Phase equilibria in Fe-Cu-X (X: Co, Cr, Si, V) ternary systems

Phase equilibria on the Fe-Cu side in the Fe-Cu-X (X: Co, Cr, Si, V) system were experimentally determined over the temperature range of 1073–1273 K. Based on the present results and previous works, the thermodynamic assessments of the phase equilibria in the Fe-Cu-X system were evaluated using the Calculation of Phase Diagram (CALPHAD) method. The Gibbs energies (G) of the bcc, fcc, and liquid phases are described by the subregular solution model, and a set of thermodynamic parameters enable us to calculate various isothermal and vertical sections and the miscibility gaps of the solid and liquid phases.     

A thermodynamic analysis of the Al-Re system

Phase equilibria and thermodynamic data of the Al-Re system are critically reviewed. In addition to the three solution phases, liquid, fcc Al, and hcp Re, there exist six intermetallic compounds in this binary. The thermodynamic properties of the system are analyzed using thermodynamic models for the Gibbs energy of individual phases of the system. A regular solution model is used for the three substitutional solution phases, and the intermetallic phases are treated as stoichiometric compounds. The model parameters are optimized from a limited amount of experimental data. The calculated phase diagram and thermodynamic values are in accord with the available experimental values.     

Experimental Study and Thermodynamic Re-optimization of the FeO-Fe<Subscript>2</Subscript>O<Subscript>3</Subscript>-SiO<Subscript>2</Subscript> System

Phase equilibria and thermodynamic data in the FeO-Fe₂O₃-SiO₂ system were critically reviewed. New experiments were undertaken to resolve discrepancies found in previous data. The liquid oxide/slag phase was described using the modified quasichemical model. New optimized parameters of the thermodynamic models for the Gibbs energies of slag and other phases in the selected system were obtained. The new parameters reproduce all available phase equilibria and thermodynamic data within the experimental error limits from 298 K (25 °C) to above the liquidus temperatures at all compositions and oxygen partial pressures from metal saturation to 1 atm of O₂. This study was carried out as part of the development of a self-consistent thermodynamic database for the Al-Ca-Cu-Fe-Mg-Si-O-S multi-component system.     

Experimental investigation of phase equilibria and thermodynamic modeling of the CaO–Al2O3–CaS and the CaO–SiO2–CaS oxysulfide systems

Phase equilibria of the CaO–Al₂O₃–CaS and the CaO–SiO₂–CaS systems were experimentally investigated using equilibration and quenching techniques. Equilibrium phases were analyzed by means of electron probe X-ray microanalysis, X-ray diffraction analysis and differential thermal analysis. Solubility limits of all solid phases in these liquid oxysulfide phases were successfully constructed in the temperature range investigated in the present study (1500–1600 °C). In order to supplement understanding the phase equilibria, a thermodynamic modeling of these liquid oxysulfides was conducted by taking into account strong chemical short-range ordering (SRO) in the framework of the modified quasichemical model in the quadruplet approximation. As for the solubility of CaS in the liquid oxysulfides, the solubility increases with increase in CaO in the case of the CaO–Al₂O₃–CaS system, whereas it decreases with increase in CaO in the case of the CaO–SiO₂–CaS system. Such opposite behavior is explained by differences in the effect of the SRO in different liquid phases. It is shown that consideration for the SRO in the thermodynamic modeling is essential in order to properly describe the Gibbs energy of the liquid oxysulfide phase. Using the thermodynamic model and the database developed in the present study, liquidus projections of these oxysulfide systems are proposed for the first time.     

Mo-RE二元合金相图的热力学数据库

利用CALPHAD方法,选择和建立合理的热力学模型,并结合相平衡及热力学性质的相关实验信息,对Mo-RE (RE: Ce, Pr, Nd, Sm, Eu, Tb, Ho, Er, Tm, Yb, Lu)各二元系相图进行了热力学优化与计算。其中,液相和端际固溶体相的Gibbs自由能采用亚正规溶体模型描述,气相的Gibbs自由能采用理想气体模型描述。计算结果与实验数据取得了良好的一致性,最终得到了一组自洽的合理描述Mo-RE二元系各相自由能的热力学参数,建立了Mo-RE (RE: Ce, Pr, Nd, Sm, Eu, Tb, Ho, Er, Tm, Yb, Lu)二元合金相图的热力学数据库。该热力学数据库可以提供相平衡及热力学性质等多种信息,为外推计算三元以及更多组元体系的相平衡提供理论基础,并为相关体系的合金设计及制备提供重要的理论指导。     

Thermodynamic Database and the Phase Diagrams of the (U,Th, Pu)-X Binary Systems

A thermodynamic database for nuclear materials, including U-Th, U-Pu, Th-Pu, and (U, Th, Pu)-X (X = Al, Co, Cr, Cu, Fe, Ga, Mg, Mn, Mo, Nb, Ni, Si, Ta, W, Zr) binary system has been developed by the Calculation of Phase Diagrams (CALPHAD) method. Thermodynamic parameters describing Gibbs free energies of different phases have been evaluated by optimizing experimental data on phase equilibria and thermodynamic properties. The present thermodynamic database can provide much-needed information such as stable and metastable phase equilibria, phase fractions, and various thermodynamic quantities that is important to the design of nuclear materials. This database is also an essential starting point to construct thermodynamic databases for the multicomponent systems.     

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 Description of the Ti-Al-O System Based on Experimental Data

Phase equilibria of the TiO₂-Al₂O₃ system were investigated experimentally using XRD, SEM/EDX and DTA methods. Temperature stability limits of the aluminum titanate (Al₂TiO₅) were detected. The thermodynamic parameters of the liquid phase as well as solid solution phases were assessed by CALPHAD approach using obtained experimental results. The thermodynamic data for the Ti-Al, Al-O and Ti-O systems and available experimental data for the Ti-Al-O system were critically evaluated and optimized to develop database of the Ti-Al-O system.     

Thermodynamic assessments of the Cu–Th and Mo–Th systems

The thermodynamic assessments of the Cu–Th and Mo–Th binary systems were carried out by using Calculation of Phase Diagrams (CALPHAD) method on the basis of the experimental data including the thermodynamic properties and phase equilibria. The Gibbs free energies of the liquid, bcc, and fcc phases are described by the subregular solution model with the Redlich–Kister equation and those of the four intermetallic compounds Cu₆Th, Cu_3.6Th, Cu₂Th and CuTh₂ in the Cu–Th binary system were described by the sublattice model. A set of self-consistent thermodynamic parameters are obtained, and the calculated phase diagrams and thermodynamic properties are presented and compared with the experimental data from literatures. The calculated thermodynamic properties as well as phase diagrams are in good agreement with the experimental data.     

Thermodynamic modeling and phase equilibria calculations of the quaternary Al-Ga-In-Sb Sastem

Quasi sub-subregular solution model with additional ternary parameters, used by Sharma et al. to model the thermodynamic properties of the liquid phases in the ternary Al-Ga-Sb, Al-In-Sb, and GaIn-Sb systems, has been extended to predict the thermodynamic properties of the liquid phase in the quaternary Al-Ga-In-Sb system. The (AlGaln)Sb compound phase in the quaternary Al-Ga-In-Sb system is considered a quasi-regular solution of AlSb, GaSb, and InSb compounds. Phase equilibria in the quaternary Al-Ga-In-Sb system are then calculated and compared with the limited experimental data available in the literature. The ternary Al-Ga-In phase diagram, required for the quaternary calculations, has also been modeled and calculated.     

Thermodynamic modeling and phase equilibria calculations of the quaternary Al-Ga-In-Sb Sastem

Quasi sub-subregular solution model with additional ternary parameters, used by Sharma et al. to model the thermodynamic properties of the liquid phases in the ternary Al-Ga-Sb, Al-In-Sb, and GaIn-Sb systems, has been extended to predict the thermodynamic properties of the liquid phase in the quaternary Al-Ga-In-Sb system. The (AlGaln)Sb compound phase in the quaternary Al-Ga-In-Sb system is considered a quasi-regular solution of AlSb, GaSb, and InSb compounds. Phase equilibria in the quaternary Al-Ga-In-Sb system are then calculated and compared with the limited experimental data available in the literature. The ternary Al-Ga-In phase diagram, required for the quaternary calculations, has also been modeled and calculated.     

Thermodynamic Assessment of the Ti-Ir System

The thermodynamic assessment of the binary system Ti-Ir has been carried out by modeling the Gibbs energy of all individual phases using the calculation of phase diagrams approach based on the available literature data including the phase equilibria and thermodynamic properties. The Gibbs free energies of the liquid, bcc, fcc and hcp phases were described by the subregular solution model with Redlich-Kister formula, and those of the intermetallic compounds (Ti₃Ir, γTiIr, βTiIr and TiIr₃) in the Ti-Ir binary system were described by the two-sublattice model. The calculations are in good agreement with the literature data on both phase equilibria and thermodynamic properties in the Ti-Ir system.     

Phase equilibria in the Cu-Fe-Mo and Cu-Fe-Nb systems

Phase equilibria in the Cu-Fe portion of the Cu-Fe-Mo and the Cu-Fe-Nb systems, in the temperature ranges 1073 to 1573 K and 1373 to 1573 K, respectively, were determined by metallography and scanning electron microscopy-energy dispersive x-ray methods. Based on the present experimental data combined with the previous assessments of the component binary systems, thermodynamic calculations of phase equilibria were carried out adopting the subregular solution model to describe the Gibbs energies of the liquid, bcc, and fcc phases. The evaluated thermodynamic parameters lead to a better fit between calculations and experimental data in both the Cu-Fe-Mo and Cu-Fe-Nb systems.     

Phase equilibria in the Cu-Fe-Mo and Cu-Fe-Nb systems

Phase equilibria in the Cu-Fe portion of the Cu-Fe-Mo and the Cu-Fe-Nb systems, in the temperature ranges 1073 to 1573 K and 1373 to 1573 K, respectively, were determined by metallography and scanning electron microscopy-energy dispersive x-ray methods. Based on the present experimental data combined with the previous assessments of the component binary systems, thermodynamic calculations of phase equilibria were carried out adopting the subregular solution model to describe the Gibbs energies of the liquid, bcc, and fcc phases. The evaluated thermodynamic parameters lead to a better fit between calculations and experimental data in both the Cu-Fe-Mo and Cu-Fe-Nb systems.     

Thermodynamic assessment of the Cu−Pt system

A CALPHAD assessment of the Cu−Pt system has been carried out. Two and four sublattice models were applied to describe the Gibbs free energies of ordered phases where the contribution of SRO is taken explicity into account through the reciprocal parameters. The disordered fcc A1 and liquid phases were treated as substitutional solutions. A consistent set of parameters for the phases in the Cu−Pt system as obtained, and those parameters can satisfactorily reproduce the experimental phase equilibria and thermodynamic properties, such as enthalpies, activity of Cu, and long-range order parameters. This paper was presented at the International Symposium on User Aspects of Phase Diagrams. Materials Solutions Conference and Exposition, Columbus, Ohio, 18–20 October, 2004.     

Experimental determination and thermodynamic calculation of phase equilibria in the Fe−Mn−Al system

The phase equilibria among the face-centered cubic (fcc), body-centered cubic (bcc), and βMn phases at 800, 900, 1000, 1100, and 1200 °C were examined by electron probe microanalysis (EPMA), and the A2/B2 and B2/D0₃ ordering temperatures were also determined using the diffusion couple method and differential scanning calorimetry (DSC). The critical temperatures for the A2/B2 and B2/D0₃ ordering were found to increase with increasing Mn content. Thermodynamic assessment of the Fe−Mn−Al system was also undertaken with use of experimental data for the phase equilibria and order-disorder transition temperatures using the CALPHAD (Calculation of Phase Diagrams) method. The Gibbs energies of the liquid, αMn, βMn, fcc, and ε phases were described by the subregular solution model and that of the bcc phase was represented by the two-sublattice model. The thermodynamic parameters for describing the phase equilibria and the ordering of the bcc phase were optimized with good agreement between the calculated and experimental results. This paper was presented at the International Symposium on User Aspects of Phase Diagrams, Materials Solutions Conference and Exposition, Columbus, Ohio, 18–20 October, 2004.     

Thermodynamic and Experimental Study of the Mg-Sn-Ag-In Quaternary System

Phase equilibria in the Mg-rich region of the Mg-Sn-Ag ternary system were determined by quenching experiments, differential scanning calorimetry, electron probe micro-analysis, and X-ray diffraction techniques. No ternary compounds were found in the studied isothermal sections. A critical evaluation of the available experimental data and a thermodynamic optimization of the Mg-Sn-Ag-In quaternary system were carried out using the calculation of phase diagrams method. The modified quasichemical model in the pair approximation was used for the liquid solution, which exhibits a high degree of short-range order. The solid phases were modeled with the compound energy formalism. All available and reliable experimental data were reproduced within experimental error limits. A self-consistent thermodynamic database was constructed for the Mg-Sn-Ag-In quaternary system, which can be used as a guide for Mg-based alloys development.