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 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.     

Thermodynamic study of phase equilibria in the Ni-Si-B system

A thermodynamic analysis of the phase equilibria in the Ni-Si-B ternary system was conducted. A regular solution approximation based on a sublattice model was adopted to describe the Gibbs energies for the individual phases in the binary and ternary systems. A set of thermodynamic parameters for the individual phases was evaluated from literature data on phase boundaries and thermochemical properties. The optimized parameters reproduced the experimental data, for the most part, satisfactorily. However, in the calculated isothemal section at 850 °C, phase equilibria between the fcc phase and Ni₆Si₂B or Ni₃Si(β ₁) and Ni₆Si₂B were found instead of the experimentally observed equilibria between Ni₃Si(β ₁) and Ni₃B or Ni₅Si₂(γ) and Ni₃B. Further, in the primary crystal surface for the fcc phase, the calculated liquidus temperatures were higher than the reported values by approximately 80 °C. Therefore, it is considered that the fcc phase evaluated in the Ni-Si system by Lindhólm and Sundman is too stable.     

Thermodynamic study of phase equilibria in the Ni-Si-B system

A thermodynamic analysis of the phase equilibria in the Ni-Si-B ternary system was conducted. A regular solution approximation based on a sublattice model was adopted to describe the Gibbs energies for the individual phases in the binary and ternary systems. A set of thermodynamic parameters for the individual phases was evaluated from literature data on phase boundaries and thermochemical properties. The optimized parameters reproduced the experimental data, for the most part, satisfactorily. However, in the calculated isothemal section at 850 °C, phase equilibria between the fcc phase and Ni₆Si₂B or Ni₃Si(β ₁) and Ni₆Si₂B were found instead of the experimentally observed equilibria between Ni₃Si(β ₁) and Ni₃B or Ni₅Si₂(γ) and Ni₃B. Further, in the primary crystal surface for the fcc phase, the calculated liquidus temperatures were higher than the reported values by approximately 80 °C. Therefore, it is considered that the fcc phase evaluated in the Ni-Si system by Lindhólm and Sundman is too stable.     

Thermodynamic calculation of the O-Ti system

The O-Ti binary system has been assessed to produce Gibbs energy parameters for the condensed phases and were evaluated as representations of thermodynamic models. The liquid phase was described in terms of an association model with one associate, the bcc, A 2; cph, A 3 and fcc, A 1 phases were described as interstitial solid solutions, and the O₂Ti, O₃Ti₅, O₃Ti₂, and OTi oxides were considered to be stoichiometric compounds. The thermodynamic parameters were optimized taking into account experimental phase diagram and thermodynamic values from the literature. The phase diagram and the thermodynamic properties were calculated and compared with experimental data.     

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 study of phase equilibria in the Pb-Sn-Sb system

A thermodynamic analysis of the phase equilibria in the Pb-Sn-Sb ternary system was conducted. A regular solution approximation based on a two-sublattice model was adopted to describe the Gibbs energy of formation of the individual phases in the binary and ternary systems. In the case of some component binary systems, the effect of pressure also was considered. Experimental data obtained by differential thermal analysis (DTA) and electron probe microanalysis (EPMA) in the present study, along with literature data on phase boundaries and thermochemical properties, form the basis for the evaluated thermodynamic parameters used in the calculation. Calculated and experimental phase boundaries agree fairly well. Present address: Kawasaki Steel Corporation, Chiba 260, Japan.     

Critical thermodynamic evaluation and optimization of the MgO-Al2O3, CaO-MgO-Al2O3, and MgO-Al2O3-SiO2 Systems

A complete literature review, critical evaluation, and thermodynamic modeling of the phase diagrams and thermodynamic properties of all oxide phases in the MgO-Al₂O₃, CaO-MgO-Al₂O₃, and MgO-Al₂O₃-SiO₂ systems at 1 bar total pressure are presented. Optimized model equations for the thermodynamic properties of all phases are obtained that reproduce all available thermodynamic and phase equilibrium data within experimental error limits from 25 °C to above the liquidus temperatures at all compositions. The database of the model parameters can be used along with software for Gibbs energy minimization to calculate all thermodynamic properties and any type of phase diagram section. The modified quasichemical model was used for the liquid slag phase and sublattice models, based upon the compound energy formalism, were used for the spinel, pyroxene, and monoxide solid solutions. The use of physically reasonable models means that the models can be used to predict thermodynamic properties and phase equilibria in composition and temperature regions where data are not available.     

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.     

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.     

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。     

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 optimization of the boron-cobalt-iron system

A thermodynamic optimization of the boron-cobalt-iron ternary system is performed based on thermodynamic models of the three constitutional binary systems and the experimental data on phase diagrams and thermodynamic properties of the ternary system. The liquid, fcc_A1, bcc_A2 and hcp_A3 solution phases are described by the substitutional solution model. The three intermediate line compounds, (Co,Fe)B, (Co,Fe)₂B and (Co,Fe)₃B, are described by the two sublattice model. A set of thermodynamic parameters are obtained. The calculated phase diagram and thermodynamic properties are in reasonable agreement with most of the experimental data.     

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.     

Phase equilibria of the cu-in system II: Thermodynamic assessment and calculation of phase diagram

The phases in the Cu-In binary were modelled thermodynamically using the Redlich-Kister expression for the Gibbs energies of the solution phases, the Wagner-Schottky model for those of the η (η)’)-Cu₂ln phase (taking η and η)’ to be a single phase), and assuming line compound behavior for the other intermetallic phases. The model parameters were obtained using primarily the thermodynamic data, as well as the phase equilibrium data. The thermodynamic values for the various phases calculated from the models are in reasonable agreement with the experimentally determined thermodynamic data that are available in the literature. The entropies of melting for the intermetallic phases obtained from the models are in accord with the values calculated from the empirical formulas suggested by Kubaschewski. The calculated phase diagram is also in reasonable agreement with the experimentally determined diagram, with the calculated temperatures for all the invariant equilibria within 1°C of the experimental values. The discrepancies between the calculated and experimental phase boundaries at the invariant temperatures are less than 1 at.% except those involving βCu₄Inn and γCu₇ln₃. These two phases were taken to be line compounds in the present study, although experimentally they exist over appreciable ranges of homogeneity. Current address: Dept. of Chemical Engineering, National Tsing Hua University, Taiwan.     

Experimental Investigation and Thermodynamic Description of the Cu-Zr System

The Cu-Zr binary system is re-investigated via experiment and thermodynamic modeling. Four alloys were prepared by arc melting in order to check the controversial phase equilibria reported in the literature. Both as-cast and annealed alloys were examined by optical microscopy, x-ray diffraction and electron probe microanalysis, and the phase transformation temperatures were measured by differential scanning calorimetry. The intermetallic compounds, Cu₂₄Zr₁₃, Cu₂Zr and Cu₅Zr₈, were demonstrated to be not the stable phases. Based on the literature information and present experimental data, the Cu-Zr system was critically evaluated by means of CALculation of PHAse Diagram approach. A set of self-consistent thermodynamic parameters was obtained, and the calculated phase diagram and thermodynamic properties are in a satisfactory agreement with the experimental data.     

Thermodynamic Treatment of Undercooled Cu-Mg Liquid and the Limits for Partitionless Crystallization

The thermodynamic properties of the binary Cu-Mg system are examined with a focus on equilibria involving the liquid phase, which is described with a four-species association model, incorporating a two-state treatment for the pure component liquids below their respective melting temperatures. The terminal and intermediate crystalline phases are described as substitutional solid solutions, employing two sublattices for the latter. Model parameters are fitted using available experimental data, and the resulting phase diagram is reported over the full range of compositions in the binary system. We also report the associated T ₀ curves, indicating the limits of partitionless crystallization and compare these with reports of amorphous solid formation during rapid solidification processing.