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.     

A thermodynamic assessment of the Al-Cu-Mg ternary system

A thermodynamic assessment of the Al-Cu-Mg ternary system is presented. The Gibbs energies for the liquid and solid solution phases were modeled using the Redlich-Kister polynomial and the Wagner-Schottky model represented by the compound-energy formalism. The model parameters were obtained after fitting to previously critically assessed experimental phase diagram and thermodynamic data available in the literature. The thermodynamic functions and phase diagram calculated using the model parameters describe quite well the known experimental information. The complete set of Gibbs energies for all phases appearing in this system enables the calculation of thermodynamic values as a function of composition and temperature even for those ranges where no experimental information is available.     

Thermodynamic assessments of the phase diagrams of the hafnium-vanadium and vanadium-zirconium systems

Thermodynamic assessments have been made for the hafnium-vanadium (Hf-V) and vanadium-zirconium (V-Zr) systems using the Calphad-Thermocalc approach. The Gibbs energies of the liquid, body-centered cubic, and close-packed hexagonal phases were described by a substitution solution model with a Redlich-Kister formalism to express the excess Gibbs energy. The C15-Laves phase was treated first as stoichiometric and then with a composition range. A consistent set of optimized thermodynamic parameters was obtained, and calculated phase equilibria were compared with the experimental data. The enthalpy of formation of the C15-Laves phase was calculated equal to approximately −3 and −5 kJ/mol, respectively, in the Hf-V and V-Zr systems, which is in good agreement with predicted values.     

Thermodynamic assessment of ZnO-SiO2 system

ZnO-containing slags are common in pyrometallurgical processing of the base metals and steel. This caused the interest to the thermodynamics of the ZnO-SiO₂ system. A complete literature survey, critical evaluation of the available experimental data and a thermodynamic optimization of the phase equilibria and thermodynamic properties of the system ZnO-SiO₂ at 1.013×10⁵ Pa are presented. The molten oxide was described as an associate solution. The properties of liquid were reassessed and enthalpy term of the Gibbs energy of solid Zn₂SiO₄ was re-fitted to be compatible with the new data in the willemite primary phase field. The thermodynamic data set agrees well with the recent experimental observations. It can be used for predicting, e.g., the thermodynamic properties and the domains of the phase diagram, like critical point of the liquid miscibility gap, with a better accuracy than using the previous assessments. A set of optimized model parameters were obtained, reproducing the reliable thermodynamic and phase equilibrium data within their experimental errors from 298 K to liquidus temperatures, over the entire composition range. The created database can be used in a Gibbs energy minimization software to calculate the thermodynamic properties and the phase diagram sections of interest.     

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.     

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.     

Solid-State Phase Equilibria of the Cu-S System: Thermodynamic Modeling

All phase equilibria and thermodynamic data available in the literature on the copper sulfides high- and low-temperature chalcocite, djurleite and anilite have been critically analyzed for optimization of the solid-state phase diagram of the Cu-S system at 1 bar total pressure. A two-sublattice approach derived from a recently developed Gibbs energy model for digenite enables the consideration of the solid solution nature of both modifications of chalcocite and for the first time of djurleite. Anilite is considered as stoichiometric compound. The sulfur solubility of metallic copper is described by a substitutional approach. The obtained Gibbs energy functions for high- and low-temperature chalcocite, djurleite, anilite and copper alloy phase allow computations and predictions of phase equilibria and thermodynamic properties in good accordance with experimental data of the Cu-S solid-state system.     

Thermodynamic assessment of the Mo-Zr system

The Mo-Zr system was critically assessed using the calculation of phase diagrams (CALPHAD) technique. The solution phases (liquid, bcc, and cph) were modeled with the Redlich-Kister expression for the excess Gibbs energy. The intermetallic Mo₂Zr Laves phase, which has a measurable homogeneity range, was treated by a two-sublattice model with Mo and Zr on both sublattices. A set of self-consistent thermodynamic parameters for the Mo-Zr system was obtained. With the optimized functions for the Gibbs energy of the individual phases, most of the experimental information can be well reproduced.     

Thermodynamic optimization of Mg-Nd system

Based on the reported experimental data,the phase diagram of Mg-Nd binary system was optimized using the CALPHADapproach.Gibbs energies of the disordered BCC_A2 and ordered BCC_B2 phases were modeled with a single expression based on a2-sublattice model.Liquid and terminal solutions,such as dHCP and HCP,were modeled as substitutional solutions.Intermediatephases Mg2Nd,Mg3Nd and Mg41Nd5 were treated as stoichiometric compounds.The optimization was carried out in theThermo-Calc package.A set of thermodynamic parameters is obtained.Calculated phase diagram,enthalpies of formation and Gibbsenergies of formation are in reasonable agreement with the experimental data.     

Assessment of the Te-Tl (tellurium-thallium) system

The optimized thermodynamic data for the Te- TI binary system have been obtained by the computer operated least squares method from measured data. The Gibbs energy of the liquid phase was modeled as a two- sublattice model for ionic melt after Hillert.³¹ The intermediate compounds, Te₃Tl{2}and TeTl, were treated as stoichiometric phases, and the nonstoichiometric γ phase was expressed as a sublattice model. A strong tendency for chemical short- range order in the liquid state at the composition close to TeTh was confirmed by calculated results, but the existence of the TeTh phase was not justified. The experimental thermodynamic and phase diagram data were closely reproduced by the optimized thermodynamic data. Parameters describing the Gibbs energies of all the phases in this calculation and the calculated phase diagram and thermodynamic functions are presented and compared with experimental information.     

Thermodynamic assessment of the Mo-Zr system

The Mo-Zr system was critically assessed using the calculation of phase diagrams (CALPHAD) technique. The solution phases (liquid, bcc, and cph) were modeled with the Redlich-Kister expression for the excess Gibbs energy. The intermetallic Mo₂Zr Laves phase, which has a measurable homogeneity range, was treated by a two-sublattice model with Mo and Zr on both sublattices. A set of self-consistent thermodynamic parameters for the Mo-Zr system was obtained. With the optimized functions for the Gibbs energy of the individual phases, most of the experimental information can be well reproduced.     

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.     

Assessment of the Te-Tl (tellurium-thallium) system

The optimized thermodynamic data for the Te- TI binary system have been obtained by the computer operated least squares method from measured data. The Gibbs energy of the liquid phase was modeled as a two- sublattice model for ionic melt after Hillert.³¹ The intermediate compounds, Te₃Tl{2}and TeTl, were treated as stoichiometric phases, and the nonstoichiometric γ phase was expressed as a sublattice model. A strong tendency for chemical short- range order in the liquid state at the composition close to TeTh was confirmed by calculated results, but the existence of the TeTh phase was not justified. The experimental thermodynamic and phase diagram data were closely reproduced by the optimized thermodynamic data. Parameters describing the Gibbs energies of all the phases in this calculation and the calculated phase diagram and thermodynamic functions are presented and compared with experimental information.     

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.