Thermodynamic assessment of the Al–Cu–Er system

The Cu–Er binary system had been thermodynamically assessed with the CALPHAD approach. The solution phases including Liquid, Fcc and Hcp were treated as substitutional solution phases, of which the excess Gibbs energies were formulated with the Redlich–Kister polynomial function. All the binary intermetallic compounds were treated as stoichiometric phases. Combining with the thermodynamic parameters of the Al–Cu and Al–Er binary systems cited from the literature, the Al–Cu–Er ternary system was thermodynamically assessed. The calculated phase equilibria were in good agreement with the experimental data.     

Thermodynamic assessment of Sn–Cu–Ce system

Phase relations of Sn–Cu–Ce system are important in understanding metallurgical role of Ce in Sn–Cu based lead-free solder alloys. Thermodynamic assessment of Sn–Cu–Ce ternary system has been done based on experimental data about phase equilibria and thermodynamic properties by using the CALPHAD approach combined with first-principle calculations of formation enthalpy of key compounds. The solution phases (liquid, Fcc_A1, Bcc_A2 and Bct_A5) were treated as substitutional, of which the excess Gibbs energies were modeled by the Redlich–Kister polynomial. Considering its crystal structure and solid solubility range, intermetallic compound Ce₁₁Sn₁₀ was described with a three-sublattice model (Ce)_0.429(Sn)_0.429(Ce,Cu,Sn)_0.142. Other binary and ternary intermetallic compounds were described as stoichiometric phases because of their limited homogeneity ranges. During optimization, Ce–Sn binary system was first assessed; then phase relations in Sn–Cu–Ce ternary system were modeled by combining with the optimized Ce–Cu and Cu–Sn binary systems in literatures. A set of thermodynamic parameters for all known phases were obtained, which can reproduce most experimental data. The Scheil model was used to simulate the process of non-equilibrium solidification for a series of alloys.     

Thermodynamic assessment of the Ag–Ga system

The thermodynamics of the Ag–Ga system are assessed by the CALPHAD approach (calculation of phase diagram). The liquid phase, the solid solution phases of fcc (α$\alpha$-Ag) and hcp (ζ)$\left(\zeta \right)$, the solution compound Ag₂Ga (ζ^′)$\left({\zeta }^{\prime }\right)$, the stoichiometric compound Ag₃Ga₂, and the terminal phase of orthorhombic Ga are taken into consideration in this optimization. The liquid phase is described by the association model. The subregular solution model is used for the solid solution phases of fcc and hcp. The solution compound Ag₂Ga is described by the two-sublattice compound energy model (CEM). A set of self-consistent thermodynamic parameters is obtained and the calculated phase diagram and thermodynamic properties are presented and compared with the experimental data from literatures.     

Thermodynamic assessment of the Au–Pb system

The Au–Pb system has been thermodynamically assessed by the CALPHAD method. The excess Gibbs energies of the solution phases were modeled assuming random mixing of components, while the three intermetallic phases were described as stoichiometric compounds. Based on the experimental phase diagram and thermochemical data, a set of self-consistent parameters describing all phases in this system has been obtained.     

Thermodynamic re-assessment of the Al–Ir system

The thermodynamic assessment of the Al–Ir binary system was performed using the CALPHAD technique. The B2-AlIr phase was described, using the two sublattice model with the formula (Al,Ir,V a)_1/2(Al,Ir,V a)_1/2, while Al₉Ir₂, Al₃Ir, Al₁₃Ir₄, Al₄₅Ir₁₃, Al₂₈Ir₉, and Al_2.7Ir compounds were treated as stoichiometric compounds. The fcc-based phases (L1₀-AlIr, L1₂-Al₃Ir, L1₂-AlIr₃ and A1) were described using the four sublattice model with the formula, (Al,Ir)_1/4(Al,Ir)_1/4(Al,Ir)_1/4(Al,Ir)_1/4. From ab initio calculations (VASP) the formation enthalpies of the stable/metastable intermetallic phases involved in the Al–Ir system were estimated. The thermodynamic quantities, such as the phase equilibria, invariant reactions, and formation enthalpies of the intermetallic phases, were calculated using the obtained parameter set, and agree well with experimental data.     

Thermodynamic assessment of the Fe–V–O system

The Fe–V–O system over the whole composition range was optimized according to the reliable phase equilibria and thermodynamic data. The modified quasichemical model was used to describe the liquid phase from metal alloy to oxide melt. Based upon the Compound Energy Formalism, the FeV₂O₄–Fe₃O₄ spinel solution was described by a sublattice model considering the cation distribution between tetrahedral and octahedral sites. Wüstite, corundum and (VO₂)_s.s. were described using a simple Bragg-Williams model. A set of self-consistent model parameters was obtained and the available phase diagram and thermodynamic data were reproduced well within experimental error limits. The complex phase relations in the Fe–V–O system at various temperatures and oxygen partial pressures were elucidated.     

Thermodynamic assessment of the Ga–Se–Te system

In this study, the Ga–Te binary system was reassessed by means of the CALPHAD method using a modified lattice stability parameter for Te as well as experimental data for this binary system. The two-sublattice ionic solution model was applied for the liquid phase, and the intermediate phases were described by the sublattice model. A set of self-consistent thermodynamic parameters was optimized for all the phases in the Ga–Te binary system, which reproduced the phase diagram and the thermodynamic properties well. Using the reevaluated Ga–Te system, previously assessed Ga–Se system, and modified Se–Te system, a critical evaluation of the Ga–Se–Te ternary system was performed. The calculated vertical sections, isothermal sections, and liquidus projection agreed reasonably well with the experimental data. Immiscibility in the liquid phase was observed, and the origin of this behavior is discussed from a thermodynamic perspective.     

Thermodynamic assessment of the Ni–Sc binary system

On the basis of the experimental data of the phase equilibria and the thermochemical properties, a critical evaluation for the Ni–Sc binary system has been carried out using the CALPHAD (Calculation of Phase Diagrams) method. The associated model is used for the liquid phase containing the constituent species Ni, Sc and ScNi. The terminal solid solutions Fcc_A1 (Ni), Hcp_A3 (Sc), and Bcc_A2 (Sc) are described by the solution model with the Redlich–Kister polynomial. The intermetallic compounds, ScNi₅, Sc₂Ni₇, ScNi and Sc₂Ni, are treated as strict stoichiometric compounds. The compound with a homogeneity range, (ScNi₂), is modeled using two sublattices as (Sc,Ni)_0.333(Sc,Ni)_0.667. A set of self-consistent thermodynamic parameters for the Ni–Sc binary system is obtained. The calculated results agree well with the available experimental data from literatures.