Thermodynamic assessment of the Cu-In binary system

On the basis of thermodynamic properties and phase diagram data, the Cu-In binary system was thermodynamically assessed. The phases in this system were modeled using the Redlich-Kister expression for the Gibbs energies of the solution phases, adopting three-sublattice models for γ and η′, and assuming stoichiometric compounds for other intermetallic phases. Then a set of consistent parameters was obtained by the CALPHAD method, by which reasonable agreement can be realized between the thermodynamic properties for various phases and phase relations of this system.     

Thermodynamic evaluation of the Fe-Mn-Si system and the γ/ε martensitic transformation

The thermodynamic properties of the Fe-Mn-Si system are analyzed by means of thermodynamic models for the individual phases. Special attention is paid to the γ → ε martensitic transition. A complete set of parameters, from which arbitrary sections of the phase diagram as well as the M_s and A_s temperatures may be calculated, is given.     

Thermodynamic Assessment of the Mn-B System

The phase equilibrium and thermodynamic data on the Mn-B system are critically reviewed. Based on the experimental data, a thermodynamic modeling is performed on this system. A set of self-consistent thermodynamic parameters is obtained and the calculated results are in general agreement with the experimental data. A parameter ξ is introduced to compare the degree of flatness of the δMn/L liquidus with those in other metal-boron systems. It is found that the δMn/L liquidus is the flattest, which causes difficulties in its modeling. An effective approach to evaluate the thermodynamic parameters for o-Mn₂B_0.982 phase is developed. Such an approach is valid for evaluating thermodynamic parameters of the phases with limited phase diagram data.     

Calculating phase diagrams using <Emphasis Type="Italic">PANDAT</Emphasis> and panengine

Knowledge of phase equilibria or phase diagrams and thermodynamic properties is important in alloy design and materials-processing simulation. In principle, stable phase equilibrium is uniquely determined by the thermodynamic properties of the system, such as the Gibbs energy functions of the phases. PANDAT, a new computer software package for multicomponent phase-diagram calculation, was developed under the guidance of this principle. Author’s Note: Trial versions of PANDAT and PanEngine may be downloaded at www.computherm.com. Editor’s Note: A related article, “Our Experience in Teaching Thermodynamics at the University of Wisconsin, Madison,” by Y. Austin Chang and W.A. Oates, is available on-line only at www.tms.org/pubs/journals/JOM/0312/Chang/Chang-0312.html. For more information, contact S.-L. Chen, Compu-Therm LLC, 437 South Yellowstone Drive, Madison, Wisconsin 53719, USA; chen@chorus.net.     

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.     

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.     

Assessment of Co-Cr-Ni ternary system by CALPHAD technique

The Co-Cr-Ni ternary system was critically assessed using the CALPHAD technique.The solution phases including the liquid,γ(Co,Ni),εCo and αCr phases were described by a substitutional solution model.The σ phase was characterized by a three-sublattice model of (Co,Ni)8Cr4(Co,Cr,Ni)18 in order to reproduce its homogeneity range determined by experiments.A self-consistent set of thermodynamic parameters for each phase was derived.     

Thermodynamic evaluation and optimization of the Ca−Si system

All available phase equilibria and thermodynamic data for the Ca−Si system were collected and critically evaluated. In a first step, the thermodynamic properties of Ca(g) were obtained from experimental vapor pressure data over pure Ca. The new vapor pressure of calcium over pure solid and liquid was used as a new reference to model the thermodynamic properties of the intermediate stoichiometric Ca−Si compounds together with other thermodynamic and phase diagram data found in the literature (liquidus temperatures, heat capacities, pressures of Ca, and heats of reaction). Optimization was performed to obtain the parameters of one set of model equations for the different solid and liquid phases to best reproduce all the experimental data simultaneously. In this way, the data are rendered self-consistent, discrepancies among the data are identified, and extrapolations and interpolations can be performed. For the liquid phase, the Modified Quasichemical Model in the Pair Approximation for short-range ordering was used.     

Thermodynamic assessment of the Hg-Sn system

A thermodynamic assessment of the Hg-Sn system has been carried out using the CALPHAD method. The comprehensive assessment covers the extensive phase diagram data as well as the enthalpy, activity, and vapor pressure data. Two cases of intermetallic compounds in the Hg-Sn system are considered. Case 1 considers the intermetallic compounds β, γ, and HgSn₄ as having no solubility and can thus be treated as the stoichiometric phases β-HgSn₃₈, γ-HgSn₁₂, and HgSn₄. Case 2 uses a sublattice model to more accurately describe a solubility of the γ phase; it also considers the stoichiometric δ-HgSn₇ phase. The ε phase was considered to be metastable and neglected in the thermodynamic assessment. Thermodynamic parameters have been optimized using all the assessed experimental thermodynamic and phase equilibrium data. Both calculated phase diagrams of the Hg-Sn system (Cases 1 and 2) and the thermodynamic data are reasonable and satisfactory when compared with literature data. Future crucial experiments are suggested.     

Thermodynamic assessment of the Hg-Sn system

A thermodynamic assessment of the Hg-Sn system has been carried out using the CALPHAD method. The comprehensive assessment covers the extensive phase diagram data as well as the enthalpy, activity, and vapor pressure data. Two cases of intermetallic compounds in the Hg-Sn system are considered. Case 1 considers the intermetallic compounds β, γ, and HgSn₄ as having no solubility and can thus be treated as the stoichiometric phases β-HgSn₃₈, γ-HgSn₁₂, and HgSn₄. Case 2 uses a sublattice model to more accurately describe a solubility of the γ phase; it also considers the stoichiometric δ-HgSn₇ phase. The ε phase was considered to be metastable and neglected in the thermodynamic assessment. Thermodynamic parameters have been optimized using all the assessed experimental thermodynamic and phase equilibrium data. Both calculated phase diagrams of the Hg-Sn system (Cases 1 and 2) and the thermodynamic data are reasonable and satisfactory when compared with literature data. Future crucial experiments are suggested.     

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.     

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.     

Thermodynamic optimization of the Ni-Zn system

Optimization of thermodynamic and phase diagram data has been performed and consistent sets of coefficients for the calculation of the phase equilibria in the system Ni-Zn have been obtained using the program BINGSS. The δ phase has been modeled as a stoichiometric compound (NiZn₈). The binary liquid and the solid Ni-based solutions have been treated as disordered substitutional phases. The intermediate β, β ₁, and γ compounds have been modeled as phases with substitutional defects and vacancies on two sublattices. The calculated phase diagram and thermodynamic quantities are in excellent agreement with the experimental data.     

Thermodynamic optimization of the Ni-Zn system

Optimization of thermodynamic and phase diagram data has been performed and consistent sets of coefficients for the calculation of the phase equilibria in the system Ni-Zn have been obtained using the program BINGSS. The δ phase has been modeled as a stoichiometric compound (NiZn₈). The binary liquid and the solid Ni-based solutions have been treated as disordered substitutional phases. The intermediate β, β ₁, and γ compounds have been modeled as phases with substitutional defects and vacancies on two sublattices. The calculated phase diagram and thermodynamic quantities are in excellent agreement with the 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.