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.     

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.     

Thermodynamic evaluation and optimization of Al–Gd, Al–Tb, Al–Dy, Al–Ho and Al–Er systems using a Modified Quasichemical Model for the liquid

The Al–Gd, Al–Tb, Al–Dy, Al–Ho and Al–Er (Al–heavy rare earths) binary systems have been systematically assessed and optimized based on the available experimental data and ab-initio data using the FactSage thermodynamic software. A systematic technique (reduced melting temperature proposed by Gschneidner) was used for estimating the Al–Tb phase diagram due to lack of experimental data. Optimized model parameters of the Gibbs energies for all phases which reproduced all the reliable experimental data to satisfaction have been obtained. The optimization procedure was biased by putting a strong emphasis on the observed trends in the thermodynamic properties of Al–RE phases. The Modified Quasichemical Model, which takes short-range ordering into account, is used for the liquid phase and the Compound Energy Formalism is used for the solid solutions in the binary systems. It is shown that the Modified Quasichemical Model used for the liquid alloys permits one to obtain entropies of mixing that are more reliable than that based on the Bragg–Williams random mixing model which does not take short-range ordering into account.     

Thermal destabilization of binary and complex metal hydrides by chemical reaction: A thermodynamic analysis

Some alkali and alkali-earth metal hydrides and their complex hydrides have very high hydrogen storage capacities and reversibility. Unfortunately, most of them have decomposition temperatures that are too high. This must be overcome before these hydrides can be considered seriously as practical hydrogen storage materials for on-board applications. In the present study, the CALPHAD approach has been adopted to evaluate thermodynamically the possibility of destabilizing these high temperature binary ionic hydrides and ternary complex hydrides by reacting them with light elements or other hydrides. The MgH₂+Si, LiBH₄+MgH₂, and LiBH₄+Al systems are predicted to show a significant decrease in decomposition temperature. On the other hand, the decrease in the decomposition temperatures of the MgH₂+Al and NaBH₄+Al systems is relatively small. The LiH+Si system also presents a considerable destabilization effect, which is consistent with experiment.     

Thermodynamic assessment of the Pt–Si binary system

The Pt–Si binary system was thermodynamically assessed using the CALPHAD method based on the available experimental data from the literature. The solution phases, including Liquid, Fcc_A1 (Pt) and Diamond_A4 (Si), were treated as substitutional solution phases, of which the excess Gibbs energies were expressed with Redlich–Kister polynomial functions. Meanwhile, the intermetallic compounds, PtSi, Pt₆Si₅, Pt₂Si, Pt₁₇Si₈, Pt₅Si₂, Pt₃Si and Pt₂₅Si₇, were modeled as stoichiometric compounds. Subsequently, a set of self-consistent thermodynamic parameters formulating the Gibbs energies of various phases were obtained and the calculated values of phase diagram and thermodynamics were found to be in reasonable agreement with 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.     

Prediction of the thermodynamic properties for the Ga–Sb–Pb ternary system

The results of some thermodynamic prediction methods applied to the Ga–Sb–Pb ternary system are presented in this paper. The Chou general solution model and the traditional models of Kohler and Toop were included in the calculation for the comparison and discussion. Integral enthalpy of mixing and integral excess Gibbs energy dependences on composition for the 15 investigated cross sections at 973 K and 1073 K, respectively, were obtained according to the applied models. The comparison between the results of the three models shows good mutual agreement. Obtained results were used for the further calculation of partial molar quantities for every component of the investigated ternary system. Calculated activity values at 1073 K for all components are given in the form of isoactivity diagrams.     

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.     

A thermodynamic reassessment of the Ca–Pb system

New experimental measurements of the mixing enthalpy of the liquid phase and the enthalpies of formation of the intermetallic compounds along with the data already taken into account in previous thermodynamic assessments have been used in a reassessment of the thermodynamic parameters of the Ca–Pb system. The calculations based on the thermodynamic modelling are in good agreement with the phase diagram data and experimental thermodynamic values.     

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 evaluation and optimization of Al-La, Al-Ce, Al-Pr, Al-Nd and Al-Sm systems using the Modified Quasichemical Model for liquids

The Al-La, Al-Ce, Al-Pr, Al-Nd and Al-Sm (Al-light rare earth) binary systems have been systematically assessed and optimized based on the available experimental data and ab-initio data using the FactSage thermodynamic software. Optimized model parameters of the Gibbs energies for all phases which reproduced all the reliable experimental data to satisfaction have been obtained. The optimization procedure was biased by putting a strong emphasis on the observed trends in the thermodynamic properties of Al-RE phases. The Modified Quasichemical Model, which takes short-range ordering into account, is used for the liquid phase and the Compound Energy Formalism is used for the solid solutions in the binary systems. It is shown that the Modified Quasichemical Model used for the liquid alloys permits us to obtain entropies of mixing that are more reliable than that based on the Bragg-Williams random mixing model which does not take short-range ordering into account.     

Experimental study and thermodynamic modelling of the ZrO2–LaO1.5 system

Phase relations in the ZrO₂–LaO_1.5 system were studied experimentally in the temperature range from 1673 to 1973 K. X-ray diffraction and scanning electron microscopy were employed to obtain the structural information and the compositions of the tetragonal and pyrochlore (La₂Zr₂O₇) phases. The solubility of LaO_1.5 in the tetragonal phase was determined to be very small. The homogeneity range of the pyrochlore phase is estimated to be less than 2 mol% at 1973 K, and less than 1 mol% at 1673 K according to the present work. Based on the experimental results obtained in this work, as well as the available phase diagram and thermodynamic data in literature, a self-consistent thermodynamic assessment was carried out by using the ionic sublattice solution model.