Critical evaluation and thermodynamic optimization of the V–O system

The V–O system has been critically evaluated and thermodynamically assessed based on the available phase diagram and thermodynamic data using the CALPHAD method. The liquid phase over the whole composition range from metallic liquid to oxide melt is described by the modified quasichemical model with five species: V^II, V^III, V^IV, V^V and O, which takes short-range ordering in liquid solution into account. All solid solutions are modeled considering respective crystal structures. A set of self-consistent thermodynamic parameters of the V–O system is obtained and the available experimental data are reproduced well within experimental error limits. Especially for the VO_x solid solution, the site fractions of vacancies in both vanadium and oxygen sublattices are reproduced well using the present model and parameters.     

Critical thermodynamic evaluation and optimization of the Pb–Pr,Pb–Nd,Pb–Tb and Pb–Dy systems

All available experimental data on phase equilibria and thermodynamic properties of the Pb–Pr, Pb–Nd, Pb–Tb and Pb–Dy binary systems were reviewed and critically examined. A thermodynamic optimization of these systems is presented for the first time. A set of optimized model parameters for all solid stoichiometric compounds, terminal solid solutions and liquid phase was built to reproduce all available reliable thermodynamic properties and phase diagram data within experimental error limits. The Modified Quasichemical Model in the pair approximation was used to describe the thermodynamic properties of the liquid solution accurately. In view of the limited experimental phase diagram and thermodynamic data available for these systems, trends in the rare earth-lead and rare earth–tin systems were examined to estimate the missing information and evaluate whether the predictions are reasonable. Based on these trends, a predicted phase diagram for the Pb–Nd and Pb–Tb systems, which are not established to date, is presented.     

Critical evaluation and thermodynamic optimization of Fe–Cu,Cu–C,Fe–C binary systems and Fe–Cu–C ternary system

Development of an efficient process for recycling ferrous scrap containing Cu requires reliable thermodynamic knowledge of Fe–Cu based alloy system. It is shown that there still remain discrepancies in existing databases from known experimental data. In order to provide an accurate prediction tool for the process development, a CALPHAD type thermodynamic modeling for the Fe–Cu–C system is presented with re-optimization of its binary sub-systems, Fe–Cu, Cu–C, and Fe–C. Liquid phase was modeled using the Modified Quasichemical Model in the pair approximation which generally gives better results in systems exhibiting positive deviation from ideality (such as in Fe–Cu). Solid solutions such as fcc and bcc were described using Compound Energy Formalism. A supplement experimental work was carried out in order to provide more accurate solid/liquid equilibria in Fe–Cu binary system. The obtained model parameters along with the model equations were shown to reproduce significantly better correspondence to the experimental data, such as the phase equilibria, activity of component in the Fe–Cu–C system, liquidus projections etc., within experimental uncertainty. High temperature stabilization of bcc phase in Fe–C binary system in previous thermodynamic modeling was revisited, and was resolved in the present study.     

Critical evaluation and thermodynamic optimization of Mg–Ga system and effect of low pressure on phase equilibria

A complete literature review and critical evaluation of the Mg–Ga binary system are presented. All stable phases known in this system were thermodynamically modeled in the framework of CALPHAD. Liquid phase was modeled using the Modified Quasichemical Model in the pair approximation which takes into account short-range ordering. α-(Mg) solid solution of hcp structure was modeled as a substitutional solution. All intermetallic phases Mg₅Ga₂, Mg₂Ga, MgGa, MgGa₂, Mg₂Ga₅, as well as Ga-rich phase, were treated as stoichiometric compounds. Gas phase was assumed to behave as an ideal solution. Thermodynamic optimization was carried out by evaluating enthalpic and entropic contributions to the Gibbs free energy of all phases independently. It showed that the optimized model parameters along with the model equations could reproduce the available and reliable experimental data in the Mg–Ga system. Representation of partial excess Gibbs free energy of Mg in Ga-rich liquid was improved compared to the previous thermodynamic modeling. Low pressure phase equilibria in this system were analyzed using the developed thermodynamic model, and it was compared with a recent observation of an Mg nanopillar fabricated by Ga⁺ ion beam in a focused ion beam (FIB), followed by in-situ heating in a transmission electron microscope (TEM). Reported surface melting of Mg nanopillar in the TEM column pressure (~10⁻¹⁰ bar) is attributed to the fact that decreasing pressure enhanced sublimation of Mg from the Mg nanopillar significantly, leaving Ga-rich liquid.     

Thermodynamic modeling of the Al–Bi,Al–Sb,Mg–Al–Bi and Mg–Al–Sb systems

All available thermodynamic and phase diagram data of the binary Al–Bi and Al–Sb systems and ternary Mg–Al–Bi and Mg–Al–Sb systems were critically evaluated, and all reliable data were used simultaneously to obtain the best set of the model parameters for each ternary system. The Modified Quasichemical Model used for the liquid solution shows a high predictive capacity for the ternary systems. The ternary liquid miscibility gaps in the Mg–Al–Bi and Mg–Al–Sb systems resulting from the ordering behaviour of the liquid solutions can be well reproduced with one additional ternary parameter. Using the optimized model parameters, the experimentally unexplored portions of the Mg–Al–Bi and Mg–Al–Sb ternary phase diagrams were more reasonably predicted. All calculations were performed using the FactSage thermochemical software package.     

First-principles study of binary special quasirandom structures for the Al–Cu,Al–Si,Cu–Si,and Mg–Si systems

Based on special quasirandom structures (SQS’s) and first-principles calculations, enthalpies of mixing have been predicted for four binary fcc solid solutions in the Al–Cu, Al–Si, Cu–Si, and Mg–Si systems at nine compositions (x=0.0625$x=0.0625$, 0.125, 0.1875, 0.25, 0.5, 0.75, 0.8125, 0.875, 0.9375, where x$x$ is the mole fraction of A atoms in the A–B binary system). The present results are compared with previous first-principles calculations and thermodynamic modeling results available in the literature. In order to provide insight into the understanding of mixing behavior for these solid solutions, the spatial charge density distributions in these binary solid solutions are also analyzed. The results obtained herein indicate that the SQS model can be used to estimate the thermodynamic properties of solid solutions, especially for metastable phases, the thermodynamic qualities of which are rarely measured.     

Thermodynamic modeling of the Mg–Bi and Mg–Sb binary systems and short-range-ordering behavior of the liquid solutions

In order to investigate the short range ordering behavior of liquid Mg–Bi and Mg–Sb solutions, thermodynamic modeling of the Mg–Bi and Mg-Sb binary systems has been performed. All available thermodynamic and phase diagram data of the Mg–Bi and Mg–Sb binary systems have been critically evaluated and all reliable data have been simultaneously optimized to obtain one set of model parameters for the Gibbs energies of the liquid and all solid phases as functions of composition and temperature. In particular, the Modified Quasichemical Model, which accounts for short-range-ordering of nearest-neighbor atoms in the liquid, was used for the liquid solutions. A comparative evaluation of both systems was helpful to resolve inconsistencies of the experimental data. The thermodynamic modeling shows the strong ordering behavior in the liquid Mg–Bi and Mg–Sb solutions at Mg₃Bi₂ and Mg₃Sb₂ compositions, respectively, and predicts the metastable liquid miscibility gaps at sub-solidus temperatures. All calculations were performed using the FactSage thermochemical software.     

Critical evaluation and thermodynamic modeling of the Fe–P and Fe–C–P system

Phosphorus is known to be a strongly segregating element in steel; even small amounts influence the solidification phenomena and product quality during casting processes. In order to provide an accurate prediction tool for process control in steelmaking, a CALPHAD-type thermodynamic optimization of the Fe–C–P system was performed including modeling of the binary Fe–P subsystem. The liquid phase was modeled using the Modified Quasichemical Model (MQM) in the pair approximation, which generally yields better results for strong short-range ordering (SRO) tendency in the solution. The solid bcc and fcc solutions were described using the Compound Energy Formalism (CEF). In addition, ab-initio calculations were performed to estimate the enthalpies of formation of the corresponding end-member for fcc and bcc, respectively. The phosphides Fe₃P, Fe₂P and FeP were treated as stoichiometric compounds. Higher order phosphides were not considered, since there is no reliable experimental information available in literature. The present model successfully reproduces most of the literature data within the experimental uncertainty in the Fe–C–P system without introducing a ternary parameter for the liquid phase. Compared with previous thermodynamic assessments, the agreement with recently published thermal analysis measurements of Fe–P and Fe–C–P alloys is significantly improved.     

Atomistic Modeling of pure Mg and Mg–Al systems

Interatomic potentials for pure Mg and the Mg–Al binary system have been developed based on the modified embedded-atom method (MEAM) potential formalism. The potentials can describe various fundamental physical properties of pure Mg (bulk, point defect, planar defect and thermal properties) and alloy behaviors (thermodynamic, structural and elastic properties) in reasonable agreement with experimental data or higher-level calculations. The applicability of the potential to atomistic investigations on the deformation behavior of pure Mg and the effect of alloying element Al on it is discussed.     

Thermodynamic calculations of the Au–Sc and Fe–Sc systems

Thermodynamic optimization of the Au–Sc and Fe–Sc systems was carried out by means of the CALPHAD (CALculation of PHAse Diagram) method on the basis of the available experimental data in literature. Redlich–Kister polynomials were used to describe the excess Gibbs energy of solution phases, and all the compounds are treated as stoichiometric ones. The Au–Sc system was described thermodynamically for the first time, and the Fe–Sc system was re-optimized by considering the new experimental data about enthalpies of mixing of the liquid phase. A set of self-consistent parameters was obtained for each of these two binary systems, respectively.     

Thermodynamic evaluation and optimization of the As–Co,As–Fe and As–Fe–S systems

A critical evaluation of all available phase diagram and thermodynamic data for the As–Co and As–Fe binary systems as well as the As–Fe–S ternary system has been performed and thermodynamic assessments over the whole composition ranges are presented using the CALPHAD method. To predict thermodynamic properties and phase equilibria for these systems, the Modified Quasichemical Model (MQM) for short range ordering was used for the liquid phases. The Compound Energy Formalism (CEF) was used for the solid solutions. Since Co and Fe are ferromagnetic, magnetic contributions were added to describe the Gibbs energy of cobalt and iron rich solid solutions. Important uncertainties remain for the liquidus of As-rich regions in the binary subsystems.     

Thermodynamic optimization of the binary PbO–CaO and ternary PbO–CaO–SiO2 systems

Liquidus phase equilibrium data from the recent study for the PbO–CaO and the PbO–CaO–SiO₂ systems (as a part of research program on the characterization of the multicomponent PbO–ZnO–FeO–Fe₂O₃-“Cu₂O”-CaO-SiO₂ system), combined with phase equilibrium and thermodynamic data from the literature, have been used to obtain a self-consistent set of parameters of the thermodynamic models for all phases: liquid, (Ca,Pb)₂SiO₄, (Ca,Pb)₃SiO₅, (Ca,Pb)SiO₃ (wollastonite and pseudowollastonite), Pb₃(Ca,Pb)₂Si₃O₁₁ (ganomalite) solutions, SiO₂ (quartz, tridymite, cristobalite), Ca₃Si₂O₇ (rankinite), CaO (lime), PbSiO₃ (alamosite), Pb₂SiO₄, Pb₁₁Si₃O₁₇, Pb₅SiO₇ lead silicates, PbO (massicot), Ca₂PbO₄, Pb₈CaSi₆O₂₁ (barysilite), PbCa₂Si₃O₉ (margarosanite) and Pb₃Ca₁₂Si₅O₂₅ compounds. Analysis of available data has shown the lack of data in the two immiscible liquids range over cristobalite, where several new experiments were done to support the model. The modified quasichemical model is used to describe the liquid slag phase. From these model parameters, the optimized ternary phase diagram is back calculated.     

Thermodynamic optimization of the binary CaO–ZnO and ternary CaO–ZnO–SiO2 systems

Liquidus phase equilibrium data of the present authors for the CaO–ZnO–SiO₂ system (as a part of research program on the characterization of the multicomponent PbO–ZnO–FeO–Fe₂O₃-“Cu₂O”-CaO-SiO₂ system), combined with phase equilibrium and thermodynamic data from the literature, have been used to obtain a self-consistent set of parameters of the thermodynamic models for all phases. The modified quasichemical model is used for the liquid slag phase; lime (Ca,Zn)O, zincite (Zn,Ca)O, α- and α′-dicalcium silicate (Ca,Zn)₂SiO₄ and tricalcium silicate (Ca,Zn)₃SiO₅ are described within Bragg-Williams formalism; tridymite, cristobalite SiO₂, wollastonite, pseudowollastonite CaSiO₃, rankinite Ca₃Si₂O₇, willemite Zn₂SiO₄, melilite (hardystonite) Ca₂ZnSi₂O₇ and Ca–Zn feldspar CaZnSi₃O₈ are treated as stoichiometric compounds. From these model parameters, the optimized ternary phase diagram is back calculated.     

Thermodynamic assessment of the Ca–Zn,Sr–Zn,Y–Zn and Ce–Zn systems

Published experimental thermodynamic and phase diagram data for the Ca–Zn, Sr–Zn, Y–Zn and Ce–Zn systems have been critically evaluated to provide assessed thermodynamic parameters for the different phases of the systems. The parameters allow all thermodynamic properties and phase boundaries for each system to be calculated within reasonable error limits. Because a strong compound-forming tendency and pronounced minimum in the enthalpy of mixing curve is observed for the liquid phase of all the systems, the Modified Quasichemical Model (MQM) in the pair approximation has been used throughout the assessment work to treat short-range ordering in the liquid.