Alloying behavior of zinc with rare earth metals: The Dy–Gd–Zn system

The isothermal section at 400 °C of the Dy–Gd–Zn system was studied, and the vertical sections at the Dy/Gd ratio=1 was investigated. The experimental techniques used were Differential Thermal Analysis (DTA), X-ray powder diffraction (XRPD) and scanning electron microscopy (SEM) coupled with electron probe microanalysis (EPMA-EDX).No ternary compounds were found in the system. As regard to the intermetallic phases, the (Dy,Gd)Zn, (Dy,Gd)Zn₂, (Dy,Gd)Zn₃, (Dy,Gd)₃Zn₁₁, (Dy,Gd)₁₃Zn₅₈, (Dy,Gd)₂Zn₁₇ and (Dy,Gd)Zn₁₂ solid solutions form in the full field of composition, while the Gd₃Zn₂₂ compound did not show dysprosium dissolution.     

Critical thermodynamic evaluation and optimization of the Pb–Pr,Pb–Nd,Pb–Tb and Pb–Dy systems

All available experimental data on phase equilibria and thermodynamic properties of the Pb–Pr, Pb–Nd, Pb–Tb and Pb–Dy binary systems were reviewed and critically examined. A thermodynamic optimization of these systems is presented for the first time. A set of optimized model parameters for all solid stoichiometric compounds, terminal solid solutions and liquid phase was built to reproduce all available reliable thermodynamic properties and phase diagram data within experimental error limits. The Modified Quasichemical Model in the pair approximation was used to describe the thermodynamic properties of the liquid solution accurately. In view of the limited experimental phase diagram and thermodynamic data available for these systems, trends in the rare earth-lead and rare earth–tin systems were examined to estimate the missing information and evaluate whether the predictions are reasonable. Based on these trends, a predicted phase diagram for the Pb–Nd and Pb–Tb systems, which are not established to date, is presented.     

Thermodynamic assessment of the Ga-Sn-Zn system

The integral molar mixing enthalpy of liquid ternary Ga-Sn-Zn alloys has been investigated using drop calorimetry method along five intersections as follows: X_Ga/X_Zn = 3/1 at 720 K, x_Ga/x_Zn = 1/1 at 718 K and 720 K, x_Ga/x_Zn = 1/3 at 718 K, x_Ga/x_Sn = 3/17 at 718 K and for x_Ga/x_Sn = 1/3 at 720 K. Based on obtained thermodynamic results and those available in the literature the thermodynamic optimization was done using Thermo-Calc software. Next, the phase equilibria in the binary and ternary systems were calculated and the results were compared with those obtained using different experimental techniques.     

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.     

Phase equilibria of the Zn-Ti system: Experiments,first-principles calculations and Calphad assessment

The phase equilibria and thermodynamic properties of the Zn-Ti system have been investigated by experiments, first-principles calculations and Calphad assessment. Differential scanning calorimetry measurement and microstructure characterization confirmed the Zn richest eutectic reaction to occur at 691.3 ± 0.4 K with about 0.27 at% Ti in the liquid. Density functional theory (DFT) calculations have been performed to calculate the finite-temperature heat capacity (C_p) of the intermetallics, providing also the absolute entropies. A full thermodynamic assessment of the Zn-Ti system has been performed by using the experimental and DFT results obtained in this work together with the collection of all available data from previous publications. In the present work, the Calphad results show good agreement not only in thermodynamic properties with DFT data, but also phase equilibria data with experimental results, especially in the Zn-rich side, which significantly improved from previous Calphad assessment. Phase diagrams including the gas phase have also been calculated and discussed.     

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.     

Thermodynamic assessment of the Au–Ni system

The phase diagram and thermodynamic properties of the Au–Ni system have been assessed from experimental thermodynamic and phase diagram data by means of the CALPHAD method. A consistent set of thermodynamic parameters for each phase was obtained. Good agreement is reached between the calculated and experimental results. The calculated congruent point is 1214.3 K and 42.6 at.% Ni and the critical point of the miscibility gap is 1089.5 K and 73.0 at.% Ni.     

Thermodynamic assessment of the Au-Ga binary system

The Au-Ga binary system was assessed thermodynamically using the CALPHAD method through Thermo-calc^® software based on the critical review of the available experimental data from the published literature. The solution phases including liquid, fcc(Au), D0₂₄ and orthorhombic(Ga) are modeled by the substitutional solution model and their excess Gibbs energies are expressed with the Redlich-Kister polynomial. The intermetallic compounds, β- Au₇Ga₂, β^′- Au₇Ga₂, γ- Au₇Ga₃, AuGa and AuGa₂ are treated as stoichiometric compounds. A set of self-consistent thermodynamic parameters obtained finally to describe the Gibbs energies of various phases in the Au-Ga binary system can be used to reproduce well the reported phase equilibria and thermodynamic properties data.     

Experimental investigation and thermodynamic assessment of the Al-Co-Ni system

The Al-Co-Ni system is essential to both Co- and Ni-based superalloys. In this study phase relationships among A1, L1₂ and B2 at 800 °C have been investigated by using equilibrated alloys. Four samples were prepared and annealed at 800 °C for 14 days. SEM-EDXS and XRD were used to analyze the annealed samples. The results indicated that two-phase L1₂+B2 and three-phase A1+L1₂+B2 regions exit.A thermodynamic reassessment of the entire Al-Co-Ni system has been made according to the CALPHAD method. Compared to the previous assessments, more recent experimental results have been considered. In the Al-Co binary system, the phase named Y-Co₄Al₁₃ has been added on the basis of the available literature. The order-disorder model has been adopted to describe the A1/L1₂ and A2/B2 phase relations, respectively. Three ternary compounds in the Al-rich region have been introduced. Three-sublattice model has been selected to describe the τ₁ phase with a considerable solubility extension. Thermodynamic interaction parameters have been optimized, considering the available experimental data. In this work several diagrams were calculated, which can fit experimental results in the whole composition range. A satisfactory agreement was obtained. As a result phase equilibria in the interested ferromagnetic shape memory alloys are calculated.     

Thermodynamic modeling of the water – Nitric acid – Rare earth nitrate systems

An excess Gibbs energy model describing the properties of aqueous electrolyte solutions, mixed solvent electrolyte systems and nonelectrolyte systems, has been developed. The suggested electrolyte version of the Generalized Local Composition Model (eGLCM) contains three contributions to the excess Gibbs energy: a long–range electrostatic interaction term represented by the modified Pitzer-Debye-Hückel equation, which takes into account concentration dependence of the solution dielectric permittivity, the contribution of the short–range interaction between all the species, represented by the GLCM model, and the middle–range interaction term responsible for interactions involving charged species that are not explained by the long–range term. The developed model is applicable over a whole concentration range, from pure water to saturation and fused salts. The water – nitric acid system, 15 water – rare earth element nitrate systems (Y, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb and Lu) and eight water – nitric acid – REE nitrate systems (Y, La, Ce, Pr, Nd, Sm, Eu and Gd) have been modeled with the proposed electrolyte version of the Generalized Local Composition Model at 25 °C, using experimental data on both the vapor – liquid (VLE) and solid – liquid (SLE) equilibria, in a concentration range from dilute solutions to saturation. SLE data in the ternary systems were critically reviewed and correlated with the thermodynamic properties of the solutions.     

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 assessment of the Molybdenum–Rhenium system

A thermodynamic optimization of the Mo–Re system by the Calphad method is proposed, taking into account new experimental data obtained in this work. According to recent crystal chemistry work, the χ and σ Frank–Kasper phases were modeled using two independent sublattices of variable occupation. This was made possible by including experimental site fractions in the different sublattices as input data for the parameter optimization. A consistent set of parameters is proposed. Good agreement is found between calculated and selected experimental values for different kinds of data: phase diagram, thermodynamic and crystallographic data.