Thermodynamic description of the interaction processes in the Cu–Ce–O system in the temperature range 1100–1300°C

A thermodynamic simulation and an experimental study of the interaction between cerium and oxygen in liquid copper have been performed. The thermodynamic analysis of the interaction processes in the Cu–Ce–O system is carried out using the technique of constructing the surface of solubility of components in a metal in the temperature range 1100–1300°C. As a result of simulation, data on changes in the Gibbs energy ΔG _T ° and the equilibrium constants of formation of cerium oxides Ce₂O₃ and CeO₂ from the components of a copper-based metallic melt are obtained. The first-order interaction parameters (according to Wagner) of cerium and oxygen dissolved in liquid copper, namely, e _Ce ^Ce, e _O ^Ce, and e _Ce ^O, are evaluated. Experimental studies of the Cu–Ce–O system have been performed. The morphological features, the size, and the composition of nonmetallic inclusions formed as a result of interaction in the Cu–Ce–O system are studied using scanning electron microscopy and electron-probe microanalysis.     

The activity coefficient of oxygen in binary liquid metal alloys

The Wagner model with one energy parameter,h, for describing the effect of alloying elements on the activity coefficients of nonmetallic solutes in liquid metals is extended to have two energy parameters,h ₁andh ₂. The validity of both the Wagner one-parameter equation and the newly derived two-parameter equation is tested using data available in the literature for twelve ternary metal-oxygen systems. In order to have consistent thermodynamic data, all the relevant binary, as well as the twelve ternary metal-oxygen systems are evaluated using the same thermodynamic values for the reference materials which were used in carrying out the experimental measurements. It is found that the twoparameter equation is capable of quantitatively accounting for the compositional dependences of the activity coefficients of oxygen in all twelve ternary systems while the Wagner one-parameter equation is not. A correlation between the Wagner parameter,h, and the thermodynamic properties of the respective binary metal-oxygen and binary metals systems is found, from which the value of this parameter may be predicted without referring to any ternary data. Accordingly, the two-parameter equation is more useful in evaluating ternary experimental data while the Wagner one-parameter equation in connection with the correlation betweenh and binary data is capable of predicting ternary data without any experimental investigation in the ternary region. Based on the one-parameter and the two-parameter equations, theoretical equations for the first-order and second-order free energy interaction parameters,(∈ ₀ ^j )_sand(ρ ₀ ^j )_s, are derived in terms of the model parameters. The values of(∈ ₀ ^j )_s and(ρ ₀ ^j )_s for all the systems are derived and are found to vary linearly with the reciprocal of temperature. Furthermore, linear relationships between these two interaction parameters and their slopes with 1/T are found, from which the temperature dependence of the interaction parameters may be estimated in the absence of experimental data.     

Aluminum deoxidation equilibrium in liquid Fe-16 pct Cr alloy

For thermodynamic prediction, the deoxidation equilibrium of aluminum in liquid Fe-16 pct Cr alloy was studied by employing the electromagnetic levitation technique with a cold crucible in an Ar gas atmosphere at 1923 K. The interaction parameters were determined to be e _Al(Fe) ^Cr =0.0001 (0.19/T, 1823 K≤T<1923 K) and r _Al(Fe) ^O,Cr =−0.001. The calculated relationship between aluminum and oxygen contents in Fe-16 pct Cr alloy by thermodynamic data obtained in this study is in good accordance with the experimental results of the present study and other research.     

Representation of thermodynamic properties of dilute multi-component solutions – options and constraints

The different formalisms for the representation of thermodynamic data on dilute multicomponent solutions are critically reviewed. The thermodynamic consistency of the formalisms are examined and the interrelations between them are highlighted. The options and constraints in the use of the interaction parameter and Darken's quadratic formalisms for multicomponent solutions are discussed in the light of the available experimental data. Truncated Maclaurin series expansion is thermodynamically inconsistent unless special relations between interaction parameters are invoked. However, the lack of strict mathematical consistency does not affect the practical use of the formalism. Expressions for excess partial properties can be integrated along defined composition paths without significant loss of accuracy. Although thermodynamically consistent, the applicability of Darken's quadratic formalism to strongly interacting systems remains to be established by experiment.     

The activity coefficient of nitrogen in binary liquid metal alloys

Literature data for the limiting thermodynamic properties of nitrogen in liquid Fe, Co, Ni, and Cr, as well as in the six binary alloys consisting of two of the above elements, are critically evaluated. The ternary data are evaluated in terms of the Wagner model for quasi-interstitial liquid alloys and values of the Wagner parameter h are obtained for each system. The correlation formulated by Chiang and Chang between the Wagner parameter h and the relevant binary thermodynamic properties for oxygen in binary alloys has been found to be equally valid for nitrogen in binary alloys. From this correlation, a value of h may be predicted in the absence of any ternary experimantal data. Utilizing the Wagner model and the value of h obtained for each system, values for the first-order and second-order Gibbs energy interaction parameters ∈N(s) and ρsujN(s) are derived.. The parameters are expressed as a linear function of the reciprocal temperature, i.e. ∈^jN(s) =α + β/T and.ρ^jN_(s) = α′ + β′/T. A linear correlation found by Chipman and Corrigan between β and ∈^jN(s) for systems where Fe is the solvent is also valid for systems with non-ferrous solvents. A linear correlation between β′ and ρ^jN_(s) is also found in the present study.     

Experimental investigation of the thermodynamics of Fe-Nb-C austenite and nonstoichiometric niobium and titanium carbides (T = 1273 to 1473 K)

The thermodynamics of Fe-Nb-C austenite and nonstoichiometric binary niobium carbide and titanium carbide in the temperature range of 1273 to 1473 K has been investigated using a dynamic gas equilibration technique. Methane-hydrogen mixtures have been used for fixing carbon potentials, and the carbon contents have been determined as dynamic weight changesvia a sensitive Cahn microbalance. The niobium-carbon interactions, similar to the titaniumcarbon interactions, are manifested as a minimum in the niobium carbide solubility in austenite, as increased amounts of dissolved carbon with niobium additions, and as the variation of solubility limit of the carbide with carbon content at high carbon levels. The results on the isoactivity measurements in the ternary Fe-Nb-C have been analyzed using the modified Wagner formalism, and the ternary interaction parameter ε _C ^Nb has been evaluated. The solubility of niobium carbide in Fe-Nb-C in austenite has been determined as the deflection in the variation of carbon content with Nb additions at constant carbon activity. The dissolution free energy of body-centered cubic (bcc) Nb in face-centered cubic (fcc) Fe has also been determined from the solubility data. Rational correlation between the dissolution free energies of transition metal solutes in fcc Fe and the group number in the Periodic Table has been shown to exist. A correlational relationship between the ternary interaction parameter and the free energy of formation of carbides has been established. These relationships are utilized in the assessment, as well as the systematization of thermodynamic data. The results on the activity-composition relationship in the binary niobium and titanium carbides have been analyzed using the sublattice-subregular model proposed by Hillert and Staffansson, [2] and the interaction parameters in the model were determined. The thermodynamic calculations based on this model and our experimental results were carried out, and very good agreement between experimental and calculated results was obtained. K. BALASUBRAMANIAN, Formerly with McMaster University,     

Thermodynamics of iron-nickel alloys by mass spectrometry

A Knudsen cell-mass spectrometer combination was used to determine the activities of iron and nickel in solid and liquid iron-nickel alloys in the temperature range 1500 to 1900 K. This has provided thermodynamic data which are consistent in both the solid and liquid regions. The δH^M@#@ values obtained are in fair agreement with calorimetric data. A subregular model gives a good representation of the thermodynamic properties of this system.     

Thermodynamics of iron-nickel alloys by mass spectrometry

A Knudsen cell-mass spectrometer combination was used to determine the activities of iron and nickel in solid and liquid iron-nickel alloys in the temperature range 1500 to 1900 K. This has provided thermodynamic data which are consistent in both the solid and liquid regions. The δH^M@#@ values obtained are in fair agreement with calorimetric data. A subregular model gives a good representation of the thermodynamic properties of this system.     

The thermochemistry of magnesium in nickel-base alloys: Part II. activity of magnesium

The experimental method described in Part I^[49] of this article was applied to the liquid nickel-magnesium system for the determination of magnesium activity. From a practical point of view, knowledge of the thermodynamic properties of magnesium is becomming increasingly important as the control of processing parameters tightens. Magnesium is added to nickel-base alloys for improved ductility, at levels typically less than 100 parts per million (ppm). Thus, experimental results presented are applicable to levels of less than 100 ppm Mg. The following parameters were determined: the equilibrium constant for the formation of spinel, the magnesium-oxygen and aluminum-oxygen interaction coefficients, the equilibrium constant for solution of magnesium in liquid nickel, and the Raultian activity coefficient of magnesium in an infinitely dilute solution. Formerly Graduate Student, University of British Columbia     

碳饱和三元金属熔体热力学性质的计算方法

为了简化金属熔体热力学性质的计算过程和获得任意温度下熔体组元的热力学性质，基于一种碳饱和三元金属熔体热力学性质的计算方法，将三元金属熔体中碳的饱和溶解度分解为温度T和第三组元j的影响因子kj(或mj)两项，得到用T和kj(或mj)表示的组元活度相互作用系数的计算公式。用该公式可以计算出M—C-j三元熔体中组元j在任意温度下的活度相互作用系数，并可得到组元j的活度相互作用系数与温度的关系式。将计算的Fe-C—Cr体系和Mn—C—Fe体系的性质应用于热力学分析，获得了与实际生产比较吻合的结果。     

Transformations of non-metallic inclusions formed during interaction in a cupreous melt containing nickel and oxygen

The values of thermodynamic parameters, which characterize thermodynamic features for interaction processes in the Cu-Ni-O system under the conditions of cupreous-melt and condensed-oxide-phase coexistence, were obtained. The solubility surface of components in metal is constructed for the Cu-Ni-O system at temperatures of 1100–1300°C. The structure and form of oxide inclusions formed during interaction in a cupreous melt containing nickel and oxygen were experimentally investigated.     

A comparison of the molecular interaction volume model with the subregular solution model in multicomponent liquid alloys

The molecular interaction volume model (MIVM) is a two-parameter model, meaning it can predict the thermodynamic properties in a multicomponent liquid alloy system using only the coordination numbers calculated from the ordinary physical quantities of pure liquid metals and the related binary infinite dilute activity coefficients, γ _∞ ⁱ and γ _∞ ^j , which avoids somewhat adjustable fitting for the binary parameters of B _ji and B _ij. In comparison with the subregular solution model (SRSM), the prediction effect of the MIVM is of better stability and safety because it has a good physical basis.     

Modification and Minimization of Spinel(Al<Subscript>2</Subscript>O<Subscript>3</Subscript>·<Emphasis Type="Italic">x</Emphasis>MgO) Inclusions Formed in Ti-Added Steel Melts

High-melting-point inclusions such as spinel(Al₂O₃·xMgO) are known to promote clogging of the submerged entry nozzle (SEN) in a continuous caster mold. In particular, Ti-alloyed steels can have severe nozzle clogging problems, which are detrimental to the slab surface quality. In this work, the thermodynamic role of Ti in steels and the effect of Ca and Ti addition to the molten austenitic stainless steel deoxidized with Al on the formation of Al₂O₃·xMgO spinel inclusions were investigated. The sequence of Ca and Ti additions after Al deoxidation was also investigated. The inclusion chemistry and morphology according to the order of Ca and Ti are discussed from the standpoint of spinel formation. The thermodynamic interaction parameter of Mg with respect to the Ti alloying element was determined. The element of Ti in steels could contribute to enhancing the spinel formation, because Ti accelerates Mg dissolution from the MgO containing refractory walls or slags because of its high thermodynamic affinity for Mg ( e_\textMg^\textTi = - 0. 9 3 3). ( {e_{\text{Mg}}^{\text{Ti}} = - 0. 9 3 3}). Even though Ti also induces Ca dissolution from the CaO-containing refractory walls or slags because of its thermodynamic affinity for Ca ( e_\textCa^\textTi = - 0.119 ), \left( {e_{\text{Ca}}^{\text{Ti}} = - 0.119} \right), dissolved Ca plays a role in favoring the formation of calcium aluminate inclusions, which are more stable thermodynamically in an Al-deoxidized steel. The inclusion content of steel samples was analyzed to improve the understanding of fundamentals of Al₂O₃·xMgO spinel inclusion formation. The optimum processing conditions for Ca treatment and Ti addition in austenitic stainless steel melts to achieve the minimized spinel formation and the maximized Ti-alloying yield is discussed.     

Influences of non-stoichiometry on thermodynamics and kinetics of iron oxides reduction processes

Abstract

Non-stoichiometry influences both the thermodynamic and kinetic analyses of the iron oxide redox processes. The thermochemical data of iron oxide redox reactions in various textbooks are not consistent, and the kinetic characteristics are not well understood because of the non-stoichiometry. To clarify such confusions, some famous thermodynamic data are compared, and highly precise experimental work conducted for verification. It is shown that the thermodynamic data for the pure iron oxide reduction reactions from JANAF agree well with the experimental results; the eutectoid temperature of iron oxides was proven to be 576°C; Dieckmann’s defect model of magnetite was proven in good agreement with the experimental results only at high oxygen activities but not low oxygen activities; and the dependences of iron deficiency on Δwt-% (weight loss ratio) and Fe²⁺% (ferrous ratio) were calculated and experimentally verified in pure iron oxides reduction processes.     

Luminescence investigation of Eu~（3＋）-Bi~（3＋） co-doped CaMoO_4 phosphor

A series of Eu³⁺-Bi³⁺ co-doped CaMoO₄ red phosphors were synthesized via the solid-sate reaction method. The crystal structures of the obtained samples were identified by X-ray powder diffraction (XRD). The photoluminescence property was investigated, and the results showed that the intensity of excitation spectra and emission spectra could be changed with different doping ratios of Bi³⁺/Eu³⁺. The proposed explanation of these changes was from the energy transfer between Bi³⁺ and Eu³⁺ and the unbalanced charge from the substitution of Eu³⁺ and Bi³⁺ for Ca²⁺ in CaMoO₄. The obtained samples are a promising red light emitting phosphor for the needs of different excitation sources with near-UV and blue GaN-based chips.     

Thermodynamic analysis of interaction processes in the Pb-Ag-Zn system

The values of thermodynamic parameters that allow one to calculate the equilibrium compositions of liquid lead and related intermetallic phases in the Pb-Ag-Zn system are calculated at t = 325–425°C. Via thermodynamic calculations, the solubility surface of components in metal is constructed for this system. The diagram can be used for analysis of the known literature data and evaluation of technical processes associated with interaction of zinc with silver in the lead melt. The results of calculation are compared with the experimental data.     

Estimation of Activity Coefficients and Interaction Parameters of Solutes in Silicon Melts

Because the speed and cost performance of computing has been dramatically increased and computational science has been progressed concomitantly, their utilization should be considered also in thermodynamic property estimation. When thermodynamic property data are not available, their estimation by the use of computation might be useful as their first guess. From this viewpoint, the estimation of activity coefficients of solutes and interaction parameters among them in dilute silicon solution has been tried by the use of ab initio calculation and Monte Carlo simulation.     

Thermodynamic properties of liquid metallic alloys

Experimental data on the activity of components in concentrated (nondilute) liquid metallic alloys must be approximated by characterizing the alloy’s thermodynamic properties on the basis of logγ/(1 ? x ²) rather than logγ. Here γ and x are, respectively, the activity coefficient and molar fraction of the component in the alloy. In that case, the error in calculating the alloy’s integral thermodynamic characteristics—the mixing energy, the regular function—is reduced.     

A Critical Evaluation and Thermodynamic Optimization of the CaO-CaF2 System

A critical evaluation and thermodynamic optimization of all the available literature experimental data of the CaO-CaF₂ system was conducted to obtain a set of thermodynamic functions which can reproduce all available and reliable experimental phase diagrams and thermodynamic data. The liquid solution was described using the Modified Quasichemical Model which assumes the mixing of O² and F^? in the pseudo anionic sublattice and CaF₂ solid solution was described using the compound energy formalism. The discrepancies in the CaO and CaF₂ liquidii among the available experimental data were resolved. The recent experimental data on the solubility of CaO in solid CaF₂ phase were well reproduced, which is critical to explain the eutectic temperature of the system.