Chebyshev approximation for the roots of the equation BiWГ(μ)=μVГ(μ)

A minimax approximation, uniform for Bi [0, ), is developed for the roots of the equation BiW()=V(), by means of Chebyshev polynomials.Translated from Inzhenero-Fizicheskii Zhurnal, Vol. 28, No. 4, pp. 710–715, April, 1975.     

Influence of stabilizers on Na-β′′-Al2O3 phase formation in Li2O(MgO)-Na2O-Al2O3 ternary systems

The influences of stabilizers on - and -Al2O3 phase formations in Li2O(MgO)-Na2O-Al2O3 systems were investigated. When stabilized with 4MgCO3Mg(OH)25H2O, most of the -Al2O3 phase formed below 1200°C and further - to -Al2O3 transformation with an increase of temperature was not observed. On the other hand, when stabilized with Li2CO3,-Al2O3 formation occurred by two steps. First, -Al2O3 was partly formed below 1200°C, and, second, noticeable transformation from -Al2O3 to -Al2O3 occurred at higher temperature ranges. It was shown that transient eutectic liquid in the Li2O-Na2O-Al2O3 system promoted the - to -Al2O3 transformation at higher temperatures. Uniform distribution of both Mg2+ and Li+ stabilizing ions enhanced -Al2O3 formation at low temperatures. In the Li-stabilized systems, however, homogeneous distribution of Li+ ions hindered both the formation of transient eutectic liquid and the second - to -Al2O3 phase transformation at high temperatures.     

Paramagnetic resonance in a “dirty” spin-glass

For a spin-glass with nonmagnetic defects (n _m ^1/3l 1, where n _m is the magnetic impurity concentration and l is the mean free path) an absorption function () is derived. Three ranges of temperature and external magnetic field are considered. In the vicinity of the transition the value of () d is estimated as a function of temperature and field.     

Microstructure and mechanical properties of rapidly quenched L20 and L20+L12 alloys in Ni-Al-Fe and Ni-Al-Co systems

Ductile L2₀-type wires and+L1₂-type duplex wires with high strengths and large elongation in the Ni-Al-Fe and Ni-Al-Co ternary systems have been manufactured directly from the liquid state by an in-rotating-water spinning method. The wire diameter was in the range 80 to 180m and the average grain size was 2 to 4m for the wires and 0.2 to 1.0m for the+ wires. _y, _f and _p of the wires were found to be about 360 to 760 MPa, 560 to 960 MPa, and 0.2 to 5.5%, respectively, for the Ni-Al-Fe system, those of the+ wires were about 395 to 660 MPa, 670 to 1285 MPa, and 3.5 to 17%, respectively, for the Ni-Al-Fe system, and about 260 to 365 MPa, 600 to 870 MPa, and 4.0 to 7.0%, respectively, for the Ni-Al-Co system. Cold-drawing caused a significant increase in _y and _f and the values attained were about 1850 and 2500 MPa, respectively, for Ni-20Al-30Fe and Ni-25Al-30Co wires drawn to about 90% reduction in area. The high strengths, large elongation and good cold-workability of the melt-quenched and+ compound wires have been inferred to be due to the structural change into a low-degree ordered state containing a high density of phase boundaries, suppression of grain-boundary segregation and refinement of grain size.     

Mössbauer studies of α″-Fe16N2 and α′-Fe8N films

Conversion-electron Mössbauer spectra of epitaxial -Fe₁₆N₂ and -Fe₈N films have been studied and their differences are discussed in detail. The Mössbauer spectrum of -Fe₁₆N₂ can be decomposed into three subspectra, which correspond to the 4d, 8h and 4c sites. The Mössbauer spectrum of -Fe₈N can be fitted using four spectra based on a nitrogen-atom-random-distribution model. The average hyperfine field is larger (3%) for -Fe₁₆N₂ than for -Fe₈N, which is approximately consistent with a 4.1% enhancement of the magnetic moments for -Fe₁₆N₂. The iron moments tend to locate in the film plane for -Fe₁₆N₂ and to arrange perpendicularly to the film plane for -Fe₈N.     

γ′ Formation and morphology evolution in the undercooled structure of DD3 Single crystal superalloy

An investigation of the formation and its morphology evolution in the bulk undercooled DD3 single crystal superalloy is performed. The application of a molten salt denucleating technique combined with thermal cycle enables such investigation over a wide range of undercooling up to 210 K. The microstructure formation has been respectively discussed with respect to undercooling, nucleation and solute segregation during solidification and post-solidification, by employing the classical nucleation theory. Furthermore, TEM and SEM technique are adopted to reveal the microscopy and to illustrate other factors correlated to the precipitation. It is found that the size, fraction, and distribution of precipitated in as-solidified DD3 single crystal superalloy are all influenced by melt undercooling.     

First principles study of effect of lattice misfit on the bonding strength of Ni/Ni3Al interface

By using a discrete variational X (DV-X) method, the electronic structures and bonding strengths of Ni/Ni₃Al (or /) interface with different lattice misfits () were calculated in the framework of the nonrelativistic first-principles theory. In order to describe the effect of on the interfacial binding strength and the structural stability of coherent / interface, we calculated the interfacial binding covalent bond density (CBD) and the local environmental total bond overlap population (LTBOP). Very obvious effects of lattice misfits on the electronic structures of coherent / interface were found. On one hand, less than –0.6% negative lattice misfit can increase the binding strength of the /' interface. On the other hand, the local environmental total bonding strength of the /' interface decreases with increasing magnitude of . Therefore, the magnitude and sign of lattice misfit must be carefully controlled to balance the high-temperature creep strength of Ni-base single crystal superalloy and the structural stability of the /' interface when one designs new alloys.     

A finite volume technique to simulate the flow of a viscoelastic fluid

Hydrodynamically developing flow of Oldroyd B fluid in the planar die entrance region has been investigated numerically using SIMPLER algorithm in a non-uniform staggered grid system. It has been shown that for constant values of the Reynolds number, the entrance length increases as the Weissenberg number increases. For small Reynolds number flows the center line velocity distribution exhibit overshoot near the inlet, which seems to be related to the occurrence of numerical breakdown at small values of the limiting Weissenberg number than those for large Reynolds number flows. The distributions of the first normal stress difference display clearly the development of the flow characteristics from extensional flow to shear flow.List of symbols D rate of strain tensor - L slit halfheight - P pressure, indeterminate part of the Cauchy stress tensor - R the Reynolds number - t time - U average velocity in the slit - u velocity vector - u,v velocity components - W the Weissenberg number based on the difference between stress relaxation time and retardation time - W ₁ the Weissenberg number based on stress relaxation time - x,y rectangular Cartesian coordinates - ratio of retardation time to stress relaxation time - zero-shear-rate viscosity, ₁ + ₂ - ₁ non-Newtonian contribution to - ₂ Newtonian contribution to - ₁ stress relaxation time - ₂ retardation time - density - (, , ) xx, yy and xy components of ₁, respectively - determinate part of the Cauchy stress tensor - ₁ non-Newtonian contribution to - ₂ Newtonian contribution to      

Analysis of the effect of the decomposition of char-forming heat-insulating materials on the free discharge of a gas mixture

The article presents results of a numerical solution of a nonsteady problem on the free discharge of a mixture of gases from a hemispherical volume with allowance for thermal decomposition of heat-insulating materials.Notation V volume - S area - t - P p - T - u v - Q q, dimensional and dimensionless time, pressure, temperature, TIM decomposition rate, and heat flux - adiabatic exponent - R gas constant - density - H specific enthalpy - c specific heat - thermal conductivity - , , _s dimensionless complexes - coefficient expressing the radiative properties of the gas medium and the heat-transfer surface - Stefan-Boltzmann constant Indices 0 initial state and scale factors - s surface - coke - M TIM material - P pyrolysis front - A ablation front - v volatile degradation products - adiabatic conditions - c completion of discharge Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 54, No. 5, pp. 787–793, May, 1988.     

Computational thermography: Numerical modeling of the thermal regimes of building structures

We consider numerical methods of simulating thermal regimes of building structures that make it possible to create optimum structures as regards power consumption by using more accurate calculations than those available in existing construction specifications and regulations. Possible means of reducing energy expenditures for formation of an optimum microclimate in living quarters are described.Notation R thermal resistance to heat transfer - _i thermal conductivity - c _i heat capacity - _i moisture content - i number of a layer - S thermal inertia of the material - density of the substance - frequency of harmonic vibrations - t time - Fo Fourier number - thermal diffusivity - t time step - x spatial step - Bi Biot number - h _c coefficient of convective heat transfer - k thermal conductivity - T ambient temperature - T _w wall temperature - Nu Nusselt number - Ra _l Rayleigh number - Gr _l Grashof number - Pr Prandtl number - g free fall acceleration - coefficient of thermal volumetric expansion of air - l characteristic length - coefficient of kinematic viscosity of air - determining temperature - thermal conductivity of the material - q heat flux - s area of the heat transfer surface - perimeter of the heat transfer surface - T free stream velocity - air viscosity Academic Scientific Complex A. V. Luikov Heat and Mass Transfer Institute of the Academy of Sciences of Belarus, Minsk. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 66 No. 6, pp. 733–738, June, 1994.     

Characterization of α ? β PbF2 phase transition by several techniques

X-ray Diffraction (XRD), Dynamic-Mechanical Analysis (DMA), Impedance Spectroscopy (IS), and Scanning Electron Microscopy (SEM) have been used to the study of phase transition in PbF₂ pellets pressed uniaxially in the 37 MPa–480 MPa range. A mixture of and phases is detected and the -phase content at room temperature is found to be dependent on the applied load. The dilation results on DMA, the phase identification by XRD, the ionic conductivity results by IS analysis and the SEM micrographs of -PbF₂ pellets show evidences for the increase in -phase content at the expense of the -phase. SEM analysis provided further evidence for specimen sintering under heating at approximately 498 K.     

Microstructure and crystallographic texture of rolled polycrystalline Fe3Al

An imperfectly B₂ ordered Fe₃Al aggregate was cast, thermomechanically hot rolled and finally annealed at 870 K. Subsequently, the specimen was rolled at 800–830 K to a strain of 80%. The microstructure and the crystallographic texture of the rolled polycrystalline sample was investigated within the range =20–80%. The microstructure consisted of flat, elongated grains. In numerous grains straight slip lines were detected. Even after =80% recrystallization was not observed. The rolling texture of Fe₃Al considerably deviates from that of non-ordered body centered cubic (b.c.c.) alloys and pure b.c.c. metals. The {111}uvw texture fibre (7-fibre) was very pronounced, while the {hkl}110 fibre (-fibre) was very weak. The {112}110 orientation which represents the strongest texture component in non-ordered b.c.c. alloys did not occur at all. The textures are discussed in terms of the {110}111, {112}111, {112}111 and {123}111 slip systems. The contribution of crystallographic slip of the various types of potential slip systems was simulated by means of the Taylor theory.     

Integral results for nonlinear diffusion equations

We show how to construct integral results for the multi-dimensional nonlinear diffusion equation c/t=·(D(c)c) and for some generalisations of this. For appropriate boundary conditions these become integral invariants. An application of these results to determining the large-time behaviour of some radially symmetric problems is indicated.     

Application of coherent-optical methods in physical studies of evaporation

The application of the methods of laser and holographic interferometry to the problems of measuring evaporation rates is examined. Mass transfer accompanying evaporation in the region of extradiffusion monitoring is studied.Notation j_v specific mass flux of the vapor, kg/(m²·sec) - _c coefficient of condensation - _v coefficient of evaporation - D coefficient of diffusion - m²/sec, wetting angle - R radius of the vessel, m - time, sec - h height of the segment, m - wavelength of the laser radiation, m - N order of the interference fringe or the number of fringes passing through a given point - density of the matter, kg/m³ - length of the cell with the liquid of interest, m - T temperature, K - n refractive index of the medium - m mass - kg, V volume of the spheroidal segment, m³ - _liq and _g molar mass, kg/mole - C₀ and C_p concentration of vapor in the gas, kg/m³ - a and b semiaxes of the spheroid, m - _e ellipsoidal coordinate of a point on the surface, m² - c/n derivative along the normal - r coordinate of a point on the surface of evaporation, m - n change in the refractive index of the medium Indices st standard liquid - liq liquid - g gas - 0 starting state - p equilibrium pressure Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 55, No. 4, pp. 605–611, October, 1988.     

Supercarrier Effective Mass Isotope Effect by Interband Scattering

Supercarrier effective mass isotope effect (exponent ) is investigated using a two-band model with interband pair scattering. The corresponding repulsive interaction incorporates besides the dominating electronic (Coulomb) part an electron-phonon contribution inversely proportional to the ionic mass factor. Calculations illustrating the behaviour of T _c , its isotope exponent , and with doping in La _2–x Sr _x CuO ₄ type underdoped system reflect the observed tendencies. ² Both and diminish with doping, the sign of is opposite to . A typical estimation gives || 0.2.     

Effect of crystalline phase, orientation and temperature on the dielectric properties of poly (vinylidene fluoride) (PVDF)

The effect of crystalline phase, uniaxial drawing and temperature on the real () and imaginary () parts of the relative complex permittivity of poly (vinylidene fluoride) (PVDF) was studied in the frequency range between 10² and 10⁶ Hz. Samples containing predominantly and phases, or a mixture of these, were obtained by crystallization from a DMF solution at different temperatures. phase samples were also obtained from melt crystallization and from commercial films supplied by Bemberg Folien. Different molecular orientations were obtained by uniaxial drawing of and phase samples. The results showed that the crystalline phase exerts strong influence on the values of and , indicating that the _a relaxation process, associated with the glass transition of PVDF, is not exclsively related to the amorphous region of the polymer. An interphase region, which maintains the conformational characteristics of the crystalline regions, should influence the process decisively. The molecular orientation increased the values of for both PVDF phases and modified its dependence with temperature over the whole frequency range studied. The influence of the crystallization and molecular orientation conditions on the dc electric conductivity (_dc) were also verified. The value of _dc was slightly higher for samples crystallized from solution at the lowest temperature and decreased with draw ratio.     

Preferentially orientated precipitation in MnTiO3 single crystals

Preferentially orientated precipitation of -TiO₂ (rutile) needles in single crystals of MnTiO₃ grown by a floating-zone method under a controlled atmosphere of oxygen fugacity was studied. Optical microscopy and X-ray analysis revealed that the orientation relation between the -TiO₂ precipitates and the MnTiO₂ matrix is: {000 1}MnTiO₃// {111}-TiO₂ and 11¯20MnTiO₃// 110-TiO₂. The precipitation phenomenon was explained by introducing a nucleation and growth mechanism which was experimentally supported by heat treating experiments.     

Vortex imaging in superconducting films by scanning hall probe microscopy

We have used a low noise Scanning Hall Probe Microscope (SHPM) to study vortex structures in superconducting films. The microscope has high magnetic field (2.9×10^–8T/Hz at 77K) and spatial resolution, 0.85m. Magnetic field profiles of single vortices in High T_c YBa₂Cu₃O_7– thin films have been successfully measured and the microscopic penetration depth of the superconductor has been extracted as a function of temperature. Flux penetration into the superconductor has been imaged in real time (8s/frame).     

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.     

Temperature and randomness dependence of the pair-breaking parameter in superconducting aluminum films

Magnetoconductance and excess conductance due to superconducting fluctuations in aluminum films are measured in order to study the temperature dependence of the pair-breaking parameter at temperatures nearT _c . The parameter _M is estimated from the relation =/8k _B T_in, where _in is the inelastic scattering time deduced from the analysis of the magnetoconductance. The parameter _F is determined by fitting theories to data on the excess conductance at zero magnetic field. It is shown that: (1) For films with a wide range of the sheet resistanceR , 12R 200 /, the temperature dependence of _M nearT _c agrees well with the theory of Brenig et al. (2) For clean films withR 100 /, the value of _F analyzed with theories including the correction term to the Maki-Thompson contribution shows almost the same temperature dependence as _M . In a film withR 200 /, however, a discrepancy between _M and _F remains.On leave from College of General Education, Kyushu University, Ropponmatsu, Fukuoka, Japan.