Thermodynamic assessments of the In-Eu and In-Yb systems

Based on the experimental data including thermodynamic properties and phase equilibria, thermodynamic assessments of the In-Eu and In-Yb binary systems have been carried out by using the CALPHAD (Calculation of Phase Diagrams) method. The Gibbs free energies of the solution phases (liquid, fcc, bcc and tetragonal_A6) were described by subregular solution model with the Redlich-Kister equation. The intermetallic compounds, except the InYb phase, were treated as stoichiometric phases, and the InYb phase was described using the sublattice model. A consistent set of thermodynamic parameters has been derived for describing the Gibbs free energy of each solution phase and intermetallic compound in the In-Eu and In-Yb systems. A good agreement between the calculated results and the experimental data in the In-Eu and In-Yb systems is obtained.     

Thermodynamic assessments of the Bi-Lu and Lu-Sb systems

The phase diagrams and thermodynamic properties in the Bi-Lu and Lu-Sb binary systems have been assessed by using the CALPHAD (Calculation of Phase Diagrams) method on the basis of experimental data including the thermodynamic properties and phase equilibria. The Gibbs free energies of the liquid, hexagonal close-packed (hcp) and rhombohedral phases were described by the substitutional solution model, and the intermetallic compounds (Bi₂Lu, BiLu, Bi₃Lu₅, Lu₃Sb, Lu₅Sb₃, αLuSb, βLuSb and LuSb₂ phases) were treated as stoichiometric compounds. The thermodynamic parameters of the Bi-Lu and Lu-Sb binary systems were obtained, and agreement between the calculated results and experimental data was obtained for each binary system.     

Thermodynamic assessment of the RE-B (RE=Ho,Er, Tm) binary systems

To develop novel Nd-Fe-B-based permanent magnets with rare earth (RE) metals, phase equilibria and thermodynamic information of multi-component RE-Fe-B-based alloy systems is indispensable. In this work, thermodynamic assessment of the RE-B (RE=Ho, Er, Tm) binary systems as the important binary systems in the RE-Fe-B-based alloy systems were carried out using the CALPHAD (Calculation of Phase Diagram) method. The solution phases including liquid, hcp(α-Ho, α-Er and α-Tm) and rhombohedral(β-B) in the RE-B (RE=Ho, Er, Tm) binary systems are modeled by the substitutional solution model. The intermetallic compounds, HoB₂, HoB₄, HoB₆, HoB₁₂, HoB₆₆, ErB₂, ErB₄, ErB₁₂, ErB₆₆, TmB₂, TmB₄, TmB₁₂ and TmB_66, are treated as the stoichiometric compounds. Self-consistent thermodynamic parameters to describe Gibbs energies of phases in the RE-B (RE=Ho, Er, Tm) binary systems were obtained finally. The calculated results agree well with the reported data.     

Thermodynamic modeling of the ternary Ce–Fe–Sb system: Assessment of the Ce–Sb and Ce–Fe systems

The two Ce–Sb and Ce–Fe binary systems have been evaluated using the calculation of phase diagram method (CALPHAD). All of the binary compounds are treated as stoichiometric compounds. Solution phases are described with an ordinary substitutional solution model. The model parameters were derived from an optimization procedure using all available experimental data. The reproduction of the thermochemical and phase diagram information is reported in a series of figures and tables.     

Thermodynamic optimizations of the Nd-Sn and Sn-Tb systems

The thermodynamic optimizations of the Nd-Sn and Sn-Tb binary systems were carried out by means of the Calculation of Phase Diagram (CALPHAD) method on the basis of the available experimental data including the thermodynamic properties and phase equilibria. The Gibbs free energies of the liquid, bcc, bct, dhcp and hcp phases were described by the substitutional solution model with the Redlich-Kister equation, while all of the intermetallic compounds (Nd₅Sn₃, Nd₅Sn₄, Nd₁₁Sn₁₀, NdSn, Nd₃Sn₅, NdSn₂, Nd₃Sn₇, Nd₂Sn₅, NdSn_3, Sn₃Tb, βSn₇Tb₃, αSn₇Tb₃, Sn₂Tb, Sn₅Tb₄, SnTb₄, Sn₁₀Tb₁₁, Sn₄Tb₅ and Sn₃Tb₅) were described by the sublattice model. A set of self-consistent thermodynamic parameters of each phase in the Nd-Sn and Sn-Tb binary systems has been obtained, and the calculated results are in good agreement with the available experimental data.     

Thermodynamic re-assessment of the Fe-Tm and Fe-Ho binary systems

Thermodynamic re-assessment of the Fe-Tm and Fe-Ho binary systems were carried out with the help of the CALPHAD method based on the previous optimizations and the critical review of the available experimental information in the published literature. The substitutional solution model was used to describe liquid phase and fcc-Fe, bcc-Fe, hcp-Tm, bcc-Ho and hcp-Ho solid solution phases and their excess terms of Gibbs energies were expressed with the Redlich-Kister polynomial. The intermetallic compounds, Fe₁₇Tm₂, Fe₂₃Tm₆, Fe₃Tm, Fe₂Tm, Fe₁₇Ho₂, Fe₂₃Ho₆, Fe₃Ho and Fe₂Ho, were treated as stoichiometric compounds considering the experimental heat capacity of two intermetallic compounds (Fe₂Tm and Fe₂Ho) in the low temperature range. Self-consistent thermodynamic parameters to describe the Gibbs energies of various phases in the Fe-Tm and Fe-Ho binary systems were obtained finally. The calculated results in this work are in good agreement with available phase equilibira data and thermodynamic 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 re-assessment of the Fe-Gd and Fe-Sm binary systems

The Fe-Gd and Fe-Sm binary systems were re-assessed thermodynamically using the CALPHAD method based on the critical evaluation of previous optimizations and available experimental information in the published literature. The solution phases including liquid, fcc-Fe, bcc-Fe, bcc-Gd, hcp-Gd, bcc-Sm, hcp-Sm and rhombohedral-Sm, were described by the substitutional solution model and their excess Gibbs energies were expressed with the Redlich-Kister polynomial. The intermetallic compounds, α-Fe₁₇Gd₂, β-Fe₁₇Gd₂, Fe₂₃Gd₆, Fe₃Gd, Fe₂Gd, Fe₁₇Sm₂, Fe₃Sm and Fe₂Sm, were modeled as stoichiometric compounds due to their narrow homogeneity ranges. Self-consistent thermodynamic parameters to describe Gibbs energies of various phases in the Fe-Gd and Fe-Sm binary systems were obtained finally. The calculated results in this work are in good agreement with the reported phase equilibria and thermodynamic properties.     

Thermodynamic assessments of binary phase diagrams in organic and polymeric systems

The Sanchez–Lacombe (SL) model and the Flory–Huggins model were used for the calculation of binary phase diagrams in organic and polymer systems, respectively. The thermodynamic parameters of the liquid and gas phases in acetone–carbon disulfide (CS₂), butane–heptane, cyclohexane–aniline systems, and liquid phases in polystyrene–polybutadiene and polystyrene–bisphenol A poly-carbonate systems were optimized, based on the experimental data. The calculated results with various pressures are in good agreement with the experimental data. It is hoped that this method will be widely applied in the prediction of binary phase diagrams in organic and polymer systems.     

Thermodynamic assessment of the RE-B (RE = Ce,Dy, Lu) binary systems

Phase equilibria and thermodynamic properties of Nd-Fe-B-based alloys are fundamental to design novel Nd-Fe-B-based permanent magnets with outstanding magnetic properties and lower costs. In order to develop thermodynamic database of multi-component Nd-Fe-B-based alloys with the rare earth (RE) metals, in this work, the RE-B (RE = Ce, Dy, Lu) binary systems were assessed thermodynamically using the CALPHAD method based on the available phase diagram and thermodynamic data reported in the literature. In the thermodynamic modeling, the solution phases including liquid, bcc, fcc, hcp and rhombohedral, are described as the substitutional solution model and their excess Gibbs energies are described by Redlich-Kister polynomial. The binary intermetallic compounds, CeB₄, CeB₆, DyB₂, DyB₄, DyB₆, DyB₁₂, DyB₆₆, LuB₂, LuB₄, LuB₁₂ and LuB₆₆, are treated as the stoichiometric compounds considering the experimental heat capacities and enthalpy increments of some intermetallic compounds. The calculated results are in good agreement with the reported experimental data.     

Experimental investigation and thermodynamic calculation of the Cu–In–Sb phase diagram

The phase diagram of the Cu–In–Sb ternary system is of importance in predicting the interface reaction between In-based solder materials and the Cu substrate.     

Thermodynamic modeling of the Co-Sm system

The phase diagram of the Co-Sm system has been assessed by applying the Calculation of Phase Diagram (CALPHAD) technique. Thermochemical and phase equilibrium information from the literature have been critically evaluated, and a series of self-consistent thermodynamic parameters capable of describing the Gibbs free energies of each phase of the system has been obtained. There are eight compounds in this system. Based on an analysis of experimental data and the crystal structures of the phases, SmCo₅ was modeled as (Co,V a)_0.833333(Co₂,Sm)_0.166667 and Sm₂Co₁₇ as (Co)_0.833333(Sm)_0.111111(Co₂,Sm)_0.055556. The remaining six intermetallic phases, Sm₃Co,Sm₉Co₄, SmCo₂, SmCo₃, Sm₂Co₇, and Sm₅Co₁₉, were treated as stoichiometric compounds. Calculations based on these parameters can reproduce most of the experimental data very well.     

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.