Thermal conductivity of methane

This paper reports thermal conductivity data for methane measured in the temperature range 120–400 K and pressure range 25–700 bar with a maximum uncertainty of ± 1%. A simple correlation of these data accurate to within about 3% is obtained and used to prepare a table of recommended values.Nomenclature a _k ,b _ij ,b _k Parameters of the regression model, k= 0 to n; i =0 to m; j =0 to n - P Pressure (MPa or bar) - Q _kl Heat flux per unit length (mW · m^–1) - t time (s) - T Temperature (K) - T _cr Critical temperature (K) - T _r reduced temperature (= T/T _cr) - T _w Temperature rise of wire between times t ₁ and t ₂ (deg K) - T ^* Reduced temperature difference (TT _cr)/T _cr - Thermal conductivity (mW · m^–1 · K^–1) - ₁ Thermal conductivity at 1 bar (mW · m^–1 · K^–1) - _bg Background thermal conductivity (mW · m^–1 · K^–1) - _cr Anomalous thermal conductivity (mW · m^–1 · K^–1) - _e Excess thermal conductivity (mW · m^–1 · K^–1) - Density (g · cm^–3) - _cr Critical density (g · cm^–3) - _r Reduced density (= / _cr) - ^* Reduced density difference (– _cr )/ _cr      

Temperature-enthalpy approach to the modelling of self-propagating combustion synthesis of materials

A new temperature-enthalpy approach has been proposed to model self-propagating combustion synthesis of advanced materials. This approach includes the effect of phase change which might take place during a combustion process. The effect of compact porosity is also modelled based on the conduction, convection and radiation in the local scale. Various parametric studies are made to analyse numerically the effects of activation energy, non-reacting phase content, porosity, Biot number, etc. The model predictions of the combustion pattern are in close agreement with those observed in experiments.Nomenclature c Concentration (wt %) - B _i Biot number =hL/k - f Fractional value - c _p Specific heat (J kg^–1 K) - h Heat-transfer coefficient (W m^–2 K) - L Height of material,m - Q Heat of reaction (J kg^–1) - H _SL ^* Latent heat of fusion (J kg^–1) - H _SE ^* Latent heat of fusion at eutectic (J kg^–1) - k Thermal conductivity (W m^–1 K) - k Equilibrium partition coefficient - Reaction kinetic function - t Time (s) - Non-dimensional time - T Temperature (K) - T ₀ Initial temperature (K) - Non-dimensional temperature - H Enthalpy (J kg^–1) - Kinetic function - Non-dimensional enthalpy - v _f Volume fraction of non-reactive phase - V Volume (m₃) - k ₀ Pre-exponential constant to reaction rate (s^–1) - z Cartesian co-ordinate - z^* Non-dimensional co-ordinate - Non-dimensional reacted fraction - Density (kg m^–3) - A non-dimensional temperature - Pore surface emissivity - Planck's constant - i Initial state - r Reacted state - l, L Liquid state - s Solid state - E Eutectic - M Melting point of pure material - P Centre of control volume - s Southern side of central volume - S Southern control volume - n Northern side of central volume - N Northern control volume - * Non-dimensional term - n New time level - o Old time level - m Iteration level     

Electrical conductivity in hot-pressed nitrogen ceramics

The a.c. and d.c. electrical conductivities of some hot-pressed polycrystalline nitrogen ceramics have been measured between 400 and 1000° C. The materials examined were Si₃N₄, 5.0% MgO/Si₃N₄ and two sialons, Si_(6–z) · Al _z · O _z · N_(8–z) having z 3.2 and z 4.0 respectively. The electrical behaviour of all the materials showed similar general features. The d.c. conductivities were about 10^{–10 –1} cm^–1 at 400° C and rose to between 10^–6 and 10^{–5 –1} cm^–1 at 1000° C. The a.c. Data, taken over the frequency range 15 Hz to 5 kHz showed that below about 500° C the a.c. conductivity ( _a.c.) varied with frequency as _a.c. ^s where 0.7 _d.c.) agreed well with the relation _d.c. = A exp(–B/T ^1/4). Above 700° C both the a.c. and d.c. conductivities followed log T ^–1. Hall effect and thermoelectric power measurements enabled the Hall mobility to be estimated as less than 10^–4 cm² V^–1 sec^–1 at 400° C and showed that the materials were all p-type below 900° C and n-type above 900° C. The electrical properties of all four materials are consistent with the presence of a glassy phase.     

A process model for active brazing of ceramics

In the present investigation process modelling techniques have been applied to describe reaction layer growth during active brazing of ceramics. As a starting point, the classical solution for parabolic growth of transformation products is considered. Specific computational features are then explicitly built into the model to allow for transient effects during heating and cooling as well as changes in the growth kinetics due to depletion of the active element during brazing. This approach gives considerable scope for optimization of both process and joint properties through adjustment of the filler metal composition and the temperature-time programme under which brazing takes place. The aptness of the process model is illustrated in an accompanying paper (Part II).Nomenclature A, C B reaction products in diffusion couple - C A ceramic component - C reactive element in braze alloy - C _B concentration of element B at a given position within the reaction layer, C B (mole m^–3) - C _B ^b bulk concentration of element B in ceramic, A B (mole m^–3) - C _B ⁱ (1), C _B ⁱ (2) concentration of element B in reaction layer at C B /A B and braze metal/C B interface, respectively (mole m^–3) - C _C concentration of element C at a given position within the reaction layer, C B (mole m^–3) - C _C ⁰ initial concentration of element C in braze metal (mole m^–3) - C _C ^b bulk concentration of element C in braze metal (mole m^–3) - C _C ⁱ (1), C _C ⁱ (2) concentration of element C in reaction layer at braze metal/C B and C B /A interface, respectively (mole m^–3) - D ₀, D ₀ ^* constants in expression for diffusion coefficient (m² s^–1) - D _B intrinsic diffusivity of B in C B (m² s^–1) - D _C intrinsic diffusivity of C in C B (m² s^–1) - J _B molar flux of element B (mole m^–2 s^–1) - J _C molar flux of element C (mole m^–2 s^–1) - k ₀ constant in expression for k_p (m² s^–1) - k ₀ ^* rate constant referring to infinite diffusion couple analogue (m² s^–1) - k _p parabolic growth rate constant (m² s^–1) - L half width of braze metal zone (m) - m proportionality constant (equal to the ratio between C _C ⁱ (1) and C _C ^b ) - Q _app apparent activation energy for diffusion of C in C B (J mole^–1) - Q _app ^* apparent activation energy for diffusion of B in C B (J mole^–1) - R universal gas constant (8.314 J mole^–1 K^–1) - t time (s) - t ₀ incubation time (s) - t ₁, t ₂ limits of integration (s) - t _i isothermal hold time (s) - t _i time increment used in the numerical integration procedure (s) - T absolute temperature (K or °C) - T _c chosen reference temperature (K or °C) - T _i isothermal hold temperature (K or °C) - X thickness of reaction layer (m) - X _c contribution of the cooling leg of the brazing cycle to the total reaction layer thickness (m) - X _h contribution of the heating leg of the brazing cycle to the total reaction layer thickness (m) - X _i contribution of the isothermal hold period to the total reaction layer thickness (m) - X _lim limiting thickness of reaction layer, C B (m) - X _i increase in reaction layer thickness due to a small time increment t _i (m) - y ₁, y ₂, y ₃ molar partitioning factors - , , , , , ) molar stoichiometric factors - molar volume of reaction product, C B (m³ mole^–1)     

Interaction between a dislocation and an impurity in KCl: Mg2+ single crystals

The interaction between a dislocation and the impurity in KCl: Mg²⁺ (0.035 mol% in the melt) was investigated at 77–178 K with respect to the two models: one is the Fleischer's model and the other the Fleischer's model taking account of the Friedel relation. The latter is termed the F-F. The dependence of strain-rate sensitivity due to the impurities on temperature for the specimen was appropriate to the Fleischer's model than the F-F. Furthermore, the activation enthalpy, H, for the Fleischer's model appeared to be nearly proportional to the temperature in comparison with the F-F. The Friedel relation between effective stress and average length of the dislocation segments is exact for most weak obstacles to dislocation motion. However, above-mentioned results mean that the Friedel relation is not suitable for the interaction between a dislocation and the impurity in the specimen. Then, the value of H(T _c) at the Fleischer's model was found to be 0.61 eV. H(T _c) corresponds to the activation enthalpy for overcoming of the strain field around the impurity by a dislocation at 0 K. In addition, the Gibbs free energy, G ₀, concerning the dislocation motion was determined to be between 0.42 and 0.48 eV on the basis of the following equation ln / = G ₀/(kT_p0)1 – (T/T _c)^{1/2 –1}(T/T _c)^1/2 + ln ₀/where k is the Boltzmann's constant, T the temperature, T _c the critical temperature at which the effective stress due to the impurities is zero, _p0 the effective shear stress without thermal activation, and ₀ the frequency factor.     

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.     

Slow Dynamics of Nonequilibrium Density Fluctuations in Concentrated Hard-Sphere Suspensions

The coupled diffusion equations recently proposed for concentrated hard-sphere suspensions of interacting Brownian particles, the nonlinear deterministic diffusion equation with the self-diffusion coefficient D _S((x, t)) for the average local volume fraction (x, t), and the linear stochastic diffusion equation with D _S((x, t)) for the density fluctuations n(x, t) are numerically solved under a spatially inhomogeneous, nonequilibrium initial state. Thus, in a supercooled region where < _g, the slow evolution of the cluster-like glassy domains with (x, t) _g and the slow relaxation of the nonequilibrium density fluctuations are shown to be caused by the dynamic singularity of the self-diffusion coefficient, D _S((x, t)) (1–(x, t)/_g)², where is a particle volume fraction, _g = (4/3)³/(7 ln 3 – 8 ln 2 + 2) is the colloidal glass transition volume fraction, and is the crossover volume fraction.     

Correlation of burst pressure of GRP cylinders with the stress wave factor

Glass fibre-reinforced plastic (GRP) cylinders are increasingly used for highly stressed structural elements. The higher the demands on the materials, the higher are the fault detection requirements to be met by non-destructive materials testing methods. Acousto-ultrasonics is a valuable aid for the non-destructive evaluation of GRP composite materials, because it may be the answer to evaluating effects of subtle defects in composites. The aim of the research is to evaluate the burst pressure of GRP cylinders by acousto-ultrasonics techniques. The theoretical results have been found to be in good agreement with the experimental values. Hence the results strongly suggest that stress wave factor measurements can be exploited successfully to predict burst pressure of GRP cylinders.Nomenclature P Internal pressure, kgf cm^–2 - d Internal diameter, cm - t Thickness of cylinder, cm - (N ,N ,N ) Resultant forces, kgf - (M ,M ,M ) Moments, kg cm - [A] Extensional stiffness matrix - [B] Bending stretching coupling matrix - [D] Flexural stiffness matrix - ( ⁰ , ⁰ , ⁰ ) Midplane strains - (k ,k ,k ) Curvatures - n Number of laminae - Z Distance from midplane, cm - _u Ultimate tensile strength of GRP composite, kg cm^–2 - S _W Stress wave factor - m Material parameter - Filament winding angle     

Surface tension of helium at the superfluid critical end-point

The singularity in the vapor-liquid interfacial tension, (T), of helium at the transition to superfluidity is analyzed theoretically. The universal amplitude ratio R ⁺ =K₊( ₀ ⁺ )^d–1/k _B T , where K₊ and K_– are the amplitudes of the |T–T|^µ singularity in , with =1.34 ₃ , is known from recent work to first order in =4–d for the general n-vector model in d dimensions. Extrapolation to d=3 for n=2 indicates R ⁺ =0.05–0.08, which is shown to be consistent with the experimental data. Further analysis of the experiments establishes that the universal ratio Q=K₊/K _– exceeds 0.35, and is consistent with the recent prediction Q0.9; this demonstrates the inadequacies of earlier theoretical treatments. The existence in the observed surface tension of an anomalous, negative contribution of unknown origin at a few millikelvin beneath T is stressed.     

Thermal conductivity and quantum diffusion in solid H2

The thermal conductivity of solid H₂ and the NMR absorption signal of isolated o-H₂ were measured simultaneously along isotherms 0.07<T<1.5 K as a function of time after a rapid cooldown from 2 K. The o-H₂ concentration ranged from 3.4% to 0.4%, and the pressure was 90 atm. During the measurements, clustering of o-H₂ particles occurred as seen from the changes both of the NMR signal amplitude and of with time t. The difference ^–1 = ^–1 ()– ^–1(0) between the thermal resistivity ^–1 (t=0) just after cool down and in equilibrium, ^–1 (), was found to change sign near 0.23 K, and this result is discussed with respect to previous experiments. The equilibrium resistivity attributed to the o-H₂ impurities, , is derived and is compared with previous determinations and with predictions. An analysis of the equilibration process for ^–1 and for the NMR signal amplitude is presented. It shows that the characteristic times are of comparable but not equal magnitude. Comparison of the derived from NMR data atP=90 and 0 atm favors resonant ortho-para conversion over quantum tunneling as the leading mechanism for quantum diffusion.     

Dependence of the flux flow viscosity coefficient on the Ginzburg-Landau parameter κ in superconducting indium films

The flux flow viscosity coefficient b ^–1 (in units of ₀ H _{c n} ^–1 c ^–2) of vacuum-deposited indium thin films with low values (1.0–2.8) is measured at temperatures between 0.5T _cand 0.98T _cin the weak magnetic field region. At each temperature, b ^–1 decreases as increases for larger than 1.7. The decrease of b ^–1 with increasing is more rapid as the temperature increases. From an analysis of the present results as well as the existing data on intermediate- and high- superconducting alloys, the relation between b ^–1 and is established over a wide range of . The dependence of b ^–1 on is qualitatively explained by taking into account the contribution of the normal electron dissipation to the viscosity coefficient in the Bardeen-Stephen model.Financial support provided by the Fonds National Suisse de la Recherche Scientifique.On leave from the Department of Electronic Engineering, Faculty of Engineering, Kyushu Industrial University, Fukuoka, Japan.     

Application of a new iterative method for elastic-plastic stress analysis

A new iterative method for elastic-plastic stress analysis based on a new approximation of the constitutive equations is proposed and compared with standard methods on the accuracy and the computational time in a test problem. The proposed method appears to be better than the conventional methods on the accuracy and comparable with others on the computational time. Also the present method is applied to a crack problem and the results are compared with experimental ones. The agreement of both results are satisfactory.List of symbols u = (u ₁, u ₂) displacements u ^(H) = u ⁽ⁿ⁺¹⁾ - u ⁽ⁿ⁾ u _k ⁽ⁿ⁾ = u _(k ^{(n + 1)} - u ⁽ⁿ⁾ (n, k = 0, 1, 2, ...) - = ₁₁, ₂₂, ₁₂) stresses - = (₁₁, ₂₂, ₁₂) strains - = (₁₁, ₂₂, ₁₂) center of yield surface - D elastic coeffficient matrix, C = D ^–1 - von Mises yield function. The initial yielding is given by f() = _Y - f {f/} - ^* transposed f - H hardening parameter (assumed to be a positive constant for kinematic hardening problems) - time derivative of - [K] total elastic stiffness matrix - T traction vector - = [B] relation between nodal displacements and strains     

Optimal choice of descent steps in gradient methods of solution of inverse heat-conduction problems

Modifications are proposed for the methods of steepest descent and conjugate gradients for the solution of multiparameter inverse problems in heat conduction.Notation A, B, L linear operators - u element of the solution space U - f exact initial data - f error in the initial data - value of the error in the initial data - A^–1 inverse operator - u^(k)() k-th derivative of the function u - _i() polynomials of degree i–1 - A^*, B^*, L^* operators conjugate to the operators A, B, L - J(g) discrepancy functional - J'g gradient of the discrepancy functional - _n ⁱ depth of descent with respect to the i-th component of the antigradient of the discrepancy in the n-th iteration - _m length of the observation interval Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 2, pp. 264–269, August, 1980.     

Carrier Mobility in GaSb–V2Ga5and GaSb–GaV3Sb5 Eutectic Alloys

Experimental evidence is presented that semiconductor–metal eutectics with a low content of the metallic phase (4 vol %) are similar in electronic structure to inhomogeneous semiconductors. The microstructure of undoped and Te-doped GaSb–V₂Ga₅ and GaSb–GaV₃Sb₅ eutectic alloys is examined, and the Hall mobility of carriers in these alloys is determined. The anomalous temperature variation of Hall mobility in GaSb–V₂Ga₅ ( T ²) and GaSb–GaV₃Sb₅ ( T ⁵) is interpreted in terms of infinite clusters ofn-type metallic inclusions embedded in a p-type semiconductor matrix and interconnected through overlapping inhomogeneous interfaces. It seems likely that the difference in conductivity type between the semiconductor matrix and the infinite clusters gives rise to a random large-scale potential relief. Te compensation of GaSb in the eutectic alloys causes the Hall mobility to vary more rapidly with temperature, T ³ to T ¹⁰, which is interpreted as due to an increase in the amplitude of the random large-scale potential relief, the formation of infinite clusters, and partial compensation of unintentional acceptor doping in the semiconductor matrix.     

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.     

Effectiveness of mixing coaxial flows swirled in opposite directions

The mixing of coaxial turbulent flows swirled in opposite directions is experimentally studied. The effectiveness of this mixing is compared with mixing after an agitating grid.Notation z, r, cylindrical coordinate system - r₁, r₂ inside and outside radius of annular channel - H=r₂–r₁ radial gap in annular channel - y=(r–r₁)/H dimensionless radial coordinate - V(v_z, v_r, v) mean velocity vector - v, v_z pulsative components of velocity in the direction of the mean velocity vector and in the axial direction - P_*, P total and static pressure - , loss coefficients Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 407–413, September, 1981.     

Magnetic field dependence of zero-sound attenuation close to the pair-breaking edge in3He-B due toJ=1−,J z =±1 collective modes

Our previous theory yielded for the Zeeman splitting of the imaginaryJ=1 collective mode in³He-B the result =2+0.25J _z ( is the effective Larmor frequency). In this paper we take into account the downward shift of the pair-breaking edge from 2 to 2₂– (₂ and ₁ are the longitudinal and transverse gap parameters). This leads to a complex Landé factor: the frequencies of theJ _z =±1 components become =2+0.39J _z , and the linewidths of these resonances become finite: =0.18. The coupling amplitudes of theJ _z =±1 components to density are found to be proportional to gap distortion, (₁–₂/(/)². Our results for the ultrasonic attenuation due to theJ _z =±1,J=1 modes are capable of explaining the field dependence of the attenuation close to the pair-breaking edge as observed by Dobbs, Saunders, et al. The observed peak is caused by theJ _z =–1 component: its height increases due to gap distortion as the field is increased, and the peak shifts downward in temperature and its width increases with the field due to the complex Landé factor. TheJ _z =+1 component gives rise to a corresponding dip relative to the continuum attenuation.     

Behavior of a screw dislocation near a partially bonded bimetallic interface

This paper, based upon the isotropic elastic continuum approximation, deals with the forces of interaction between a stationary screw dislocation and a partially bonded bimetallic interface. The complex variable method is used throughout and the closed form solution is obtained. The result indicates that if the material on the other side of the interface is more rigid than that in which the dislocation is present, the bonded region will act as a barrier to the dislocation located in a certain region near the interface and that there is no stable equilibrium position of single dislocation line even in the aforementioned case since the free surface operates an attractive force on it.

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Zusammenfassung Diese Arbeit behandelt die Kraefte der Wechselwirkung zwischen einer stationaeren Schraubenverschiebung und einer teilweisen unfreien zwei-metallischen Zwischenflaeche. Sie beruht auf dem isotropischen, elastischen Kontinuumnaeherungswert. Die Methode der komplexen Veraenderlichen wurde benutzt und die Loesung der geschlossenen Form wurde erhalten.Das Ergebnis zeigt, dass, sollte das Material auf der anderen Seite der Zwischenflaeche haerter sein, als jenes in welchem die Verschiebung stattfindet, das unfreie Gebiet als Barriere zu der Verschiebung, die sich in einem bestimmten Gebiet in der Nahe der Zwischenflaeche befindet, auftritt. Ferner gibt es keine stabile Gleichgewichtsposition von einer einzelnen Verschiebungslinie, selbst in dem erwaehnten Falle nicht, da die frei Oberflaeche Zugkraft ausuebt.

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Résumé Se basant sur l'approximation d'un milieu continu élastique et isotrope, le mémoire est relatif aux forces d'interaction entre une dislocation-vis et l'interface de deux corps métalliques partiellement solidarisés. On utilise la méthode des variables complexes, et l'on obtient une solution particulière et limitée.Les résultats indiquent que si le mátériau qui se trouve de l'autre côte de l'interface est plus rigide que celui dans lequel se trouve la dislocation, la zone de liaison fera office de barrière pour toute dislocation située à une certaine distance de cet interface. Par ailleurs, il n'y a pas de position d'équilibre stable pour une ligne simple de dislocations se trouvent dans le cas susmentionné, puisque la surface libre opère une force d'attraction sur cette ligne.

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Notation a, h location of screw dislocation - b magnitude of Burgers vector of screw dislocation - force acting on the dislocation - F_y y component of - i –1 - i, i unit vectors in x and y directions - half length of bonded segment - L, L bonded segment and traction free one on real axis - S⁺, S^– upper and lower half-planes in z plane - u, v, w carte sian displacement components - x, y, t cartesian coordinates - X(z) (z+)^–1/2(z–)^–1/2 - z x+iy - h+ia - eeⁱ z– - tan^–1 [a/(+h)] - tan^–1 [a/(–h)] - µ^* shear modulus - - _* - _xt, _yt shear stress components - _xt ⁽ⁱ⁾ _yt(¹) shear stress components at the location of dislocation due to the interaction with the interface - (z) complex displacement potential - (z) potential as defined in text On leave from Department of Mechanical Engineering, Tohoku University, Sendai, Japan.     

Welding of thin steel plates: a new model for thermal analysis

A mathematical model for the transient heat flow analysis in arc-welding processes is proposed, based on a unique set of boundary conditions. The model attempts to make use of the relative advantages of analytical as well as numerical techniques in order to reduce the problem size for providing a quicker solution without sacrificing the accuracy of prediction. The variation of thermo-physical properties with temperature has been incorporated into the model to improve the thermal analysis in the weld and heat-affected zones. The model has been evaluated using a five-point explicit finite difference method for analysing the welding heat flow in thin plates of two different geometric configurations. The temperature distribution closer to the heat source, primarily in the weld zone and the heat-affected zones, are predicted by the numerical technique. The thermal characteristics beyond the heat-affected zone are amenable to standard analytical techniques. The behaviour of the boundary condition in the model has been investigated in detail.Nomenclature q Rate of heat per unit thickness (Wm^–1) - d Plate thickness (m) - v Velocity of source (m s^–1) - t Time (s) - T Temperature value at the desired point (K) - T ₀ Initial temperature (K) - K Thermal conductivity (W m^–1 K^–1) - Density (kg m^–3) - c _p Specific heat (J kg^–1 K^–1) - Thermal diffusivity (m² s^–1) - n - Distance of point considered from the source (=x–vt) (m) - K ₀ Modified Bessel function of second kind and zero order - r Radial distance from the source (r=(x ²+y ²)^1/2) (m) - Model width (m) - a Plate width (m) - Distance from the source =(²+4 ×10^–4)^1/2 (m) - _n      

Influence of metal components in Hopeite films on IR and laser Raman spectra

Hopeite films on galvannealed steel were formed in various zinc phosphate solutions. The metal component composition of various Hopeite films was determined by atomic absorption. By measuring the infrared (IR) spectra and the laser Raman spectra for these films, the influence of metal component composition on these spectra could be investigated. In IR spectra, peaks corresponding to ₃ and ₄, the basic vibration mode of PO ₄ ^3– , were seen, but the peak patterns of ₄ were different for Hopeite containing manganese and that not containing it. In the Raman spectra, four clear peaks for various films were found in the region 1300 to 800 cm^–1 . Although these spectra are due to PO ₄ ^3– , ₁ and ₃ are found in this region. Essentially, ₃ degenerates triply, but in the crystalline state of Hopeite films, the symmetry of the regular PO ₄ ^3– tetrahedron will be distorted by the interaction. At that moment, the degenerations of ₃ are untied and split into three peaks. Thus it was thought that spectra with four peaks of ₁ were generated. However, the main peak corresponds to ₁ and other three peaks correspond to ₃. The values of the Raman band for various Hopeite films were compared. The band shifted to the lower wavenumber region according to the increase of manganese or nickel in these films. The structure of Hopeite films modified by the action of manganese or nickel has been analysed to be Zn_3–x Me _x (PO₄)₂ · 4H₂O (Me = Mn or Ni), but this structure is different from that of normal Hopeite films (Zn₃(PO₄)₂ · 4H₂O).