Temperature-dependent Equation Research Articles

Hydrogen diffusion coefficient in liquid metals evaluated by solid–gas eutectic unidirectional solidification

Based on the solid–gas eutectic unidirectional solidification technique and the principle of unidirectional solidification of single-phase alloy, a new method for evaluating the diffusion coefficient of hydrogen in liquid metals was proposed. Taking Cu–H2 system for example, the influences of argon partial pressure and superheat degree of melt on the diffusion coefficient of hydrogen in liquid metal were studied and the predicted values were similar to each other. The obtained temperature-dependent equation for diffusion coefficient of hydrogen in liquid copper is comparable with experimental data in literature, which validates the effectiveness of this method. The temperature-dependent equations for diffusion coefficient of hydrogen in liquid Mg, Si and Cu–34.6%Mn alloy were also evaluated by this method, along with the values at the melting point of each metal and alloy.

Analytical and numerical treatment of electro-thermo-mechanical coupling

Single-field problems are well understood concerning their numerical treatment and their numerical problems. In coupled situations, this is not always the case. This article is an attempt to fill the gap for the three-field problem of small strain electro-thermo-elasticity. Apart from the quasi-static equilibrium conditions, also, the nonlinear heat equation and the stationary but temperature-dependent electrical current equation are treated. The following aspects are investigated: First, analytical equations for code verification purposes are provided for particular subproblems. Secondly, we apply the method of vertical lines, which leads to a system of differential-algebraic equations—after the spatial discretization—that can be solved using stiffly accurate, diagonally implicit Runge–Kutta methods. This enables to apply high-order time integration schemes and to make use of step-size control by embedded schemes. Here, the known problems of the connection between mesh- and the temporal step-size must be studied, also focusing on the order reduction caused by nonlinear Dirichlet boundary conditions. Additionally, the resulting system of nonlinear equations is treated with different methods such as the Newton–Raphson scheme, the Newton–Chord method and a Newton–Chord method with Aitken relaxation leading to very efficient computations.

Shortwave-infrared photoluminescence from Ge1−xSnx thin films on silicon

Ge1−xSnx thin films with Sn composition up to 7% were epitaxially grown by chemical vapor deposition on silicon. Temperature-dependent photoluminescence was investigated and the peaks corresponding to the direct and indirect transitions were observed in a wavelength range from 1.6 to 2.2 μm. The exact peak positions obtained from Gaussian fitting were fitted with an empirical temperature dependent band-gap equation (Varshni relationship). The separation between direct and indirect peaks was equal to 0.012 eV for GeSn thin film with 7% Sn content at room temperature. This observation indicates that the indirect-to-direct crossover would take place at slightly higher Sn compositions.

Predicting the viscosity and electrical conductivity of ionic liquids on the basis of theoretically calculated ionic volumes

Selected physical properties of the ionic liquids might be quantitatively predicted based on the volumes of the ions these systems are composed of. It is demonstrated that the ionic volumes calculated using relatively simple theoretical quantum chemistry methods can be utilised to estimate the viscosities and electrical conductivities of various commonly used ionic liquids. The fitting formulas of the exponential form are offered and their predictive usefulness is verified. The quality of such predictions is discussed on the basis of several ionic liquids involving [Tf2N]‑ and [BF4]‑ anions and 16 various cations. The dependence of the viscosity and electrical conductivity of the ionic liquids on the temperature is also investigated and the temperature-dependent equations are derived and compared to the experimentally measured values.

Application of Optical Basicity for Estimation of Viscosity of SiO<sub>2</sub>-CaO-MgO-Al<sub>2</sub>O<sub>3</sub> System

A viscosity model based on NPL model with the corrected optical basicity is proposed for quaternary SiO2-CaO-MgO-Al2O3 slag system in the present work. The modified Arrhenius type of equation for temperature dependence of slag viscosity is employed. By means of fitting measured viscosity values for slags with basicity from 0.4 to 1.0 and temperature from 1593 to 1803 K, model parameters are optimized against values of optical basicity, which represents both the structure of molten slags and cationic effects. The relationship between model parameters and optical basicity, which is different from NPL model, is obtained. The present model is applied to estimate viscosity values of slag in SiO2-CaO-MgO-Al2O3 system. The comparison between estimated and measured values shows good agreement with a mean deviation of 12%. It proves fully that the present model can express the temperature dependence and composition dependence of viscosity.

Aqueous two-phase system of poly ethylene glycol dimethyl ether 2000 and sodium hydroxide at different temperatures: Experiment and correlation

In this research, liquid–liquid equilibria (LLE) data were determined for an aqueous two-phase system containing polyethylene glycol dimethyl ether 2000 (PEGDME2000)+sodium hydroxide+H2O at T=298.15, 308.15 and 318.15K. The experimental binodal data were described using two empirical nonlinear three parameter expressions developed by Merchuk and Zafarani-Moattar. The effect of temperature on the binodal and tie-lines of the investigated aqueous two-phase system (ATPS) were also studied. Moreover, the modified local composition segment-based NRTL (the extended NRTL and the modified NRTL) and Wilson models (the extended Wilson and the modified Wilson) and also a temperature dependent Setschenow-type equation were used to fit the tie-line data points. In addition, the effect of the polymers PEGDME2000 and poly ethylene glycol 2000 on the phase forming ability were studied. Also, the free energies of cloud points for this system were calculated from which it was concluded that the increase of the entropy is driving force for formation of studied aqueous two-phase system.

Theory of suppressing avalanche process of carrier in short pulse laser irradiated dielectrics

A theory for controlling avalanche process of carrier during short pulse laser irradiation is proposed. We show that avalanche process of conduction band electrons (CBEs) is determined by the occupation number of phonons in dielectrics. The theory provides a way to suppress avalanche process and a direct judgment for the contribution of avalanche process and photon ionization process to the generation of CBEs. The obtained temperature dependent rate equation shows that the laser induced damage threshold of dielectrics, e.g., fused silica, increase nonlinearly with the decreases of temperature. Present theory predicts a new approach to improve the laser induced damage threshold of dielectrics.

Development of a finite strain two-network model for shape memory polymers using QR decomposition

The aim of this paper is to develop a thermodynamically consistent finite deformation continuum model to simulate the thermomechanical response of shape memory polymers (SMPs). The SMP is modeled as a thermoviscoelastic material whose response in a thermomechanical cycle is modeled as a combination of a rubbery (viscoelastic) and a glassy (elastic) network in series. The activation criterion for the breakage of temporary network junctions is governed by a temperature dependent rate equation (akin to a thermal Bauschinger effect). We further show how the decomposition of the deformation gradient into an upper triangular matrix and a rotation (the QR) decomposition can be used instead of the more traditional polar (RU) decomposition in the development of models for such materials with persistent configurational changes. Such a decomposition has both physical meaning as well as computational advantages due to their convenient structure. Using these assumptions, we propose a specific form for the Helmholtz potential and the rate of dissipation. The model is simple (deliberately ignoring some aspects such as anisotropy that affect the quantitative but not the qualitative response features) and is able to capture the major phenomena of interest in SMPs. The efficacy of the resulting model, which is in a state evolution form, is demonstrated by comparing with published experimental data for simple shear. We study the response of the SMP model for monotonic shear deformation, different deformation rates as well as cyclic shear deformation at different temperatures. Comparisons with experiments show good agreement. Finally, we implement the thermomechanical cycle under shear deformations and study the behavior of the model.

Analytical temperature dependent model for nanoscale double-gate MOSFETs reproducing advanced transport models

In this paper we extend our compact model for nanoscale double-gate (DG) MOSFETs which considers a hydrodynamic transport model to include the effect of the temperature dependence. Temperature dependence equations are incorporated to the expressions of the mobility and saturation velocity. For model validation we have considered a symmetric 22nm double-gate MOSFET template device optimized for low-stand-by-power applications. Comparison between the numerical 2D Monte Carlo (MC) simulations and the compact model shows a good degree of agreement.

Spacetime singularity resolution in Snyder noncommutative space

Inspired by quantum gravity proposal, we construct a deformed phase space which supports the UV and IR cutoffs. We show that the Liouville theorem is satisfied in the deformed phase space which allows us to formulate the thermodynamics of the early Universe in the semiclassical regime. Applying the proposed method to the Snyder noncommutative space, we find a temperature dependent equation of state which opens a new window for natural realization of inflation as a phase transition from quantum gravity regime to the standard radiation dominated era. Also we obtain finite energy and entropy densities for the Universe, when at least the Weak Energy Condition is satisfied. We show that there is a minimum size for the Universe which is proportional to the Planck length and consequently the Big Bang singularity is removed.

English

The shelf life of a composite solid propellant is one of the critical aspects for the usage of solid propellants. To assess the ageing behavior of the composite solid propellant, the activation energy is a key parameter. The activation energy is determined by analysis of visco-elastic response of the composite solid propellant when subjected to sinusoidal excitation. In the present study, dynamic mechanical analyzer was used to characterize six different types of propellants based on hydroxyl terminated polybutadiene, aluminium, ammonium perchlorate cured with toluene diisocyanate having burning rates varying from 5 mm/s to 25 mm/s at 7000 kPa. Each propellant sample was given a multi-frequency strain of 0.01 percent at three discrete frequencies (3.5 Hz, 11 Hz, 35 Hz) in the temperature range -80 °C to + 80 °C. It was observed that all the propellants have shown two relaxation events (α- and β- transition) in the temperature range -80 °C to +80 °C. The α-transition was observed between -66 °C and -51 °C and β-transition between 7 °C and 44 °C for the propellants studied. The activation energy for both transitions was determined by Arrhenius plot from dynamic properties measured at different frequencies and also by time temperature superposition principle using Williams-Landel-Ferry and Arrhenius temperature dependence equations. The data reveal that the activation energy corresponding to α-transition varies from 90 kJ/mol to 125 kJ/mol for R-value between 0.7 to 0.9 while for β-transition the values are from 75 kJ/mol to 92 kJ/mol. The activation energy corresponding to β-transition may be used to predict the useful life of solid propellant. Defence Science Journal, 2014, 64(2), pp. 173-178. DOI: http://dx.doi.org/10.14429/dsj.64.3818

Solid-liquid stable phase equilibria of the ternary systems MgCl2 + MgB6O10+ H2O AND MgSO4 + MgB6O10 + H2O at 308.15 K

The solubilities and the relevant physicochemical properties of the ternary systems MgCl2 + MgB6O10 + H2O and MgSO4 + MgB6O10 + H2O at 308.15 K were investigated using an isothermal dissolution method. It was found that there is one invariant point, two univariant curves, and two crystallization regions of the systems. The systems belong to a simple co-saturated type, and neither double salts nor solid solutions were found. Based on the extended HW model and its temperature-dependent equations, the single-salt Pitzer parameters β(0), β(1), β(2) and CØ for MgCl2, MgSO4, and Mg(B6O7)(OH)6, the mixed ion-interaction parameters θCl,B6O10, θSO4,B6O10, ΨMg,Cl,B6O10, ΨMg,SO4,B6O10 of the systems at 308.15 K were fitted, In addition, the average equilibrium constants of the stable equilibrium solids at 308.15 K were obtained by a method using the activity product constant. Then the solubilities of the ternary systems are calculated. The calculated solubilities agree well with the experimental values.

Investigation on the effect of through thickness normal stress on forming limit at elevated temperature by using modified M-K model

The formability can be improved in warm/hot sheet hydroforming due to two important factors of temperature and through thickness normal stress. An extension of the M-K model was presented in this paper with the liquid pressure induced through thickness normal stress taken into account. The through thickness normal stress was introduced by using the general form of the Hill48 criterion. The combined effect of temperature and through thickness normal stress on the increase of FLD0 is achieved by applying a proposed temperature dependent constitutive equation for 5A06 aluminum alloy (a Chinese designation of Al-Mg alloy, corresponding to the ASTM designation of 5056 aluminum alloy) into the M-K approach. The Newton–Raphson method is used in the numerical procedure and it is proved to be stable and correct. The yield loci show a significant dependence on temperature and through thickness normal stress. Both size shrinking caused by the elevated temperature and location shifting due to the increasing thickness normal stress of the yield loci are observed. Comparison of the experimental FLDs of AISI-1012 low carbon steel (an AISI designation of steel) at plane stress and room temperature, STKM-11A steel (a Japanese designation of Steel Tube Kozo Machine) for tube hydroforming at room temperature and 5A90 aluminum alloy (a Chinese designation of Al-Li alloy) at plane stress and elevated temperature with the theoretical results show good agreements. The effect of key parameters, such as inhomogeneity factor f0, n value, m value and initial thickness T0, grain size d, initial surface roughness R0, show a strong dependence on FLDs and increase of FLD0. The increase of FLD0 is formulized in a full quadratic form, which is a function of temperature and through thickness normal stress. The left quadrant of FLD was determined by the cylindrical warm hydromechanical cup deep drawing, which shows a good accordance with the predicted results by using the modified M-K model.

Phase diagrams for (liquid + liquid) and (liquid + solid) equilibrium of aqueous two-phase system containing {polyvinylpyrrolidone 3500 (PVP3500) + sodium sulfite (Na2SO3) + water} at different temperatures

The (liquid+liquid) equilibrium (LLE) for the {polyvinylpyrrolidone (PVP3500)+Na2SO3+H2O} system has been determined experimentally at T=(298.15, 308.15 and 318.15)K. The (liquid+liquid+solid) equilibrium (LLSE) and complete phase diagram of this system were also obtained at T=298.15K. The effect of temperature on the binodal curves and the tie-lines for the investigated aqueous two-phase system (ATPS) have been studied. The Merchuk equation and an empirical equation that we proposed in our previous work were used for reproducing the experimental binodal results, and their three fitting parameters were obtained with the temperature dependence expressed in the linear form with (T−T0)K as a variable. Furthermore, the Othmer–Tobias and Bancroft, a temperature dependent Setschenow-type equation and osmotic virial model, the segment-based local composition models (i.e. the extended NRTL (E-NRTL) and modified NRTL (M-NRTL)) were used for the correlation of the (liquid+liquid) phase behavior of the studied system. Also, we estimated plait point, slope and the length of tie-lines at T=(298.15, 308.15 and 318.15)K.

A new temperature-dependent equation of state of solids

In the present paper, a temperature-dependent equation of state (EOS) of solids is discussed which is found to be applicable in high-pressure and high-temperature range. Present equation of state has been applied in 18 solids. The calculated data are found in very good agreement with the data available from other sources.

Time evolution of the sQGP with hydrodynamic models

The strongly interacting Quark-Gluon-Plasma (sQGP) created in relativis- tic nucleus-nucleus collisions, can be described by hydrodynamic models. Low energy hadrons are created after the so called freeze-out of this medium, thus their distributions reveal information about the final state of the sQGP. Photons are created throughout the evolution, so their distributions carry information on the whole expansion and cool down. We show results from an analytic, 1+3 dimensional perfect relativistic hydrodynamic so- lution, and compare hadron and photon observables to RHIC data. We extract an average equation of state of the expanding quark matter from this comparison. In the second part of this paper, we generalize the before mentioned analytic solution of relativistic perfect fluid hydrodynamics to arbitrary temperature-dependent Equation of State. We inves- tigate special cases of this class of solutions, in particular, we present hydrodynamical solutions with an Equation of State determined from lattice QCD calculations.

Design and performance of hybrid constructed wetland systems for high-content wastewater treatment in the cold climate of Hokkaido, northern Japan

The performance of six multistage hybrid constructed wetland systems was evaluated. The systems were designed to treat four kinds of high-content wastewater: dairy wastewater (three systems, average inflow content 2,400-5,000 mg·COD l(-1), 3-6 years of operation); pig farm wastewater, including liquid food washing wastewater (one system, 9,500 mg·COD l(-1), 3 years); potato starch processing wastewater (one system, 20,000-60,000 mg·COD l(-1), 3 years); and wastewater containing pig farm swine urine (one system, 6,600 mg·COD l(-1), 2.8 years) (COD = chemical oxygen demand). The systems contained three or four vertical (V) flow beds with self-priming siphons and surface partitions and no or one horizontal (H) flow bed (three to five beds). In some V flow beds, treated effluents were recirculated (Vr) through the inlet to improve performance. Mean annual temperature was 5-8 °C at all locations. To overcome clogging due to the high load in a cold climate, we applied a safety bypass structure and floating cover material to the V flow beds. Calculated average oxygen transfer rates (OTRs) increased proportionally with the influent load, and the OTR value was Vr > V> H. The relations of load-OTR, COD-ammonium, and a Arrhenius temperature-dependent equation enable the basic design of a reed bed system.

Measurement and thermodynamic model study on equilibrium solubility in the aqueous system of magnesium chloride and magnesium bromide

Abstract Solubilities of the ternary system MgCl 2 –MgBr 2 –H 2 O at T =(288.15, 308.15, 323.15 and 333.15) K were investigated, and the crystallization behaviour of solid solution Mg(Cl,Br) 2 ·6H 2 O was established. Combining our experimental results with other experimental data available in the literature at T =(298.15 and 313.15) K, the pure electrolyte solution parameters for binary systems, the T -variation mixing parameters θ Cl,Br and ψ Mg,Cl,Br and the equilibrium constants equations of the solid solution were obtained. Based on Pitzer model and Harvie–Weare solubility approach, the solubility modelling approach achieved a very good agreement with chloride and bromide salts equilibrium solubility data. Temperature-dependent equation in the system provides reasonable mineral solubility at T =(288.15–333.15) K. This model expands the solubility calculation in the systems containing solid solution by evaluating chloride–bromide mixing solution parameters. Limitations of the mixed solution models due to data insufficiencies are discussed.

Adaptive thermal modeling of Li-ion batteries

An accurate thermal model to predict the heat generation in rechargeable batteries is an essential tool for advanced thermal management in high power applications, such as electric vehicles. For such applications, the battery materials’ details and cell design are normally not provided. In this work a simple, though accurate, thermal model for batteries has been developed, considering the temperature- and current-dependent overpotential heat generation and State-of-Charge dependent entropy contributions. High power rechargeable Li-ion (7.5Ah) batteries have been experimentally investigated and the results are used for model verification. It is shown that the State-of-Charge dependent entropy is a significant heat source and is therefore essential to correctly predict the thermal behavior of Li-ion batteries under a wide variety of operating conditions. An adaptive model is introduced to obtain these entropy values. A temperature-dependent equation for heat transfer to the environment is also taken into account. Good agreement between the simulations and measurements is obtained in all cases. The parameters for both the heat generation and heat transfer processes can be applied to the thermal design of advanced battery packs. The proposed methodology is generic and independent on the cell chemistry and battery design. The parameters for the adaptive model can be determined by performing simple cell potential/current and temperature measurements for a limited number of charge/discharge cycles.

Acoustic properties of titanium nickelide

Results of the experimental investigation of the acoustic properties of titanium nickelide alloy (speed of ultrasound and ultrasonic attenuation factor) are presented. The approximating equations for the temperature dependences of experimental data on the speed of sound, relative temperature expansion, and the density and Young’s modulus values calculated on their basis are obtained.