Thermodynamic assessment of the copper-hafnium system

The thermodynamic properties of phases and phase equilibria in the Cu-Hf system are described with the CALPHAD method. The set of self-consistent model parameters is based on the thermodynamic properties of liquid alloys, intermetallic compounds, and phase equilibria. The excess Gibbs energy of the liquid phase is described using an ideal associated solution model. The models of thermodynamic properties are used to describe possible metastable transformations such as glass formation in rapid quenching from the melt, formation of bulk amorphous alloys, and formation of supersaturated terminal solid solutions.     

Phase equilibria and thermodynamics of binary copper systems with 3d-metals. II. The copper-vanadium system

Thermodynamic assessment of the Cu-V system was carried out using the CALPHAD method. The excess heat capacity of the liquid phase was taken into account in the model of its excess Gibbs free energy. Excess thermodynamic properties of limiting solid solutions were represented by regular solution models. A self-consistent set of thermodynamic parameters was obtained using data on the mixing enthalpy and information on the phase equilibria. The thermodynamic properties of the phases and the phase diagram along with its metastable extension were calculated using this set of parameters. The thermodynamic model of the system was used in order to predict the composition limits of formation of supersaturated solid solutions prepared by highly nonequilibrium methods of synthesis. __________ Translated from Poroshkovaya Metallurgiya, Nos. 5–6(449), pp. 71–79, May–June, 2006.     

Critical thermodynamic evaluation and optimization of the FeO-Fe<Subscript>2</Subscript>O<Subscript>3</Subscript>-MgO-SiO<Subscript>2</Subscript> system

A complete literature review, critical evaluation, and thermodynamic modeling of the phase diagrams and thermodynamic properties of all oxide phases in the FeO-Fe₂O₃-MgO-SiO₂ system at 1 bar total pressure are presented. Optimized model equations for the thermodynamic properties of all phases are obtained, which reproduce all available thermodynamic and phase-equilibrium data within experimental error limits from 25 °C to above the liquidus temperatures at all compositions and oxygen partial pressures. The complex phase relationships in the system have been elucidated, and discrepancies among the data have been resolved. The database of the model parameters can be used along with software for Gibbs-energy minimization in order to calculate all thermodynamic properties and any type of phase-diagram section. The modified quasichemical model was used for the liquid-slag phase. Sublattice models, based upon the compound-energy formalism, were used for the olivine, spinel, pyroxene, and monoxide solid solutions. The use of physically reasonable models means that the models can be used to predict thermodynamic properties and phase equilibria in composition and temperature regions where data are not available.     

Thermodynamic assessment of the Cu-Ti-Zr system. II. Cu-Zr and Ti-Zr systems

The thermodynamic assessment of the Cu-Zr and Ti-Zr systems is carried out using the CALPHAD method. The Gibbs energy of Cu-Zr liquid alloys is described by the ideal associated solution model. The excess Gibbs energy of Ti-Zr liquid alloys and Cu-Zr and Ti-Zr solid solutions is descried by models with Redlich-Kister polynomials. The Gibbs energy of Cu-Zr intermetallic compounds is described by models taking into account their formation enthalpy and entropy. A set of self-consistent parameters of the models is obtained using data on phase equilibria and thermodynamic properties of the phases. The calculated phase diagrams of the systems and values of thermodynamic properties of the phases are in good agreement with experimental information. The relative thermodynamic stability of supercooled liquid alloys and competitive crystal phases of the Cu-Zr system are analyzed.     

Model prediction of thermodynamic properties of Co-Fe-Ni-S mattes

The modified quasichemical model for short-range ordering has been used to predict the thermodynamic properties of liquid Fe-Co-S, Ni-Co-S, and Fe-Ni-S solutions based only upon parameters obtained from critical optimization of data for the corresponding metal-sulfur and metal-metal binary systems. Calculated equilibrium sulfur pressures over the ternary solutions and calculated tie-lines between the ternary solutions and the solid alloy phases agree with measurements, within experimental error limits, over a wide range of compositions and temperatures.     

Thermodynamic evaluation and optimization of the LiCl-NaCl-KCl-RbCl-CsCl-MgCl2-CaCl2 system using the modified quasi-chemical model

A complete critical evaluation of all available phase-diagram and thermodynamic data has been performed for all condensed phases of the LiCl-NaCl-KCl-RbCl-CsCl-MgCl₂-CaCl₂ system, and optimized model parameters have been found. The model parameters obtained for binary and ternary subsystems can be used to predict thermodynamic properties and phase equilibria for the multicomponent system. The modified quasi-chemical model for short-range ordering was used for the molten salt phase. Particularly in solutions with MgCl₂ and KCl, RbCl, or CsCl, the calculations indicate a large dregree of ordering on the cationic sublattice, with Mg-Alkali second-nearest-neighbor pairs being favored.     

Thermodynamic evaluation and optimization of the LiF-NaF-KF-MgF2-CaF2 system using the modified quasi-chemical model

A complete critical evaluation of all available phase diagram and thermodynamic data has been performed for all condensed phases of the LiF-NaF-KF-MgF₂-CaF₂ system and optimized model parameters have been found. The model parameters obtained for binary and ternary subsystems can be used to predict thermodynamic properties and phase equilibria for the multicomponent system. The modified quasi-chemical model for short-range ordering (SRO) was used for the molten salt phase. For solutions with NaF or KF together with MgCl₂ or CaCl₂, the calculations indicate a large degree of ordering on the cationic sublattice, with Mg-alkali and Ca-alkali second-nearest-neighbor (SNN) pairs being favored.     

Critical thermodynamic assessment and modeling of the Fe-Ni-S system

A thorough review and critical evaluation of phase equilibria and thermodynamic data for phases in the iron-nickel-sulfur ternary system at 1 bar pressure has been made over the entire composition range for temperatures from 25°C to above the liquidus. The Gibbs energies of system phases have been modeled, and optimized model parameters have been obtained which reproduce all data simultaneously within experimental error limits. The modeling is based on the recent evaluations by the authors of the Fe-S and Ni-S binary subsystems. For the liquid phase, the recently extended modified quasichemical model for short-range ordering is applied for the first time to a liquid metal-sulfur phase. Although the binary Fe-S and Ni-S liquid solutions were modeled with the extended modified quasichemical model, while the binary Fe-Ni liquid solution was modeled with a simple random-mixing model, it is shown, for the first time, that these can be combined into a consistent model of the ternary liquid phase. Two-sublattice models, within the framework of the compound-energy formalism, are used for the solid solutions: pyrrhotite, pentlandite, pyrite, vaesite, and high-temperature heazlewoodite. The ternary-solution model for iron-nickel pyrrhotite permits very good prediction of thermodynamic properties solely on the basis of binary-model parameters.     

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.     

Predicting the thermodynamic properties of liquid intermetallide solutions

Acceptable accuracy may be obtained in calculating the thermodynamic activity of the components in a system containing intermetallides on the basis of the model of ideal associated solutions, if the chemical composition and thermodynamic properties of the associates are assumed to be the same as for the intermetallides.     

Thermodynamics of converting lead sulfide

Available thermodynamic data on the Pb-S-O system are reviewed and collated to establish a quantitative equilibrium model for processes of converting and direct smelting of PbS concentrates to Pb. The thermodynamic properties of Pb-S liquid solutions are well represented by an empirical model which treats these solutions as “regular” mixtures of liquid Pb and liquid PbS. The calculations and equilibrium diagrams for the Pb-S-O system show that close control of oxygen activity and temperature will be required for a successful lead converting process, and that in fact a multistage countercurrent process should be advantageous.     

A thermodynamic assessment of the Fe-Mn-C system

The thermodynamic properties of the Fe-Mn-C system have been analyzed by using thermodynamic models for the Gibbs energy of individual phases. The model parameters have been evaluated from the available thermodynamic and phase diagram information and by using computerized optimization. Most of the experimental information was satisfactorily described by the present set of parameters. Comparisons between the calculations and experiments are presented.     

Thermodynamic assessment of the Cu-Ti-Zr system. I. Cu-Ti system

The CALPHAD method is used for the thermodynamic assessment of the Cu-Ti system that bounds the ternary Cu-Ti-Zr system, which is capable of forming amorphous alloys. The self-consistent parameters of thermodynamic models of the phases are obtained from data on the phase equilibria and thermodynamic properties of liquid alloys and intermetallic compounds. The Gibbs energy of the liquid phase is described using the associated ideal solution model. To describe the thermodynamic properties of the Cu₄Ti and CuTi intermetallic compounds with homogeneity range, sublattice models are used. The calculated phase diagram of the system and the thermodynamic properties of the phases are in good agreement with experimental data.     

Thermodynamic description for concentrated metallic solutions using interaction parameters

The integral molar excess Gibbs energy of a multicomponent system is expressed in terms of interaction parameters, from which the analytical formulae of the activity coefficients of the solutes and solvent, as Eqs. [23] and [24], were deduced. This approach, named the ε approach, is able to describe quantitatively the thermodynamic properties of multicomponent systems. It features thermodynamic consistency, high accuracy, and a rather small influence of the higher-interaction parameters on the thermodynamic properties of metallic solutions. A simple modification to the first-order interaction parameters extends the ε approach, to be applicable to systems with strong interactions between components at both low and concentrated levels.     

LiF-NaF-KF体系的相图计算

基于CALPHAD技术首先评估了LiF-NaF和LiF-KF两个二元熔盐体系,液相和端际固溶体Halite相均采用Redlich-Kister多项式置换熔体模型描述,模型参数的优化选取实验相平衡数据和热化学数据以及本文根据第一性原理预测的数据.结合文献中已报道的NaF-KF体系的热力学参数,用Muggianu模型扩展至LiF-NaF-KF三元体系,根据三元共晶点的实验数据调整三元交互参数.最终的相图计算结果与绝大部分实验数据和第一原理计算数据吻合较好,由此获得了一套自洽且可靠的热力学参数,其能够准确描述LiF-NaF-KF体系的相平衡与热力学性质.      

Thermodynamic optimization and calculation of phase diagrams of YbCl3-MCl (M=Na, K, Rb, Cs)

YbCl3-MCl (M = Na, K, Rb, Cs) systems were optimized and calculated using the CALPHAD (CALculation of PHAse Diagram) technique. The modified quasi-chemical model in the pair-approximation for short-range ordering was used to describe the Gibbs energies of liquid phase in the systems. On the basis of the measured phase diagram data and experimental thermodynamic properties, a series of thermodynamic functions were optimized and calculated through an interactive computer-assisted analysis. Furthermore, some reasonable discussions on the thermodynamic parameters for these strong interaction binary systems were carried out. The results showed that the optimized parameters and experimental data are thermodynamically self-consistent.     

Nucleation of substitutional solid solutions during the solidification of binary liquid solutions

The thermodynamic parameters (entropy, enthalpy, interfacial surface energy) are analyzed for the substitutional solid solutions that solidify from liquid solutions of binary systems characterized by continuous solubility. Equations determining the concentrational dependences of these parameters, the critical sizes of nuclei, and their formation energies are obtained.