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.     

Cu-Ni-Sn三元系相平衡的热力学计算

基于Cu-Ni-Sn三元系的相平衡和热力学的实验信息,采用亚正规溶体模型描述液相和fcc相的Gibbs自由能,为了预测该体系中bcc相的A2-B2有序-无序转变,bcc相的Gibbs自由能采用双亚点阵模型进行描述.利用CALPHAD(相图计算)方法评估了Cu-Ni-Sn三元系各相的热力学参数,计算的富Cu侧相图和热力学性质与实验数据比较一致.并对该三元系中bcc相的A2-B2有序-无序转变及fcc相的溶解度间隙进行了计算.这些计算结果对利用析出强化以及Spinodal分解开发高强度和高导电性的新型Cu基合金的组织设计具有一定的指导意义.     

Thermodynamic modeling of the Ce–Zn and Pr–Zn systems

In order to develop the thermodynamic database of phase equilibria in the Mg–Zn–Re (Re: rare earth element) base alloys, the thermodynamic assessments of the Ce–Zn and Pr–Zn systems were carried out by using the calculation of phase diagrams (CALPHAD) method on the basis of the experimental data including thermodynamic properties and phase equilibria. Based on the available experimental data, Gibbs free energies of the solution phases (liquid, bcc, fcc, hcp and dhcp) were modeled by the subregular solution model with the Redlich–Kister formula, and those of the intermetallic compounds were described by the sublattice model. A consistent set of thermodynamic parameters has been derived for describing the Gibbs free energies of each solution phase and intermetallic compound in the Ce–Zn and Pr–Zn binary systems. An agreement between the present calculated results and experimental data is obtained.     

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.     

高性能铜合金热力学数据库的开发及其在材料设计中的应用

利用相图计算(CALPHAD)方法,采用亚规则溶体模型描述溶体相的吉布斯自由能,采用亚点阵模型描述金属间化合物和有序相的吉布斯自由能,并结合相平衡和热力学性质的实验数据,优化与计算Cu-X二元系以及Cu-Fe、Cu-Ni、Cu-Cr、Cu-Co、Cu-Mo和Cu-W基各三元系的相图,获得自洽性良好的热力学参数,并建立铜合金热力学数据库。该数据库可以提供稳定和亚稳的相图计算、相分数计算、液相面计算、热力学性质的计算等多种信息,为外推计算铜基多元合金系的相平衡提供理论基础,并为高性能铜合金材料的设计及制备提供重要的理论指导。     

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.     

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.     

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.     

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。     

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.     

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 Database for Phase Diagrams of Mn-RE Binary Alloy Systems

Thermodynamic assessment of Mn-RE (RE: Pr, Nd, Sm, Eu, Tb, Dy, Ho, Er, Tm, Yb, Lu) binary systems has been carried out by means of the calculation of phase diagrams method on the basis of experimental data including phase equilibria and thermodynamic properties. The Gibbs free energies of liquid phase and solid solution phases in the Mn-RE systems were all described by the subregular solution model with the Redlich–Kister formulation, whereas those of intermetallic compounds were described by the sublattice model. Sets of thermodynamic functions with self-consistent parameters leading to satisfactory agreement between calculated results and experimental data were eventually obtained. A primary thermodynamic database for the phase diagrams of the Mn-RE (RE: Pr, Nd, Sm, Eu, Tb, Dy, Ho, Er, Tm, Yb, Lu) binary systems was developed from these essential thermodynamic parameters. This database can be used not only to calculate the phase equilibria and thermodynamic properties of binary Mn-RE systems but also to extrapolate to higher-order systems, which can provide theoretical guidance for design and development of high-performance Mn-RE alloy materials.     

Thermodynamic assessment of the Mo–Re binary system

The existing Mo–Re phase diagrams are reviewed and a thermodynamic calculation of the Mo–Re binary system is undertaken. The Gibbs energies are estimated for liquid, bcc (Mo), hcp (Re), σ and χ phases. The liquid, bcc (Mo) and hcp (Re) phases are described by a regular solution model, whereas the σ and χ phases are described respectively by three-sublattice models. For the σ phase, two thermodynamic models are used for calculations and the results are compared. The models take into account the crystallographic structure and similarity between the σ and χ phases. The calculated results remove the ambiguity of the existing phase diagram data and are compared with the experimental data in the literature.     

Thermodynamic Assessments of the Bi-Tb and Bi-Y Systems

By using the calculation of phase diagrams (CALPHAD) method, the thermodynamic assessments of the Bi-Tb and Bi-Y systems were carried out based on the available experimental data including thermodynamic properties and phase equilibria. Gibbs free energies of the liquid, hcp, bcc, and rhombohedral phases in the Bi-Tb and Bi-Y systems were modeled by the substitutional solution model, and the intermetallic compounds (BiTb, Bi₃Tb₄, αBi₃Tb₅, βBi₃Tb₅, BiY, and Bi₃Y₅ phases) in these two binary systems were described by the sublattice model. An agreement between the present calculated results and experimental data was obtained.     

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.     

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.     

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 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.