Thermodynamic modeling of the Mg–Ge–Pb system

All available thermodynamic and phase diagram data of the Mg–Ge and Mg–Pb binary systems, and the Mg–Ge–Pb ternary system have been critically evaluated and all reliable data have been simultaneously optimized to obtain one set of model parameters for the Gibbs energies of the liquid and all solid phases as functions of composition and temperature. The liquid phase was modeled using the Modified Quasichemical Model in order to describe the strong ordering in Mg–Ge and Mg–Pb liquid. Mg₂Ge–Mg₂Pb solid solution phase was modeled with consideration of a solid miscibility gap. All calculations were performed using the FactSage thermochemical software.     

A thermodynamic description of the Al–Ca–Zn ternary system

A comprehensive thermodynamic database of the Al–Ca–Zn ternary system is presented for the first time. Critical assessment of the experimental data and re-optimization of the binary Al–Zn and Al–Ca systems have been performed. The optimized model parameters of the third binary system, Ca–Zn, are taken from the previous assessment of the Mg–Ca–Zn system by the same authors. All available as well as reliable experimental data both for the thermodynamic properties and phase boundaries are reproduced within experimental error limits. In the present assessment, the modified quasichemical model in the pair approximation is used for the liquid phase and Al_FCC phase of the Al–Zn system to account for the presence of the short-range ordering properly. Two ternary compounds reported by most of the research works are considered in the present calculation. The liquidus projections and vertical sections of the ternary systems are also calculated, and the invariant reaction points are predicted using the constructed database.     

The phase equilibria in the Mg–Ni–Ca system

The three binary systems Mg–Ni, Ca–Ni and Mg–Ca have been re-optimized. A self-consistent thermodynamic database of the Mg–Ni–Ca system is constructed by combining the optimized parameters of these three constituent binaries. Lattice stability values are not added to the pure elements Mg-hcp, Ni-fcc, Ca-fcc and Ca-bcc to construct this database. The Redlich–Kister polynomial model is used to describe the liquid and the terminal solid solution phases, and the sublattice model is used to describe the non-stoichiometric phase, in this system. The constructed database is used to calculate the three binary and the ternary systems. The calculated binary phase diagrams along with their thermodynamic properties such as Gibbs energy, enthalpy, entropy and activities are found to be in good agreement with experimental data from the literature. This is the first attempt to construct the ternary phase diagram of the Mg–Ni–Ca system. The established database for this system predicted three ternary eutectic, five ternary quasi-peritectic, two ternary peritectic and two saddle points.     

Thermodynamic description of the Sn–Ag–Au ternary system

Gibbs energy of hcp_A3 phase in the Ag–Sn binary system has been reassessed using compatible lattice stability. Combined with previous assessments of the Ag–Au and Au–Sn binary systems, the Sn–Ag–Au ternary system has been thermodynamically optimized using the CALPHAD method on the basis of available experimental information. The solution phases including liquid, fcc_A1, hcp_A3 and bct_A5, are modeled as substitutional solutions, while the intermediate compound Ag₃Sn is treated using a 2-sublattice model because Au can be dissolved to a certain degree. The solubility of Ag in the Au–Sn intermediate phases, D0₂₄, Au₅Sn, AuSn, AuSn₂ and AuSn₄, is not taken into account. Thermodynamic properties of liquid alloys, liquidus projection and several vertical and isothermal sections of this ternary system have been calculated, which are in reasonable agreement with the reported experimental data.     

Thermodynamic assessments of the Ni–Pt and Al–Ni–Pt systems

The Ni–Pt system is assessed using the CALPHAD method. The four fcc-based phases, i.e. disordered solid solution phase, Ni₃Pt–L1₂, NiPt–L1₀ and NiPt₃–L1₂, are described by a four-sublattice model. The calculated thermodynamic properties and order/disorder phase transformations are in good agreement with the experimental data. In order to facilitate the assessment, first-principles pseudopotential calculations are also performed to calculate the enthalpy of formation at 0 K, and comparison with the assessed values is discussed. By combining the assessments of Al–Ni and Al–Pt, the Al–Ni–Pt ternary system is assessed within a narrow temperature range, focusing on the fcc-based phases and their phase equilibria with B2 phase.     

Thermodynamic optimization of the Ni–Sn binary system

Through the CALPHAD method and based on experimental data of thermodynamic properties and phase boundaries, the phase diagram of the Ni–Sn binary system has been reassessed. The liquid and fcc_A1 (terminal rich nickel solid solution) phases were described by using a simple substitutional model, the excess Gibbs energy being formulated with a Redlich–Kister expression. The other intermediate phases (Ni₃Sn_HT, Ni₃Sn₂_HT, Ni₃Sn₂_LT, Ni₃Sn₄), were described with a several sublattice model with different formula; the Gibbs energy of the reference compounds was assumed to be linear, and the binary interaction terms on the sub-lattices to be constant. Ni₃Sn_LT was treated as a stoichiometric compound. The solubility of Ni in the terminal phase bct_A5(Sn) was neglected because it is very small. Finally a set of self-consistent thermodynamic parameters for all condensed phases in the Ni–Sn binary system was obtained, which can reproduce most of the experimental data.     

Thermodynamic modeling of the Mg–Si–Sn system

All available thermodynamic and phase diagram data of the Mg–Si and Mg–Sn binary systems, and the Mg–Si–Sn ternary system have been critically evaluated and all reliable data have been simultaneously optimized to obtain one set of model parameters for the Gibbs energies of the liquid and all solid phases as functions of composition and temperature. The liquid phase was modeled using the Modified Quasichemical Model in order to describe the strong ordering in Mg–Si and Mg–Sn liquids. The Mg₂Si–Mg₂Sn solid solution phase was modeled with consideration of the solid miscibility gap. All calculations were performed using the FactSage thermochemical software.     

Thermodynamic assessment of the Si–Zn,Mn–Si,Mg–Si–Zn and Mg–Mn–Si systems

The binary Si–Zn and Mn–Si systems have been critically evaluated based upon available phase equilibrium and thermodynamic data, and optimized model parameters have been obtained giving the Gibbs energies of all phases as functions of temperature and composition. The liquid solution has been modeled with the Modified Quasichemical Model (MQM) to account for the short-range-ordering. The results have been combined with those of our previous optimizations of the Mg–Si, Mg–Zn and Mg–Mn systems to predict the phase diagrams of the Mg–Si–Zn and Mg–Mn–Si systems. The predictions have been compared with available data.     

Thermodynamic modeling of the C–Pu–U system

The ternary C–Pu–U system is thermodynamically assessed to pursue the development of a thermodynamic database for future nuclear fuels. The substitution model was used for the liquid phase, and a two-sublattice model for the PuC–UC monocarbide, PuC₂–UC₂ dicarbide and Pu₂C₃–U₂C₃ sesquicarbide phases. Ternary interaction parameters were adjusted on the experimental information for the phase relationships. Isoplethal and isothermal ternary sections, as well as some liquidus temperatures are calculated and compared with the experimental data. The overall agreement is discussed, and shows that experimental uncertainties still remain.     

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 modeling of the Mg–Bi and Mg–Sb binary systems and short-range-ordering behavior of the liquid solutions

In order to investigate the short range ordering behavior of liquid Mg–Bi and Mg–Sb solutions, thermodynamic modeling of the Mg–Bi and Mg-Sb binary systems has been performed. All available thermodynamic and phase diagram data of the Mg–Bi and Mg–Sb binary systems have been critically evaluated and all reliable data have been simultaneously optimized to obtain one set of model parameters for the Gibbs energies of the liquid and all solid phases as functions of composition and temperature. In particular, the Modified Quasichemical Model, which accounts for short-range-ordering of nearest-neighbor atoms in the liquid, was used for the liquid solutions. A comparative evaluation of both systems was helpful to resolve inconsistencies of the experimental data. The thermodynamic modeling shows the strong ordering behavior in the liquid Mg–Bi and Mg–Sb solutions at Mg₃Bi₂ and Mg₃Sb₂ compositions, respectively, and predicts the metastable liquid miscibility gaps at sub-solidus temperatures. All calculations were performed using the FactSage thermochemical software.     

Thermodynamic description of the Pb–Yb binary system

Thermodynamic modelling of the Pb–Yb binary system was carried out with the help of the CALPHAD method. The liquid phase has been described with the association solution model with ‘ Pb₁Y b₂’ as an associated complex. The solution phases BCC_A2 and FCC_A1 were modelled with the sublattice formalism. The αPbYb_LT and βPbYb_HT Pb sub-stoichiometric intermetallic compounds, which have a homogeneity range, were treated with the formula (Pb,Y b)_0.5(Y b)_0.5 by a two-sublattice model with Pb and Yb on the first sublattice and Yb on the second one. Pb₃Y b, Pb₃Y b₅ and PbY b₂ have been treated as stoichiometric compounds. The calculations based on the thermodynamic modelling are in good agreement with the phase diagram data and experimental thermodynamic values.     

First-principles calculations assisted thermodynamic assessment of the Pt–Ga–Ge ternary system

The Pt–Ga–Ge ternary system was thermodynamically assessed by the CALPHAD (CALculaton of PHAse Diagram) approach with help of first-principles calculations. Firstly, the formation enthalpies of the Pt–Ge and Pt–Ga compounds were calculated by the first-principles method. Subsequently, the Pt–Ge system was modeled and the Pt–Ga system was re-assessed. The solution phases, Liquid, Diamond_A4 (Ge) and Fcc_A1 (Pt), were modeled as substitutional solutions, of which the excess Gibbs energy was formulated with the Redlich–Kister polynomial. The binary intermetallics, Ga₇Pt₃, Ga₂Pt, Ga₃Pt₂, GaPt, Ga₃Pt₅, GaPt₂, Ge₂Pt, Ge₃Pt₂, GePt, Ge₂Pt₃ and GePt₂, were treated as stoichiometric compounds while GePt₃ was described with a two-sublattice model. Finally, based on the currently optimized Pt–Ga and Pt–Ge binary systems along with the already assessed Ga–Ge system, phase equilibria in the Pt–Ga–Ge ternary system were extrapolated. The isothermal sections at 473 K, 973 K and 1073 K of the ternary system were calculated, showing good agreement with the experimental data. In addition, the liquidus projection of the Pt–Ga–Ge ternary system was predicted using the obtained model parameters.