperature range –90 °C (the resistivity 10³ · cm) to room temperature ( > 10¹⁰ · cm). An apparent dielectric constant of >20000 and tan < 0.05 (at 100 kHz) were observed for the present materials at room temperature, and moreover, the materials exhibited nonlinear current-voltage characteristics with the nonlinear coefficient, , in the range 7–12 and the varistor field, E_v, in the range 0.3–1.0 kV/cm. The value of in the present materials increased systematically with increasing in their PTCR temperature range. It has been found that there exists a close correlation between and the grain-boundary potential barrier height, e, obtained from the -T characteristic of the materials. An almost linear relationship was also found to exist between and log E_v for the present materials.     

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.     

Nonsteady heat transfer in semi-infinite region with nonlinear heat-absorption law

The method of determining the temperature gradient at the boundary of a semi-infinite region proposed earlier for linear problems [1–3] is outlined as it applies to a nonlinear problem.Notation D fractional-differentiation symbol - T temperature - q temperature gradient - k parameter characterizing heat-transfer rate-, x, t, coordinate and time - , , coefficients of general heat-conduction equation - constant Indices s surface Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 1, pp. 143–147, July, 1980.     

Order parameters and energies of analytic and singular vortex lines in rotating3He-A

We present the expressions of the generalized Ginzburg-Landau (GL) theory for the free energy and the supercurrent in terms of thed vector, the magnetic fieldH, and operators containing the spatial gradient and the rotation. These expressions are then specialized to the Anderson-Brinkman-Morel (ABM) state. We consider eight single-vortex lines of cylindrical symmetry and radiusR=[2m/]^–1/2: the Mermin-Ho vortex, a second analytic vortex, and six singular vortices, i.e., the orbital and radial disgyrations, the orbital and radial phase vortices, and two axial phase vortices. These eight vortex states are determined by solving the Euler-Lagrange equations whose solutions minimize the GL free energy functional. For increasing field, the core radius of the texture of the Mermin-Ho vortex tends to a limiting value, while the core radius of the texture goes to zero. The gap of the singular vortices behaves liker forr 0, where ranges between and . The energy of the radial disgyration becomes lower than that of the Mermin-Ho vortex for fieldsH6.5H*=6.5×25 G (atT=0.99T _c and forR=10L*=60 µm, or=2.9 rad/sec). ForR 2 _T ( _T is the GL coherence length) or _c2 (upper critical rotation speed), the energies of the singular vortices become lower than the energies of the analytic vortices. This is in agreement with the exact result of Schopohl for a vortex lattice at _c 2. Finally, we calculate the correction of order (1 -T/T _c ) to the GL gap for the axial phase vortex.     

Heat conduction in a multilayer composite wedge

A new method for analytically solving a problem of steady-state heat conduction for multilayer composite wedge-shaped bodies is suggested based on a generalization of the integral Mellin transform.Notation T temperature - _rr, thermal conductivity coefficients - thickness of composite material layers (1) - N₁(), N ₂ ⁽¹⁾ (), N ₂ ⁽²⁾ () auxiliary local functions from the rapid variable =r/ - m(r, p) auxiliary function entering the core of the generalized integral Mellin transform - ₀ half of the wedge aperture angle Moscow Institute of Chemical Engineering. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 64, No. 4, pp. 487–491, April, 1993.     

Energy Scales in the High-Tc Superconductor YBa2Cu3O6+x

The optical conductivity sum rule is used to examine the evolution of the spectral weight N() in both the normal and superconducting states of optimally and underdoped YBa₂Cu₃O_6+x along the a axis. Differences in N() above and below T _c allow the strength of the superconducting condensate _s to be determined. In the optimally-doped material, _s is fully formed at energies comparable to the full superconducting gap maximum (0.1 eV), while in the underdoped material the energy scale for convergence is considerably higher (0.6 eV). This difference is discussed in terms of normal-state properties.     

Ageing characteristics of cast Zn-Al based alloy (ZnAl7Cu3)

Microstructure and ageing characteristics of a cast Zn-Al based alloy (ZnAl7Cu3) were studied using X-ray diffraction, electron scanning microscopy and back-scattered diffraction techniques. Two stages of phase transformation, i.e., decomposition of zinc rich phase and four phase transformation, + T + , were detected during ageing at 150°C. Electron back-scattered diffraction technique was applied in distinguishing both zinc rich and phases.     

The athermal α → ω transformation in Zr-2 at% Nb alloy

The athermal transformation in Zr-2 at.% Nb alloy has been investigated by transmission electron microscopy. Analysis of the selected-area diffraction pattern has shown that the orientation relationships between the omega and the parent-phase in quenched Zr-2 at.% Nb alloy are the same as have been previously observed for the reaction in pure zirconium. Thus it was deduced that the direct transition has taken place in the alloy during cooling. The-originated -particles were visualized using the dark-field technique. The formation of the athermal omega in the-region of-stabilized Zr-Nb alloy is discussed in terms of the relative positions of the free energy equilibrium curvesT ₀ ,T ₀ ,T ₀ and the correspondingM _s ,M _s andT _s start curves. It is concluded that the omega phase can occur over a much wider range of alloy compositions than is usually recognized on the basis of transformation data.