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.     

The experimental study of the Bi–Sn, Bi–Zn and Bi–Sn–Zn systems

The binary Bi–Sn was studied by means of SEM (Scanning Electron Microscopy)/EDS (Energy-Dispersive solid state Spectrometry), DTA (Differential Thermal Analysis)/DSC (Differential Scanning Calorimetry) and RT-XRD (Room Temperature X-Ray Diffraction) in order to clarify discrepancies concerning the Bi reported solubility in (Sn). It was found that (Sn) dissolves approximately 10 wt% of Bi at the eutectic temperature.

The experimental effort for the Bi–Zn system was limited to the investigation of the discrepancies concerning the solubility limit of Zn in (Bi) and the solubility of Bi in (Zn). Results indicate that the solubility of both elements in the respective solid solution is approximately 0.3 wt% at 200 C.

Three different features were studied within the Bi–Sn–Zn system. Although there are enough data to establish the liquid miscibility gap occurring in the phase diagram of binary Bi–Zn, no data could be found for the ternary. Samples belonging to the isopleths with w(Bi) 10% and w(Sn) 5%, 13% and 19% were measured by DTA/DSC. The aim was to characterize the miscibility gap in the liquid phase. Samples belonging to the isopleths with w(Sn) 40%, 58%, 77/81% and w(Zn) 12% were also measured by DTA/DSC to complement the study of Bi–Sn–Zn. Solubilities in the solid terminal solutions were determined by SEM/EDS. Samples were also analyzed by RT-XRD and HT-XRD (High Temperature X-Ray Diffraction) confirming the DTA/DSC results for solid state phase equilibria.     

Thermodynamic description of the Cu–Ag–Zr system

Based on the CALPHAD method, the Ag–Zr and Ag–Cu systems have been assessed thermodynamically. The excess Gibbs energy of the solution phases in the Cu–Ag–Zr system was modeled assuming random mixing of components. The ternary phase was defined as a stoichiometric compound due to the lack of efficient thermodynamic data. At first, parameters capable of describing all phases in the Ag–Zr and the Ag–Cu systems were assessed. Combined with the parameters of the Cu–Zr system assessed previously, the isothermal sections of the Cu–Ag–Zr system at 1023 K and 978 K were extrapolated, which can reproduce the measured phase-relations.     

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.     

Experimental study and thermodynamic assessment of the Ag–Ti system

A thermodynamic assessment of the binary Ag–Ti system was performed based on the evaluation of the literature and the results of the present experiments. For the experimental study, special deep embedding diffusion couples were prepared and analyzed by scanning electron microscopy (SEM) and electron probe microanalysis (EPMA). The phase equilibrium relationship and the conjugate phase compositions were determined at 1023 K, 1253 K, 1373 K and 1474 K respectively. For the thermodynamic assessment, the Redlich–Kister polynomial was used to describe the solution phases, liquid (L), bcc, hcp, and fcc. The sublattice-compound energy model was employed to describe the intermediate phase, (AgTi), with a homogeneity range. The other intermediate phase, AgTi₂, without a homogeneity range was treated as the stoichiometric phase. A set of self-consistent thermodynamic parameters of the Ag–Ti system has been obtained. The calculated phase diagram was presented and compared with the experimental 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.     

A critical thermodynamic assessment of the Mg–Ni, Ni–Y binary and Mg–Ni–Y ternary systems

A thorough review and critical evaluation of phase equilibria and thermodynamic data for the phases in the Mg–Ni–Y ternary system have been carried out over the entire composition range from room temperature to above the liquidus. This system is being modeled for the first time using the modified quasichemical model which considers the presence of short range ordering in the liquid. The Gibbs energies of the different phases have been modeled, and optimized model parameters that reproduce all the experimental data simultaneously within experimental error limits have been obtained. For the liquid phases, the modified quasichemical model is applied. A sublattice model within the compound-energy formalism is used to take proper account of the structures of the binary intermediate solid solutions. The Mg–Ni and Ni–Y binary systems have been re-optimized based on the experimental phase equilibrium and thermodynamic data available in the literature. The optimized thermodynamic parameters for the Mg–Y system are taken from the previous thermodynamic assessment of the Mg–Cu–Y system by the same authors. The constructed database has been used to calculate liquidus projection, isothermal and vertical sections which are compared with the available experimental information on this system. The current calculations are in a good agreement with the experimental data reported in the literature.     

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.     

Thermodynamic evaluation of the phase equilibria and glass-forming ability of the Fe–Si–B system

A thermodynamic study has been carried out on the Fe–Si–B ternary system, which is important in the development of transformer core materials and Ni-based filler metals. A regular solution approximation based on the sublattice model was adopted to describe the Gibbs energy for the individual phases in the binary and ternary systems. Thermodynamic parameters for each phase were evaluated by combining the experimental results from differential scanning calorimetry with literature data. The evaluated parameters enabled us to obtain reproducible calculations of the isothermal and vertical section diagrams. Furthermore, the glass-forming ability of this ternary alloy was evaluated by introducing thermodynamic quantities obtained from the phase diagram calculations into Davies–Uhlmann kinetic formulations. In this evaluation, the time–temperature-transformation (TTT) curves were obtained, which are a measure of the time required to transform to the minimum detectable mass of crystal as a function of temperature. The critical cooling rates calculated on the basis of the TTT curves enabled us to evaluate the glass-forming ability of this ternary alloy. The results show good agreement with the experimental data in the compositional amorphization range.     

A thermodynamic reassessment of the La–Sn system

Thermodynamic modelling of the La–Sn binary system was carried out with the help of the CALPHAD (CALculation of PHAse Diagram) method. The liquid phase has been described with the association solution model with a ‘ La₁Sn₁’ associated complex. The intermetallic compounds were treated as stoichiometric phases. The calculated phase diagram and the thermodynamic properties of the system are in satisfactory agreement with the majority of the 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.