Temperature-dependent Equation Research Articles

Plastic flow of tungsten-based composite under hot compression

Liquid-phase sintered tungsten composite specimens with a 92.5W–5.25Ni–2.25Fe composition were tested for temperature and strain-rate effects during hot deformation. The flow stress was measured for samples tested at constant strain rates of 0.01, 0.1 and 1 s −1 and at temperatures ranging from 25 to 1100°C for reductions in height of 30, 50 and 70%. The results show that the true stress/true strain response of the tungsten composite depends on both the test temperature and, to a lesser extent, the applied strain rate, with the rate of strain hardening decreasing with increasing temperature and strain rate. Optical microscopic observations showed a dramatic increase in grain deformation and micro-crack density as the strain rate, temperature and reduction in height are increased. Initial cracking occurred preferentially at tungsten–tungsten boundaries or at the tungsten grain/matrix interface, then cracking propagated along a minimum fracture energy path. Brittle failure of tungsten grains is mainly found at 1100°C. The results are modelled mathematically using a strain-, strain rate- and temperature-dependent equation.

Temperature dependent BCS equations with continuum coupling

The temperature dependent BCS equations are modified in order to include the contribution of the continuum single particle states. The influence of the continuum upon the critical temperature corresponding to the phase transition from a superfluid to a normal state and upon the behaviour of the excitation energy and of the entropy is discussed.

SIMULATION OF CHIP FORMATION IN ORTHOGONAL METAL CUTTING PROCESS: AN ALE FINITE ELEMENT APPROACH

Lagrangian and Eulerian finite element formulations have been traditionally used for modeling of the orthogonal metal cutting process. In this paper it is shown that a more general formulation, the arbitrary Lagrangian-Eulerian method (ALE), may be used to combine the advantages and avoid the drawbacks of both methods in a single analysis. Due to the characteristics of the cutting process, ALE formulation offers a very efficient modeling approach for the cutting process. A comprehensive ALE model along with strain rate and temperature dependent constitutive equations and a contact/friction algorithm is used to analyze the thermo-elasto-plastic process of plane strain orthogonal cutting. Simulation results for cutting of low carbon free cutting steel are presented and compared with available experimental data obtained under similar cutting conditions. Good agreement between the numerical and experimental results is observed.

Isothermal cure kinetics of epoxy/phenol-novolac resin blend system initiated by cationic latent thermal catalyst

The investigation of the cure kinetics of a diglycidyl ether of bisphenol A (DGEBA)/phenol-novolac blend system with different phenolic contents initiated by a cationic latent thermal catalyst [N-benzylpyrazinium hexafluoroantimonate (BPH)] was performed by means of the analysis of isothermal experiments using a differential scanning calorimetry (DSC). Latent properties were investigated by measuring the conversion as a function of curing temperature using a dynamic DSC method. The results indicated that the BPH in this system for cure is a significant thermal latent initiator and has good latent thermal properties. The cure reaction of the blend system using BPH as a curing agent was strongly dependent on the cure temperature and proceeded through an autocatalytic kinetic mechanism that was accelerated by the hydroxyl group produced through the reaction between DGEBA and BPH. At a specific conversion region, once vitrification took place, the cure reaction of the epoxy/phenol-novolac/BPH blend system was controlled by a diffusion-control cure reaction rather than by an autocatalytic reaction. The kinetic constants k1 and k2 and the cure activation energies E1 and E2 obtained by the Arrhenius temperature dependence equation of the epoxy/phenol-novolac/BPH blend system were mainly discussed as increasing the content of the phenol-novolac resin to the epoxy neat resin. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 2945–2956, 2000

Analysis of the equations for the temperature dependence of the retention index: I. Relation between equations

The relation between the parameters of several equations for the retention index temperature dependence was established, taking the hyperbola deduced from the retention theory as starting point. The transformation factors depend only on methylene contributions to the thermodynamic functions of solution and temperature. Their evolution with the mean temperature of the range was illustrated for SE-30 and Carbowax-20M glass capillary columns. On this basis the post-run standardisation of d I/d T values at a reference mean temperature is possible. Examples and statistical correlation between series of parameters from different equations for perfumery solutes were shown.

Comparison of Three Temperature-Dependent Equations of State of Condensed Matter

Considering temperature effects, we compare the equation of Vinet et al., the Birch equation and the K-D equation with experimental data. The results show that the Birch equation is the best.

Adsorption of Halogenated Hydrocarbons from Gaseous Streams by Amberlite XAD-4 Resin and Activated Carbon: Equilibria

Single-solute adsorption equilibria have been measured for the adsorption of the gaseous solutes chloroform, chlorobenzene, and 1,1,1-trichloroethane onto Amberlite XAD-4 resin. For 1,1,1-trichloroethane the adsorption equilibrium has also been measured with activated carbon Norit ROW 0.8 SUPRA as a sorbent. Temperature was varied between 20 and 120 °C, whereas nitrogen was used as a dilutant. All obtained experimental data could be fitted satisfactorily with two different temperature dependent Freundlich equations, one derived by Halsey (1952) and another derived in this work. Adsorption of the halogenated hydrocarbons onto Amberlite XAD-4 as well as Norit ROW 0.8 SUPRA proved to be completely reversible. The adsorption capacity of Amberlite XAD-4 was found to decrease exponentially with increasing temperature, whereas the capacity of Norit ROW 0.8 SUPRA decreased in a linear way and at a much lower rate, reflecting the bad regeneration characteristics of activated carbon sorbents.The obtained data for the adsorption of gaseous chloroform and 1,1,1-trichloroethane onto Amberlite XAD-4 resin agreed surprisingly well with data that were earlier obtained with these same hydrocarbons being adsorbed from water, in which they were dissolved, by nonwetted Amberlite XAD-4 particles. When plotted against the partial pressure of the solutes, equal adsorption capacities were found, indicating that, at least at 20 °C, the presence of water vapor inside the pores of the nonwetted resin particles does not affect the adsorption capacity of these particles with respect to the halogenated hydrocarbons in concern.

Quarkonium mass spectra from the temperature dependent Bethe-Salpeter equation with logarithmic and Coulomb plus square-root kernels

The study of meson formation in quark-gluon plasma using a temperature-dependent Bethe-Salpeter formalism presented earlier, is now extended to a logarithmic and a combination of a Coulomb plus a square-root kernel. We are able to get good fits to the meson masses with both kinds of kernels and our present results are qualitatively similar to those obtained for the Coulomb plus a linear kernel.

Thermal Contraction of Drawn Polyethylene Film I. An Empirical Equation for Temperature Dependence of Thermal Stress

Thermal stress and strain were measured during heating from 30°C to 100°C for drawn polyethylene films of various draw temperatures and ratios. Behavior of thermal strain was classified into three types, and discussed in terms of structural change in polymer chains during the drawing process. The Arrhenius plot was constructed for the temperature dependence of thermal strain, and an inflection point was observed in the plot over the temperature range studied. Temperature dependence of thermal stress showed the maximum value, which increased with draw ratio. An empirical equation for the behavior of thermal stress is derived using Boltzmann's superposition principle. Good agreement was found between calculated and measured values of thermal stress.

Mass spectrum of the temperature dependent Bethe-Salpeter equation for composites of quarks with a Coulomb plus a linear kernel

We assume that high-energy nucleus-nucleus interactions give rise to a hot and dense plasma comprising quarks and gluons due to successive nucleon-nucleon collisions. We treat this plasma as an ideal fluid at temperature T prior to its eventual particlization, and attempt a microscopic description of meson-formation by using finite temperature propagators for q and ¯q in a Bethe-Salpeter equation with a Coulomb plus a linear kernel. The equation thus obtained is reduced to a Schrodinger-like equation which then yields, for 0 < T < 86 MeV, the bound state masses for different states of b¯b and c¯c, which are in agreement with the experimental values for these states. The effects of the temperature of the plasma on the meson masses show up only when the temperature exceeds 86 MeV, pointing to the probable reason for the successes of the earlier models which did not explicitly take the temperature of the plasma into account.

Heterogeneous nucleation in photosensitive glasses

Time-temperature dependencies of the nucleation rates for lithium disilicate glasses containing impurities of Au, Ag and Pt were investigated. The absolute values of nucleation rate for lithium disilicate were determined, as were values of activation enthalpy of structural unit transitions from glass to crystal and those of glass viscous flows. An equation for temperature dependence of the heterogeneous nucleation rate was obtained.

Temperature-dependent equation of state of condensed matter

In the present paper, a temperature-dependent equation of state (EOS) of condensed matter is discussed, which is capable of predicting the high-pressure and high-temperature behaviour of solids and liquids. The EOS can be used to obtain the volume compression, the isothermal bulk modulus and its first pressure derivative, the thermal expansion coefficient and the Anderson - Grüneisen parameter, together with other thermodynamic properties as functions of pressure at different temperatures. The present EOS has been applied for Au, Mo and W and liquid Hg. Good agreement between theory and experiment is observed.

Manganese and Phosphorus Equilibria between Liquid Copper and MnO-P2O5 Slag.

The liquid copper alloys containing 0.2-1.0 mass% Mn and 0.03-0.5 mass% P were equilibrated with MnO saturated and unsaturated MnO-P2O5 slags in a molybdenum crucible under a flowing CO2/CO or CO2/H2 atmosphere in the temperature range of 1523 to 1673 K. Manganese-phosphorus and manganese-manganese interaction parameters in liquid copper were found at 1623 K as follows:ePMn= -0.010 eMnP= -0.021 eMnMn= 0.027These values were examined by considering the relationships among oxygen partial pressure, the activities of manganese and phosphorus in liquid copper. The standard free energy changes for the reduction of solid MnO, MnO(s)=Mn+1/2 O2(g), and the dissolution of pure liquid manganese in liquid copper, Mn (l)=Mn, were determined as a function of temperature. The activities of MnO and P2O5 in MnO-P2O5 slags were measured at 1573 K as a function of the composition. The temperature dependence equation of the P2O5 activity was also derived in the MnO saturated condition. On the basis of the present results, examination was done concerning phosphorus and manganese equilibria between hot metal and the MnO-P2O5 slag.

Pressure Dependence of Polymer Fluids: Application of the Lattice Cluster Theory

The lattice cluster theory is used to analyze the pressure dependence of the effective Flory interaction parameter X eff observed in recent small-angle neutron scattering experiments for polymer blends. A description of this pressure dependence in blends requires a theory that contains a minimum of four empirical parameters, three interactions energies and one lattice cell volume, a set smaller than in the seven- or eight-parameter treatments generally employed with other methods. The conventional liquid mixture philosophy is used for determining this minimal set of parameters as follows : The self-interaction parameters and pure component cell volumes are obtained from fits to pure melt PVT data. A common combining rule then provides the blend cell volume as functions of those for the pure melts, but the common geometric combining rule for the heterocontact interaction energy is found to be grossly inadequate. Hence, this interaction parameter is chosen by fitting to blend data. Explicit comparisons with experimental data for polystyrene (PS) and poly(vinyl methyl ether) (PVME) melts, PS/PVME blends, and PS-b-PMMA (poly(methyl methacrylate)) diblock copolymers demonstrate that this minimal lattice cluster theory provides a good representation of melt equations of state, the composition, temperature, molecular weight, and pressure dependence of the small-angle neutron scattering, the composition dependence of the volume change on mixing, the spinodal curves, and the composition and temperature dependence of the blend correlation length. Additional predictions are presented concerning the stabilization and destabilization of blends by diblock copolymers.

Equation of state for lambda transition in quartz

An equation of state has been developed for quartz, a substance with a lambda‐type phase transition. It has the properties of the Murnaghan equation of state in the normal region and reflects the fundamental behavior of thermodynamic functions in the anomalous region. The term jT/(i‐T)1/2 has been introduced in the temperature dependent equations of isobaric heat capacity and the volume coefficient of thermal expansion, where i and j are fitting coefficients. The i coefficient is numerically close to the temperature of the phase transition Tc and is usually in the 0.1&lt;|i‐Tc|&lt;20 K interval. The range of applicability of the Murnaghan equation is delineated in the PT stability field of quartz. In the lambda range, the derivative of thermal expansion with respect to temperature is pressure dependent according to rules that allow integration of the thermal expansion and molar volume for calculation of the change in thermodynamic functions from room pressure to any given pressure. Available phase equilibria and thermochemical data have been used with the proposed equation of state to calculate the standard thermodynamic properties for coesite and the SiO2 phase diagram including alpha quartz, beta quartz, and coesite.

Efficient computer aided design of GaAs and InP millimeter wave transferred electron devices including detailed thermal analysis

An accurate calculation of the large-signal a.c. behavior with detailed thermal considerations is presented for GaAs and InP transferred electron devices. This is accomplished by sequentially solving the temperature dependent drift and diffusion equations along with a novel heat flow analysis to update the temperature profile in the device. The drift and diffusion equations employ both field and temperature dependent mobility and diffusivity derived from Monte Carlo simulations, and the thermal analysis includes all regions of the device. Simulation results are compared to experimental devices with good agreement. The relationship between the graded active layer doping profiles, device area and device length, with the device temperature, output power and device admittance is clearly illuminated by the temperature dependent large-signal a.c. simulator. For the devices simulated, the complex device admittances are calculated over the range of stable operation and at the maximum power point.

Single and multicomponent adsorption equilibria of carbon dioxide, nitrogen, carbon monoxide and methane in hydrogen purification processes

AbstractSingle, binary, ternary and quaternary adsorption equilibria of CO2, CO, CH4 and N2 on molecular sieve 5A and activated carbon were experimentally determined over a pressure range from 10−4 to 101 MPa, a temperature range from 303 to 363 K and at various compositions. The adsorption equilibria of steam reformer gases as needed for the hydrogen purification in pressure swing adsorption units were measured by using a circulating volumetric method. For the temperature‐dependent correlation of pure gas isotherm fields the Toth equation, which is a favorable model for heterogeneous adsorbents, was extended by two parameters accounting for the temperature‐dependencies of the saturation loading and the heterogeneity parameter. Multicomponent equilibria were successfully predicted from single component isotherms by the Ideal Adsorbed Solution Theory based on the accurate representation of the pure component data by this temperature dependent Toth equation. Other thermodynamic models like the HIAS, the MIAS, the SPD or the VS theory and the Statistical Thermodynamics Model were also applied to the prediction of the adsorption equilibrium and the temperature and pressure dependence of the selectivity, with comparable success, which is due to the quasi‐ideal adsorption behavior even at a high pressure.

100-300 GHz Gunn oscillator simulation through harmonic balance circuit analysis linked to a hydrodynamic device simulator

Accurate and efficient calculations of the large-signal AC behavior of second-harmonic InP transferred electron oscillators (TEOs) are presented. This is accomplished by combining a novel harmonic balance circuit analysis technique with a hydrodynamic device simulator employing the temperature dependent drift and diffusion equations. The electron transport simulations include a detailed heat flow analysis to update the temperature profile in the device. The nonlinear circuit analysis utilizes a fixed-point iterative method derived from the robust multiple reflection algorithm. To expedite the process and aid in convergence, an acceleration technique is also employed in this algorithm. The associated reduction in computation time allows for the inclusion of a hydrodynamic treatment of the transferred electron device (TED) using the modified drift and diffusion equations. Comparisons are made with the published experimental data reported by Rydberg on second-harmonic 188 GHz InP TEOs.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A Temperature-Dependent Constitutive Equation for Strain-Rate Sensitive Material*

ABSTRACT Temperature-dependent constitutive differential equations are derived for the dynamic behavior of a strain-rate sensitive plastic material that does not exhibit strain-rate history effects. The corresponding material parameters for AISI 316H are obtained from the experimental results of Al-bertini et al. [1-3]. The proposed constitutive relations could be used in present finite element codes to obtain the dynamic response of structures under intense, short-duration loadings.

A study on the vaporization of copper(II) selenide

As reported by Esirkegenov and Valiev [1] the vapour phase above CuSe is practically constituted only of selenium gaseous species, with Se2 (g) the more abundant species. Therefore, according to the phase diagram [2], during the vaporization process of this compound in the temperature range 450-650 K, the consecutive solid phase transitions are: 7CuSe ~/3Cuz_xSe ~/3Cu2Se, where #Cu2_xSe isa defect compound at the selenium-rich side of a broad homogeneity field [2] in which the x vNue depends slightly on the temperature. These phase transitions were confirmed by an electron diffraction study [3]. The temperature dependence equation of the total vapour pressure over CuSe, in the temperature range 530-645 K, has been reported by Mills [4] from Rau's private communication. Apparently, this equation and a draft relationship derived from only four points measured at higher temperatures (673-973 K) by the dew point method [1], are the only vapour pressure data available for CuSe(s). Unfortunately these relationships are decidedly in disagreement (see Fig. 1). No vapour pressure data of the intermediate compound was found in the literature. Therefore as a part of our ongoing programme on the vaporization behaviour of the chalcogenides [5], we deemed it useful to investigate the vaporization of the CuSe by measuring its vapour pressure by the torsion method. The torsion assembly used in this work was described previously [6]. The sample used, 99.999% pure, was supplied by Strem Chemicals Inc. A preliminary run showed that the vaporization occurs in two steps: the first one starts at about 540 K and, considering Se2 the only gaseous species, it corresponds to the process