Critical assessment and thermodynamic calculation of the ternary system C-Hf-Zr (Carbon-Zirconium-Hafnium)

Based on an assessment of the available experimental thermochemical and phase diagram information available, the phase equilibria of the C-Hf-Zr system were calculated. The G of the individual phases was described with thermodynamic models. The liquid phase was described as a substitutional solution using the Redlich-Kister formalism for excess G. Graphite was treated as a stoichiometric phase. The solid solutions of carbon in α(Hf,Zr) and β(Hf,Zr), as well as the non-stoichiometric phase (Hf,Zr)C_1−x, were represented as interstitial solid solutions using the compound energy model with two sublattices. The parameters in the models were determined by computerized optimization using selected experimental data. A detailed comparison was made between calculation and experimental data.     

Critical assessment and thermodynamic calculation of the ternary system C-Hf-Zr (Carbon-Zirconium-Hafnium)

Based on an assessment of the available experimental thermochemical and phase diagram information available, the phase equilibria of the C-Hf-Zr system were calculated. The G of the individual phases was described with thermodynamic models. The liquid phase was described as a substitutional solution using the Redlich-Kister formalism for excess G. Graphite was treated as a stoichiometric phase. The solid solutions of carbon in α(Hf,Zr) and β(Hf,Zr), as well as the non-stoichiometric phase (Hf,Zr)C_1?x, were represented as interstitial solid solutions using the compound energy model with two sublattices. The parameters in the models were determined by computerized optimization using selected experimental data. A detailed comparison was made between calculation and experimental data.     

Thermodynamic assessment of ZnO-SiO2 system

ZnO-containing slags are common in pyrometallurgical processing of the base metals and steel. This caused the interest to the thermodynamics of the ZnO-SiO₂ system. A complete literature survey, critical evaluation of the available experimental data and a thermodynamic optimization of the phase equilibria and thermodynamic properties of the system ZnO-SiO₂ at 1.013×10⁵ Pa are presented. The molten oxide was described as an associate solution. The properties of liquid were reassessed and enthalpy term of the Gibbs energy of solid Zn₂SiO₄ was re-fitted to be compatible with the new data in the willemite primary phase field. The thermodynamic data set agrees well with the recent experimental observations. It can be used for predicting, e.g., the thermodynamic properties and the domains of the phase diagram, like critical point of the liquid miscibility gap, with a better accuracy than using the previous assessments. A set of optimized model parameters were obtained, reproducing the reliable thermodynamic and phase equilibrium data within their experimental errors from 298 K to liquidus temperatures, over the entire composition range. The created database can be used in a Gibbs energy minimization software to calculate the thermodynamic properties and the phase diagram sections of interest.     

A new thermodynamic description of the Cu-Zr system

An optimized set of thermodynamic functions for the Cu-Zr system was obtained by the least squares method from phase diagram and thermodynamic data available in the literature. The excess Gibbs energies of the solution phases, liquid, and three terminal solid solutions, were described by the Redlich-Kister formula. All the intermediate compounds were treated as stoichiometric phases. The calculated phase diagram, as well as the thermodynamic properties vs compositions, agree well with the experimental values. The reliability of the optimized parameters was examined using μ-T plots.     

Critical Systematic Evaluation and Thermodynamic Optimization of the Fe-RE System: RE = Gd,Tb, Dy,Ho, Er,Tm, Lu,and Y

As the second part of the thermodynamic study of binary Fe-RE system, critical evaluations and optimizations of all available phase diagrams and thermodynamic data for the Fe-heavy RE (heavy RE = Gd, Tb, Dy, Ho, Er, Tm, Lu, and Y) systems were conducted to obtain reliable thermodynamic functions of all the phases in the systems. In the thermodynamic modeling of the heavy RE systems, systematic variations in the phase diagrams and thermodynamic properties such as the enthalpy of mixing in the liquid state and enthalpy of formation of solid compounds with the atomic number of lanthanide series were observed. These systematic trends were incorporated in the optimization of the Fe-heavy RE system to resolve inconsistencies between available experimental data and to estimate unknown thermodynamic properties. The systematic trends in thermodynamic properties of solid and liquid phases and phase diagram of the entire Fe-RE systems were summarized.     

Thermodynamic optimization of the Ni-Zn system

Optimization of thermodynamic and phase diagram data has been performed and consistent sets of coefficients for the calculation of the phase equilibria in the system Ni-Zn have been obtained using the program BINGSS. The δ phase has been modeled as a stoichiometric compound (NiZn₈). The binary liquid and the solid Ni-based solutions have been treated as disordered substitutional phases. The intermediate β, β ₁, and γ compounds have been modeled as phases with substitutional defects and vacancies on two sublattices. The calculated phase diagram and thermodynamic quantities are in excellent agreement with the experimental data.     

Thermodynamic optimization of the Ni-Zn system

Optimization of thermodynamic and phase diagram data has been performed and consistent sets of coefficients for the calculation of the phase equilibria in the system Ni-Zn have been obtained using the program BINGSS. The δ phase has been modeled as a stoichiometric compound (NiZn₈). The binary liquid and the solid Ni-based solutions have been treated as disordered substitutional phases. The intermediate β, β ₁, and γ compounds have been modeled as phases with substitutional defects and vacancies on two sublattices. The calculated phase diagram and thermodynamic quantities are in excellent agreement with the experimental data.     

Thermodynamic Treatment of Undercooled Cu-Mg Liquid and the Limits for Partitionless Crystallization

The thermodynamic properties of the binary Cu-Mg system are examined with a focus on equilibria involving the liquid phase, which is described with a four-species association model, incorporating a two-state treatment for the pure component liquids below their respective melting temperatures. The terminal and intermediate crystalline phases are described as substitutional solid solutions, employing two sublattices for the latter. Model parameters are fitted using available experimental data, and the resulting phase diagram is reported over the full range of compositions in the binary system. We also report the associated T ₀ curves, indicating the limits of partitionless crystallization and compare these with reports of amorphous solid formation during rapid solidification processing.     

Experimental studies and thermodynamic optimization of the Ni-Bi system

Experimental studies by electron microprobe analyses, optical microscopy, and differential scanning calorimetry were performed. New data about the liquidus in the central and the Bi-rich regions were obtained. A narrow homogeneity region (about 50–52 at.% Bi) was found for the compound NiBi while the second intermediate phase in this system (NiBi₃) was stoichiometric. Thermodynamic optimization of the Ni-Bi phase diagram was achieved by the CALPHAD method by combining phase diagram and thermodynamic data. Thus, NiBi was modeled with two sublattices, allowing mixing of Bi and Ni on one of them only. The intermetallic phase NiBi₃ was modeled as a stoichiometric compound. Redlich-Kister polynomials were used to describe the excess Gibbs energies of the solution phases (liquid, pure bismuth, and Ni-based solid solutions).     

Critical thermodynamic evaluation and optimization of the MgO-Al2O3, CaO-MgO-Al2O3, and MgO-Al2O3-SiO2 Systems

A complete literature review, critical evaluation, and thermodynamic modeling of the phase diagrams and thermodynamic properties of all oxide phases in the MgO-Al₂O₃, CaO-MgO-Al₂O₃, and MgO-Al₂O₃-SiO₂ systems at 1 bar total pressure are presented. Optimized model equations for the thermodynamic properties of all phases are obtained that reproduce all available thermodynamic and phase equilibrium data within experimental error limits from 25 °C to above the liquidus temperatures at all compositions. The database of the model parameters can be used along with software for Gibbs energy minimization to calculate all thermodynamic properties and any type of phase diagram section. The modified quasichemical model was used for the liquid slag phase and sublattice models, based upon the compound energy formalism, were used for the 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.     

Critical evaluation and optimization of the thermodynamic properties and phase diagrams of the CrO-Cr2O3-SiO2 and CrO-Cr2O3-SiO2-Al2O3 systems

Available thermodynamic and phase diagram data have been critically assessed for all phases in the CrO-Cr₂O₃-SiO₂ and CrO-Cr₂O₃-SiO₂-Al₂O₃ systems from 298 K to above the liquidus temperatures and for oxygen partial pressures ranging from equilibrium with metallic Cr to equilibrium with air. All reliable data have been simultaneously optimized to obtain one set of model equations for the Gibbs energy of the liquid slag and all solid phases as functions of composition and temperature. The modified quasi-chemical model was used for the slag. The models permit phase equilibria to be calculated for regions of composition, temperature, and oxygen potential where data are not available.     

Critical evaluation and optimization of the thermodynamic properties and phase diagrams of the CrO-Cr2O3-SiO2 and CrO-Cr2O3-SiO2-Al2O3 systems

Available thermodynamic and phase diagram data have been critically assessed for all phases in the CrO-Cr₂O₃-SiO₂ and CrO-Cr₂O₃-SiO₂-Al₂O₃ systems from 298 K to above the liquidus temperatures and for oxygen partial pressures ranging from equilibrium with metallic Cr to equilibrium with air. All reliable data have been simultaneously optimized to obtain one set of model equations for the Gibbs energy of the liquid slag and all solid phases as functions of composition and temperature. The modified quasi-chemical model was used for the slag. The models permit phase equilibria to be calculated for regions of composition, temperature, and oxygen potential where data are not available.     

Critical evaluation and optimization of the thermodynamic properties and phase diagrams of the Al-Mg, Al-Sr, Mg-Sr, and Al-Mg-Sr Systems

All available thermodynamic and phase diagram data were critically assessed for all phases in the Al-Mg, Al-Sr, and Mg-Sr systems at 1 bar pressure from room temperature to above the liquidus temperatures. For these systems, all reliable data were simultaneously optimized to obtain a set of model equations for the Gibbs energy of the liquid alloy and all solid phases as functions of composition and temperature. The modified quasi-chemical model was used for the liquid. The Al-Mg-Sr ternary phase diagram was calculated from the optimized thermodynamic properties of the binary systems. Since no reliable ternary data were available, three assumptions were made: no ternary terms were added to the model parameters for the thermodynamic properties of the liquid, no ternary solid solutions are present in the system, and no ternary compound is present in the system. The calculated ternary phase diagram is thus a first approximation, which can be improved by the addition of new experimental data and can be used as a base for the calculation of phase diagrams of multicomponent systems.