Thermodynamic assessment of the phase diagrams of the Cu-Sb and Sb-Zn systems

Thermodynamic assessments have been made for the Cu-Sb and Sb-Zn binary systems by means of the CALPHAD technique. The Gibbs energies of the liquid, bcc, and fcc phases are described by a substitution solution model and a Redlich-Kister formalism. All of the compounds were treated as stoichiometric compounds. Moreover, the liquidus temperatures of the Zn-rich portion in the Sb-Zn system were measured to check the unusual shape reported by previous work. It was confirmed that the liquidus line is not peculiar but smooth. A consistent set of the thermodynamic parameters was optimized to obtain a better fit between calculated results and experimental data including phase diagram and thermodynamic quantities.     

A new thermodynamic study of the liquid Sb-Zn and Cd-Sb-Zn alloys

A unique behavior observed in one of the thermodynamic studies on liquid Sb-Zn alloys is a distinct curvature on the emf vs temperature plots at some compositions, indicating nonzeroΔCp values and revealing some ordering tendencies in the liquid. To confirm or negate the existence of this feature and to determine whether it is transferred to the ternary system, emf measurements were made in liquid Sb-Zn and Cd-Sb-Zn alloys. Ninety-six compositions were investigated through the temperature range from liquidus up to 650 °C; a curvature on emf vs temperature plots was found in thirty-seven cases. A computer program was written to calculate thermodynamic functions for ternary alloys and a part of the liquidus surface by the modified Flengas-Pelton method. Comparison with the available experimental data shows satisfactory agreement, the curvilinear behavior in the Sb-Zn system transfers to ternary alloys.     

Thermodynamic evaluation and optimization of the Ca−Si system

All available phase equilibria and thermodynamic data for the Ca−Si system were collected and critically evaluated. In a first step, the thermodynamic properties of Ca(g) were obtained from experimental vapor pressure data over pure Ca. The new vapor pressure of calcium over pure solid and liquid was used as a new reference to model the thermodynamic properties of the intermediate stoichiometric Ca−Si compounds together with other thermodynamic and phase diagram data found in the literature (liquidus temperatures, heat capacities, pressures of Ca, and heats of reaction). Optimization was performed to obtain the parameters of one set of model equations for the different solid and liquid phases to best reproduce all the experimental data simultaneously. In this way, the data are rendered self-consistent, discrepancies among the data are identified, and extrapolations and interpolations can be performed. For the liquid phase, the Modified Quasichemical Model in the Pair Approximation for short-range ordering was used.     

Thermodynamic Optimization of the Ni-Al-Ce Ternary System

The Ni-Al-Ce ternary system has been thermodynamically optimized in order to be integrated into the database for Ni-base alloys containing rare earth elements. A comprehensive set of thermodynamic parameters including all the ternary intermetallic compounds have been obtained. The calculated enthalpies of formation for ternary compounds by the present work are consistent with values from other sources. Isothermal sections at 1073 and 773 K and liquidus projection have been calculated. Ternary phase equilibria have been well reproduced compared to experimental data.     

Al-Fe-Si、Al-Mn-Si与Al-Fe-Mn-Si体系热力学描述的更新

采用Calphad方法对Al-Fe-Mn-Si四元系及其子体系进行热力学评估。首先，通过考虑文献中最新的实验研究结果以及对部分三元化合物应用新的热力学模型，修正Al-Fe-Si三系的热力学描述，显著地改善了整个成分范围内、尤其是富Al角的液相面投影图。随后，对三元化合物a-AlMnSi和β-AlMnSi采用新的模型，精修Al-Mn-Si体系富Al角的热力学描述。然后，通过模拟a-AlMnSi相在Al-Fe-Mn-Si体系中的固溶度，优化Al-Fe-Mn-Si四元系富Al角的热力学描述。在优化时，对a-AlMnSi作特殊考虑并加入限制条件，以确保其不会在Al-Fe-Si三元系中变得稳定。最后，将所获得的热力学描述加入TCAL数据库，通过一系列的相平衡计算与凝固模拟、以及与商业铝合金的实验数据的比较，对所获得的热力学描述进行全面的验证。更新后的TCAL数据库能够可靠地预测Al-Fe-Si基与Al-Fe-Mn-Si基合金中的相形成。     

Critical assessment and thermodynamic calculation of the ternary system boron-hafnium-titanium (B-Hf-Ti)

Experimental work on the ternary system Ti-Hf-B as well as on the two binary boundary systems Hf-B and Ti-Hf is reviewed. The individual phases of these systems are described with thermodynamic models. The models were fitted to the experimental information and the resulting optimized data sets are presented. The calculated thermodynamic properties of the two binary compounds HfB and HfB₂ are compared with experimental measurements. Phase diagrams were calculated for the bi-nary systems Hf-B and Ti-Hf as well as for the ternary Ti-Hf-B system; for the latter, several isother-mal sections, isopleths, and the liquidus surface are included. They are presented and compared with the experimental information. A reaction scheme for the ternary Ti-Hf-B system was constructed.     

Thermodynamic database of the phase diagrams in the Mg-Al-Zn-Y-Ce system

The Mg-Al-Zn-Y-Ce system is one of the key systems for designing high-strength Mg alloys. The purpose of the present article is to develop a thermodynamic database for the Mg-Al-Zn-Y-Ce multicomponent system to design Mg alloys using the calculation of phase diagrams （CALPHAD） method, where the Gibbs energies of solution phases such as liquid, fcc, bcc, and hcp phases were described by the subregular solution model, whereas those of all the compounds were described by the sublattice model. The thermodynamic parameters describing Gibbs energies of the different phases in this database were evaluated by fitting the experimental data for phase equilibria and thermodynamic properties. On the basis of this database, a lot of information concerning stable and metastable phase equilibria of isothermal and vertical sections, molar fractions of constituent phases, the liquidus projection, etc., can be predicted. This database is expected to play an important role in the design of Mg alloys.     

Thermodynamic database of the phase diagrams in Cu-Fe base ternary systems

A thermodynamic database of the Cu-Fe-X [X: aluminum (Al), cobalt (Co), chromium (Cr), manganese (Mn), molybdenum (Mo), niobium (Nb), nickel (Ni), vanadium (V)] systems was developed by the CALPHAD (Calculation of Phase Diagrams) method, where the Gibbs energies of solution phases such as the liquid, face-centered-cubic (fcc), body-centered-cubic (bcc), and hexagonal-close-packed (hcp) phases are described by the subregular solution model, while the those of the bcc phase in the Cu-Fe-Al system and of all compounds are described by the sublattice model. The thermodynamic parameters describing Gibbs energies of the different phases in this database were evaluated by fitting the experimental data for phase equilibria and thermodynamic properties. On the basis of this database, much information concerning stable and metastable phase equilibria of isothermal and vertical sections, molar fractions of constituent phases, the liquidus projection, etc., can be predicted. This database is expected to play an important role in the design of Cu-Fe base alloys.     

Thermodynamic Calculation of Phase Equilibria in the C-Mo-Zr System

The C-Mo-Zr system was assessed by means of the CALPHAD approach. All of the phase equilibria available from the literature were critically reviewed. The liquid was modeled as substitutional solution phase, while the carbides including fcc-(Mo,Zr)C_1?x, bcc-(Mo), bcc-(Zr), hcp-Mo₂C, hcp-(Zr) and η-MoC were described by using corresponding sublattice models. The laves-Mo₂Zr and shp-MoC phases were considered as binary compounds with no solubility for the third component. The existence of ternary phase was not reported in this system. The modeling of C-Mo-Zr ternary system covers the entire composition and temperature ranges, and a set of self-consistent thermodynamic parameters for the C-Mo-Zr system was systematically optimized. Comprehensive comparisons between the calculated and reported phase diagram data show that the reliable information is satisfactorily accounted for by the present modeling. The liquidus projection and reaction scheme of the C-Mo-Zr system were also generated based on the present thermodynamic assessment.     

Thermodynamic Assessment of the Mn-B System

The phase equilibrium and thermodynamic data on the Mn-B system are critically reviewed. Based on the experimental data, a thermodynamic modeling is performed on this system. A set of self-consistent thermodynamic parameters is obtained and the calculated results are in general agreement with the experimental data. A parameter ξ is introduced to compare the degree of flatness of the δMn/L liquidus with those in other metal-boron systems. It is found that the δMn/L liquidus is the flattest, which causes difficulties in its modeling. An effective approach to evaluate the thermodynamic parameters for o-Mn₂B_0.982 phase is developed. Such an approach is valid for evaluating thermodynamic parameters of the phases with limited phase diagram data.     

Thermodynamic Modeling of the Ag-Au-Sb Ternary System

A thermodynamic assessment of the Ag-Au-Sb ternary system has been carried out using the CALPHAD method based on new thermodynamic and phase equilibria data that we have recently determined. The Ag-Sb binary system has also been reoptimized. The calculated phase diagram and thermodynamic properties of the ternary system Ag-Au-Sb show satisfactory general agreement with the experimental data. The liquidus projection and monovariant valleys of the ternary system are well reproduced by the optimized thermodynamic model parameters. Additional experiments to confirm the proposed reaction scheme, which involves two ternary transition peritectic reactions, are suggested.     

An assessment of thermodynamic data for the liquid phase in the Al-rich corner of the Al-Cu-Si system and its application to the solidification of a 319 alloy

A thermodynamic database for the liquid phase in the Al-rich corner of the Al-Cu-Si system has been developed by fitting all thermodynamic and phase diagram information that is currently available from the literature. A comparison between the calculated results and the experimental data is presented, and the calculated results reproduce all the liquidus and solidus boundaries to within experimental scatter. Also, the present assessment was used to predict the solidification behavior of an Al-3.5wt.% Cu-7wt.%Si, 319-type alloy. Subsequent experimental results validate these predictions.     

Calculations of phase diagrams in associated solution model

The development of an ideal associated solution model concerned with complexes of various compositions, sizes, and shapes is described. Such models were used earlier to calculate thermodynamic characteristics and the position of the liquidus line for binary eutectic systems as well as those having a stable compound in the solid phase. In all the cases, the model parameters were not adjusted but were estimated from melting temperatures of the components. The latest studies deal with the influence of arbitrary stoichiometry associates on the equilibrium thermodynamic properties of liquid alloys. The application of the model to eutectic systems and systems having an unlimited miscibility in solid and liquid states close to the liquidus has been considered. It was shown that if the difference in melting temperatures of the components was small, different types of fusibility diagrams were possible: eutectic diagrams, cigar-shaped diagrams, or diagrams with upper or lower azeotropic points. Peritectic transformations could take place if the difference in melting temperatures of the components were large.     

Experimental Investigation of the Ternary Ge-Sn-In and Ge-Sn-Zn Systems

This paper presents results of experimental examinations of alloys from the ternary Ge-Sn-In and Ge-Sn-Zn systems. Differential thermal analysis, scanning electron microscopy with energy dispersive spectroscopy and x-ray diffraction were used for the experimental investigation of the prepared samples. Obtained experimental results were compared with the thermodynamically extrapolated phase diagrams of the Ge-Sn-In and Ge-Sn-Zn ternary systems based on the thermodynamic parameters for the constitutive binary systems. A good agreement is seen, which suggests that it is not necessary to introduce new thermodynamic parameters for the ternary Ge-Sn-In and Ge-Sn-Zn systems. By using the proposed thermodynamic dataset, a liquidus projection and invariant reactions have been predicted for both investigated ternary systems.     

Thermodynamic Assessment of the CaO-NiO System Using the Quasi-chemical Cell Model of Kapoor-Frohberg-Gaye

The knowledge of the thermodynamic features of the NiO-CaO system is of fundamental importance to the modelling of metal-slag-refractory equilibrium of Ni-based alloys melting process in electric arc furnaces as well as for development a self-consistent multi-component thermodynamic database for nickel extraction from laterite ores. The existing assessment for liquid slag, based on the quasichemical model modified by Pelton and Blander cannot be in the SLAG database used by Thermo-Calc software which is based on a different thermodynamic model to slag phase. The present work presents the modelling of CaO-NiO using the quasichemical cell model of Kapoor-Frohberg-Gaye for the liquid slag phase. The data utilized for this modelling were activities, liquidus and solvus compositions as well as magnetic parameters of the phase NiO. The optimization was performed with the PARROT^® module of Thermo-Calc^® software. The results obtained, the phase diagram and the activities diagrams, are in good agreement with the literature data.     

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.     

Thermodynamic modeling of the Fe-S system

A thorough review and critical evaluation of phase equilibria and thermodynamic data for all phases in the iron-sulfur (Fe-S) binary 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 ten phases have been modeled, and optimized model parameters have been obtained that reproduce all data simultaneously within experimental error limits. For the liquid phase, the recently extended modified quasi-chemical model is applied for the first time to a liquid metal-sulfur phase. A two-sublattice model within the framework of the compound energy formalism is used for the high-temperature monosulfide pyrrhotite solution. A substitutional model is used for the dissolution of S in solid iron. The Gibbs energies of six stoichiometric compounds are also modeled.     

Thermodynamic modeling of the CeO2–CoO phase diagram

A thermodynamic modeling of the CeO₂–CoO phase diagram was performed with recent experimental data. The excess Gibbs energies of the solution phases were described on the basis of the simple regular solution. A consistent set of optimized interaction parameters was derived for describing the Gibbs energy of each phase in this system leading to a good fit between calculation and experimental data. The liquidus, solidus, and solvus curves were calculated and also the lattice stabilities of the components were evaluated.     

Thermodynamic Assessment of Zn-Fe-Nb Ternary System

The Nb-Zn binary system has been thermodynamically assessed using CALPHAD approach by combining available experimental data and the data from ab initio calculations of the formation enthalpies for NbZn₂, NbZn₃ and NbZn₁₅. Solution phases including Liquid, Bcc, Hcp were modeled as substitutional phases, of which the excess Gibbs energies being formulated with the Redlich-Kister polynomial function. All the binary compounds were treated as stoichiometric phases. Incorporated with the reported thermodynamic parameters of Fe-Zn and Fe-Nb binary systems, two isothermal sections at 723 and 873 K of Zn-Fe-Nb ternary system were thermodynamically optimized where one stoichiometric ternary phase (τ) and the ternary solubility in intermetallic compound (ε) were taken into consideration. Furthermore, liquidus projection was predicted accordingly.