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.     

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。     

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 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.     

Experimental Investigation and Thermodynamic Calculation of Phase Equilibria in the Mg-Pb-Sn Ternary System

The phase equilibria of the Mg-Pb-Sn ternary system were investigated using a combined method of electron probe microanalyzer and x-ray diffraction. Three isothermal sections of the Mg-Pb-Sn ternary system at 200, 300 and 400 °C were experimentally established. The phase equilibria of Mg-Pb-Sn ternary system were thermodynamically assessed by using CALPHAD (Calculation of Phase Diagrams) method on the basis of the presently determined experimental data. A consistent set of thermodynamic parameters has been derived for describing the Gibbs free energies of each solution phase and intermetallic compound in the Mg-Pb-Sn ternary system. The calculated phase diagrams and thermodynamic properties in the Mg-Pb-Sn ternary system are in good agreement with experimental data.     

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.     

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 assessment of the Ga–Sc and Ga–Tb systems

The Ga–Sc and Ga–Tb binary systems have been assessed with CALPHAD method. Liquid is treated as substitutional solution phase, of which the excess Gibbs energies are modeled by Redlich–Kister polynomial function. The binary intermetallic compounds are treated as stoichiometric phases. Thermodynamic parameters of various phases have been optimized and the calculated results are in reasonable agreement with experimental data.     

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.     

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 assessment of the Cu–Dy binary system

The Cu–Dy binary system has been thermodynamically assessed with CALPHAD approach. The solution phases including liquid, Bcc, Fcc and Hcp were treated as substitutional solution phases, of which the excess Gibbs energies were formulated with Redlich–Kister polynomial functions. The binary intermetallic compounds were treated as stoichiometric phases. A set of self-consistent thermodynamic parameters for describing various phases in this system has been obtained, which can well reproduce the corresponding experimental data.     

Experimental determination and thermodynamic assessment of the phase diagram in the Co–Zr system

The phase diagram in the Co–Zr system was determined using the electron probe microanalyzer (EPMA), differential thermal analysis (DTA) and X-ray diffraction (XRD) technique. The experimental results indicate that (1) the solubility region of the Co₂Zr phase is from 25 to 34 at.% Zr; (2) the CoZr₃ phase exists and the temperature of the peritectoid reaction (CoZr₂ + (βZr) ↔ CoZr₃) is about 981 °C; (3) the solubilities of Zr in the (αCo) phase and Co in the (βZr) phase are about 0.15 and 2.5 at.%, respectively. A thermodynamic assessment of the Co–Zr binary system was carried out by the CALPHAD (calculation of phase diagrams) method. The Gibbs free energies of the solution phases (liquid, fcc, bcc and hcp) were described by the subregular solution model, and those of the intermetallic compounds (Co₁₁Zr₂, Co₂₃Zr₆, Co₂Zr, CoZr, CoZr₂ and CoZr₃) were described by the sublattice model. A proper set of the thermodynamic parameters has been derived for describing the Gibbs free energies of each phase in the Co–Zr system. An agreement between the calculated results and experimental data is obtained.     

Thermodynamic Assessments of the Au-Tb and Au-Lu Systems

The thermodynamic assessments of the Au-Tb and Au-Lu binary systems were carried out by means of the CALPHAD method based on the experimental data including the thermodynamic properties and phase equilibria. The Gibbs free energies of the liquid, bcc, fcc and hcp phases were described by the substitutional solution model, while all of the intermetallic compounds (Au₆Tb, Au₅₁Tb₁₄, Au₃Tb, Au₂Tb, Au₁₀Tb₇, Au₄Tb₃, αAuTb, βAuTb, AuTb₂, Au₄Lu, Au₃Lu, Au₂Lu, AuLu and AuLu₂ phases) in these two binary systems were treated as the sublattice model. Consequently, a set of self-consistent thermodynamic parameters of each phase in the Au-Tb and Au-Lu binary systems has been obtained, and the calculated results are in good agreement with the available experimental data.     

Experimental investigation and thermodynamic calculation of the phase equilibria in the Co–Mo–W system

The isothermal sections in the Co–Mo–W ternary system at 600 °C, 800 °C, 1000 °C, 1100 °C, 1200 °C and 1300 °C have been determined using the Electron probe micro-analyzer (EPMA) and X-ray diffraction (XRD) techniques. A thermodynamic assessment of the Co–Mo–W ternary system was carried out by the CALPHAD (Calculation of Phase Diagrams) method. The Gibbs free energies of the liquid and solution phases were described by the subregular solution models, and those of 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 Co–Mo–W ternary system. The calculated phase diagrams and thermodynamic properties in the Co–Mo–W ternary system are in good agreement with experimental data.     

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.