Thermodynamic assessment of the Be–Pu and Cd–Pu systems

Thermodynamic assessment of Be–Pu and Cd–Pu systems has been developed with the application of the CALPHAD (Calculation of Phase Diagrams) method, which is established on experimental data including thermodynamic properties and phase equilibria. The Gibbs free energies of the liquid, fcc, hcp, αPu, βPu, γPu, δPu, δ′Pu, and εPu phases were described by the subregular solution model with the Redlich–Kister equation, and those of the intermetallic compounds in the Be–Pu and Cd–Pu binary systems were described by the sublattice model. A set of thermodynamic parameters was derived for describing the Gibbs free energies of solution phases and intermetallic compounds in the Be–Pu and Cd–Pu binary systems. Calculated phase equilibria and thermodynamic parameters are in good agreement with experimental data.     

Phase diagrams and thermochemical modeling of salt lake brine systems. III. Li2SO4+H2O,Na2SO4+H2O,K2SO4+H2O,MgSO4+H2O and CaSO4+H2O systems

This paper is part of a series of studies on the development of a multi-temperature thermodynamically consistent model for salt lake brine systems. Under the comprehensive thermodynamic framework proposed in our previous study, the thermodynamic and phase equilibria properties of the sulfate binary systems (i.e., Li₂SO₄ + H₂O, Na₂SO₄ + H₂O, K₂SO₄ + H₂O, MgSO₄ + H₂O and CaSO₄ + H₂O) were simulated using the Pitzer-Simonson-Clegg (PSC) model. Various type of thermodynamic properties (i.e., water activity, osmotic coefficient, mean ionic activity coefficient, enthalpy of dilution and solution, relative apparent molar enthalpy, heat capacity of aqueous phase and solid phases) were collected and fitted to the model equations. The thermodynamic properties of these systems can be well reproduced or predicted using the obtained model parameters. Comparisons with the experimental or model values in literature indicate that the model parameters determined in this study can describe all of the thermodynamic and phase equilibria properties of these binary sulfate systems from infinite dilution to saturation and freezing point temperature to approx. 500 K.     

Coupled experimental study and thermodynamic modeling of the MnO-Mn2O3-Ti2O3-TiO2 system

A coupled experimental study and thermodynamic modeling of the MnO-Mn₂O₃-Ti₂O₃-TiO₂ system at 1 bar total pressure is presented. Classical equilibration and quenching experiments followed by the phase analysis using electron probe microanalysis (EPMA) and X-ray diffraction (XRD) were employed to obtain equilibrium compositions of the liquid and solid solutions in air. The molten oxide phase was described by using the Modified Quasichemical Model which considers short-range ordering, and the Gibbs energies of the solid solutions (pseudobrookite, ilmenite and spinel) were described using the Compound Energy Formalism based on their crystal structures. A set of optimized model parameters of all phases was obtained, which reproduces all available and reliable thermodynamic data and phase diagrams within experimental error limits from 298 K (25 °C) to above the liquidus temperatures over the entire range of composition under oxygen partial pressures from metallic saturation to 1 bar. The complex phase relationships in the system have been elucidated and discrepancies among the experimental data have been resolved. The database of the model parameters can be accessed by FactSage software with the Gibbs energy minimization to calculate any phase diagrams and thermodynamic properties of the MnO-Mn₂O₃-Ti₂O₃-TiO₂ system.     

Thermodynamic re-assessment of the Fe-Dy and Fe-Tb binary systems

In this work, based on the critical evaluation of previous optimizations and available experimental data in the published literature, the Fe-Dy and Fe-Tb binary systems were re-assessed thermodynamically using the CALPHAD method. The solution phases including liquid, fcc-Fe, bcc-Fe, bcc-Dy, bcc-Tb, hcp-Dy and hcp-Tb, were described by the substitutional solution model and their excess Gibbs energies were expressed with the Redlich-Kister polynomial. Due to their narrow homogeneity ranges, the intermetallic compounds, Fe₁₇Dy₂, Fe₂₃Dy₆, Fe₃Dy, Fe₂Dy, Fe₁₇Tb₂, Fe₂₃Tb₆, Fe₃Tb and Fe₂Tb, were modeled as stoichiometric compounds. Self-consistent thermodynamic parameters to describe the Gibbs energies of various phases in the Fe-Dy and Fe-Tb binary systems were obtained finally. The calculated results are in good agreement with the reported phase equilibria and thermodynamic properties.     

Thermodynamic assessment and database for the Cu–Fe–O–S system

The previously obtained thermodynamic databases for the Cu–Fe–S, Cu–Fe–O, Fe–O–S and Cu–O–S ternary systems have been combined and used to predict thermodynamic equilibria in the quaternary Cu–Fe–O–S system. The available experimental data were compared with model predictions. Minor modifications of model parameters were required to better describe the experimental points in the quaternary system; the effect of these changes was verified in the ternary subsystems. The procedure was developed to calculate the isothermal sections of the phase diagram of the quaternary system inside the tetrahedron. The liquid phase over the whole composition range from metallic liquid to sulfide melt to oxide melt has been described by a single model developed within the framework of the quasichemical formalism. The obtained self-consistent set of model parameters can be used as a basis for the development of a thermodynamic database for simulation of copper smelting and converting.     

Thermodynamic description of the Al-Li-Zn system

The Al-Li-Zn system was critically assessed using the CALPHAD technique. The solution phases (liquid, bcc, fcc and hcp) were described by the substitutional solution model. The compounds Al₂Li₃ and Al₄Li₉ in the Al-Li system had homogeneity ranges of Zn and were treated as (Al,Zn)₂Li₃ and (Al,Zn)₄Li₉ in the Al-Li-Zn system, respectively. The compounds αLi₂Zn₃, βLi₂Zn₃, αLi₂Zn₅, βLi₂Zn₅ and αLiZn₄ in the Li-Zn system had no solubility of the third component Al in the Al-Li-Zn system. A two-sublattice model (Al,Li,Zn)_0.2(Al,Li,Zn)_0.8 was applied to describe the compound βLiZn₄ in the Al-Li-Zn system in order to cope with the order-disorder transition between hexagonal close-packed solution (hcp-A3) and βLiZn₄ with the Mg-type structure. The ternary compound τ₂ with a NaTl-type structure (B32) had the same structure with the compounds AlLi in the binary Al-Li system and LiZn in the binary Li-Zn system. In the present work, the three compounds AlLi, LiZn and τ₂ were treated as one phase by a two-sublattice model (Al,Li,Zn)_0.5(Al,Li,Zn)_0.5 in order to cope with the order-disorder transition between B32(AlLi, LiZn and τ₂) and body-centered cubic solid solution (bcc-A2). The ternary intermetallic compounds τ₁ and τ₃ in the Al-Li-Zn system were treated as the formula Li(Al,Zn)₂ and (AlLi,Zn)Zn₃, respectively. A set of self-consistent thermodynamic parameters describing the Gibbs energy of each individual phase as a function of composition and temperature in the Al-Li-Zn system was obtained.     

Thermodynamic modeling of the Cu-Fe-Cr and Cu-Fe-Mn systems

All the thermodynamic and phase diagram information available in the literature on the Cu-Cr system, Cu-Fe-Cr system, and Cu-Fe-Mn system were critically evaluated and used in the thermodynamic optimization to obtain a set of consistent thermodynamic model parameters for the systems. The liquid solutions for the Cu-Cr, Cu-Mn, Fe-Cr, Cu-Fe-Cr, and Cu-Fe-Mn systems were described using the Modified Quasichemical Model (MQM) with pair approximation. The solid solution phases were modeled using the Bragg-Williams random mixing model. Accurate reproduction of all the reliable phase diagram and thermodynamic property data indicates the high reliability of the present thermodynamic optimizations.     

Thermodynamic assessment of the B–Ce and B–Pr systems

By using the Calculation of Phase Diagrams (CALPHAD) technique, the thermodynamic assessments of the B–Re (Re: Ce, Pr) binary system were carried out based on the experimental data including thermodynamic properties and phase equilibria. Gibbs free energies of the solution phases (liquid, fcc, bcc, dhcp) were modeled by the subregular solution model with the Redlich–Kister equation, and those of the intermediate compounds (B₄Ce, B₆Ce, B₅Pr₂, B₄Pr, B₆Pr) were described by the two-sublattice model. A consistent set of thermodynamic parameters leading to reasonable agreement between the present calculated results and experimental data was obtained.     

Thermodynamic calculations of the Au–Sc and Fe–Sc systems

Thermodynamic optimization of the Au–Sc and Fe–Sc systems was carried out by means of the CALPHAD (CALculation of PHAse Diagram) method on the basis of the available experimental data in literature. Redlich–Kister polynomials were used to describe the excess Gibbs energy of solution phases, and all the compounds are treated as stoichiometric ones. The Au–Sc system was described thermodynamically for the first time, and the Fe–Sc system was re-optimized by considering the new experimental data about enthalpies of mixing of the liquid phase. A set of self-consistent parameters was obtained for each of these two binary systems, respectively.     

Thermodynamic optimizations of the Nd-Sn and Sn-Tb systems

The thermodynamic optimizations of the Nd-Sn and Sn-Tb binary systems were carried out by means of the Calculation of Phase Diagram (CALPHAD) method on the basis of the available experimental data including the thermodynamic properties and phase equilibria. The Gibbs free energies of the liquid, bcc, bct, dhcp and hcp phases were described by the substitutional solution model with the Redlich-Kister equation, while all of the intermetallic compounds (Nd₅Sn₃, Nd₅Sn₄, Nd₁₁Sn₁₀, NdSn, Nd₃Sn₅, NdSn₂, Nd₃Sn₇, Nd₂Sn₅, NdSn_3, Sn₃Tb, βSn₇Tb₃, αSn₇Tb₃, Sn₂Tb, Sn₅Tb₄, SnTb₄, Sn₁₀Tb₁₁, Sn₄Tb₅ and Sn₃Tb₅) were described by the sublattice model. A set of self-consistent thermodynamic parameters of each phase in the Nd-Sn and Sn-Tb binary systems has been obtained, and the calculated results are in good agreement with the available experimental data.