Thermodynamic Assessment of the Ti-Ir System

The thermodynamic assessment of the binary system Ti-Ir has been carried out by modeling the Gibbs energy of all individual phases using the calculation of phase diagrams approach based on the available literature data including the phase equilibria and thermodynamic properties. The Gibbs free energies of the liquid, bcc, fcc and hcp phases were described by the subregular solution model with Redlich-Kister formula, and those of the intermetallic compounds (Ti₃Ir, γTiIr, βTiIr and TiIr₃) in the Ti-Ir binary system were described by the two-sublattice model. The calculations are in good agreement with the literature data on both phase equilibria and thermodynamic properties in the Ti-Ir system.     

Thermodynamic optimization of the boron-cobalt-iron system

A thermodynamic optimization of the boron-cobalt-iron ternary system is performed based on thermodynamic models of the three constitutional binary systems and the experimental data on phase diagrams and thermodynamic properties of the ternary system. The liquid, fcc_A1, bcc_A2 and hcp_A3 solution phases are described by the substitutional solution model. The three intermediate line compounds, (Co,Fe)B, (Co,Fe)₂B and (Co,Fe)₃B, are described by the two sublattice model. A set of thermodynamic parameters are obtained. The calculated phase diagram and thermodynamic properties are in reasonable agreement with most of the experimental data.     

Thermodynamic assessment of the Gd–Sb system

A thermodynamic assessment of the binary Gd–Sb system was performed through the CALPHAD approach (CALculation of PHAse Diagram) based on the evaluation of all phase diagram data and available thermodynamic data in the literature. The liquid, hcp-A3 (αGd) and bcc-A2 (βGd) phases were described by a substitutional solution model. All the intermediate phases, Gd₅Sb₃, Gd₄Sb₃, βGdSb, αGdSb and Gd₁₆Sb₃₉, were treated as stoichiometric compounds. A set of self-consistent thermodynamic parameters of the Gd–Sb system has been obtained. A good agreement is obtained between the experimental and the calculated phase diagrams.     

Thermodynamic Assessments of the Au-Tb and Au-Lu Systems

The thermodynamic assessments of the Au-Tb and Au-Lu binary systems were carried out by means of the CALPHAD method based on the experimental data including the thermodynamic properties and phase equilibria. The Gibbs free energies of the liquid, bcc, fcc and hcp phases were described by the substitutional solution model, while all of the intermetallic compounds (Au₆Tb, Au₅₁Tb₁₄, Au₃Tb, Au₂Tb, Au₁₀Tb₇, Au₄Tb₃, αAuTb, βAuTb, AuTb₂, Au₄Lu, Au₃Lu, Au₂Lu, AuLu and AuLu₂ phases) in these two binary systems were treated as the sublattice model. Consequently, a set of self-consistent thermodynamic parameters of each phase in the Au-Tb and Au-Lu binary systems has been obtained, and the calculated results are in good agreement with the available experimental data.     

Thermodynamic Calculation of Phase Equilibria in the C-Mo-Zr System

The C-Mo-Zr system was assessed by means of the CALPHAD approach. All of the phase equilibria available from the literature were critically reviewed. The liquid was modeled as substitutional solution phase, while the carbides including fcc-(Mo,Zr)C_1?x, bcc-(Mo), bcc-(Zr), hcp-Mo₂C, hcp-(Zr) and η-MoC were described by using corresponding sublattice models. The laves-Mo₂Zr and shp-MoC phases were considered as binary compounds with no solubility for the third component. The existence of ternary phase was not reported in this system. The modeling of C-Mo-Zr ternary system covers the entire composition and temperature ranges, and a set of self-consistent thermodynamic parameters for the C-Mo-Zr system was systematically optimized. Comprehensive comparisons between the calculated and reported phase diagram data show that the reliable information is satisfactorily accounted for by the present modeling. The liquidus projection and reaction scheme of the C-Mo-Zr system were also generated based on the present thermodynamic assessment.     

Thermodynamic Assessments of the Bi-Tb and Bi-Y Systems

By using the calculation of phase diagrams (CALPHAD) method, the thermodynamic assessments of the Bi-Tb and Bi-Y systems were carried out based on the available experimental data including thermodynamic properties and phase equilibria. Gibbs free energies of the liquid, hcp, bcc, and rhombohedral phases in the Bi-Tb and Bi-Y systems were modeled by the substitutional solution model, and the intermetallic compounds (BiTb, Bi₃Tb₄, αBi₃Tb₅, βBi₃Tb₅, BiY, and Bi₃Y₅ phases) in these two binary systems were described by the sublattice model. An agreement between the present calculated results and experimental data was obtained.     

A generalized thermodynamic treatment of phase equilibria in coherent multilayers

We present a generalized way of treating phase equilibria in coherent planar multilayers. A correct recognition of elastic stress and strain components as thermodynamic potentials or densities is crucial for the use of the criteria for intrinsic stability as well as for the applicability of the conventional method of common tangent construction and the Gibbs phase rule. It is shown that a method analogous to the conventional common tangent construction exists in thermodynamic density subspaces for which some of density variables are held constant. In a thermodynamic density subspace withm _s density variables fixed, a common tangent construction can be made between the extremized free energies for systems of (m_s+l)-phase coexistence in order to satisfy the thermodynamic equilibrium conditions of systems with more thanm _s+1 coexisting phases. This method is applied to a coherent binary system configured as plane-parallel plates to demonstrate that equilibrium states with more than two coexisting phases cannot be thermodynamically stable in the binary multilayer system under certain mechanical loading conditions.     

Experimental Study and Thermodynamic Re-optimization of the FeO-Fe<Subscript>2</Subscript>O<Subscript>3</Subscript>-SiO<Subscript>2</Subscript> System

Phase equilibria and thermodynamic data in the FeO-Fe₂O₃-SiO₂ system were critically reviewed. New experiments were undertaken to resolve discrepancies found in previous data. The liquid oxide/slag phase was described using the modified quasichemical model. New optimized parameters of the thermodynamic models for the Gibbs energies of slag and other phases in the selected system were obtained. The new parameters reproduce all available phase equilibria and thermodynamic data within the experimental error limits from 298 K (25 °C) to above the liquidus temperatures at all compositions and oxygen partial pressures from metal saturation to 1 atm of O₂. This study was carried out as part of the development of a self-consistent thermodynamic database for the Al-Ca-Cu-Fe-Mg-Si-O-S multi-component system.     

A thermodynamic analysis of the Al-Re system

Phase equilibria and thermodynamic data of the Al-Re system are critically reviewed. In addition to the three solution phases, liquid, fcc Al, and hcp Re, there exist six intermetallic compounds in this binary. The thermodynamic properties of the system are analyzed using thermodynamic models for the Gibbs energy of individual phases of the system. A regular solution model is used for the three substitutional solution phases, and the intermetallic phases are treated as stoichiometric compounds. The model parameters are optimized from a limited amount of experimental data. The calculated phase diagram and thermodynamic values are in accord with the available experimental values.     

Thermodynamic Treatment of Undercooled Cu-Mg Liquid and the Limits for Partitionless Crystallization

The thermodynamic properties of the binary Cu-Mg system are examined with a focus on equilibria involving the liquid phase, which is described with a four-species association model, incorporating a two-state treatment for the pure component liquids below their respective melting temperatures. The terminal and intermediate crystalline phases are described as substitutional solid solutions, employing two sublattices for the latter. Model parameters are fitted using available experimental data, and the resulting phase diagram is reported over the full range of compositions in the binary system. We also report the associated T ₀ curves, indicating the limits of partitionless crystallization and compare these with reports of amorphous solid formation during rapid solidification processing.