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 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.     

Experimental study and thermodynamic calculation of the Mn-Dy and Mn-Ho binary systems

In this work, twenty-four Mn-Dy and Mn-Ho alloys were investigated experimentally using the differential thermal analysis (DTA), scanning electron microscopy (SEM) and electronic probe microanalysis (EPMA) to study phase equilibria of the Mn-Dy and Mn-Ho binary systems. The temperatures of some invariant reactions and liquidus in the Mn-Dy and Mn-Ho binary systems were determined. Based on the experimental results obtained in the present work and the critical evaluation of the experimental data reported in the literature, the Mn-Dy and Mn-Ho binary systems were calculated using the CALPHAD method. In the thermodynamic calculation, the solution phases including liquid, α(Mn), β(Mn), γ(Mn), δ(Mn), α(Dy), β(Dy), α(Ho) and β(Ho), are treated as the substitutional solution model with the Redlich-Kister formula. The intermetallic compounds, Mn₂Dy, Mn₁₂Dy, Mn₂₃Dy₆, Mn₂Ho, Mn₁₂Ho and Mn₂₃Ho₆, are modeled as the stoichiometric compounds. Self-consistent thermodynamic parameters were obtained finally to describe the Gibbs energies of various stable phases in the Mn-Dy and Mn-Ho binary systems. The calculated results reproduce well the phase equilibria and thermodynamic properties.     

Experimental investigation and thermodynamic assessment of the Fe-Pr and Fe-Nd binary systems

In this work, Fe-Pr alloys and Fe-Nd alloys were investigated experimentally by means of thermal analysis. The temperatures of the invariant reactions and liquidus in the Fe-Pr and Fe-Nd binary systems were measured. Based on the experimental results determined in this work and the critical review of the available experimental data in published literature, the Fe-Pr and Fe-Nd binary systems were re-assessed thermodynamically using the CALPHAD method. The solution phases including liquid, bcc, fcc and dhcp are modeled by the substitutional solution model and their excess Gibbs energies are expressed with the Redlich-Kister polynomial. The intermetallic compounds, Fe₁₇Pr₂, Fe₁₇Nd₂ and Fe₁₇Nd₅ are treated as intermetallic compounds. The self-consistent thermodynamic parameters obtained finally to describe the Gibbs energies of various phases in the Fe-Pr and Fe-Nd binary systems can be used to reproduce well the phase equilibria and thermodynamic data.     

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 description of the Dy–Ni system

The Dy–Ni binary system has been thermodynamically assessed by means of the computer program Thermo-Calc. The Redlich–Kister polynomial was used to describe the solution phase, liquid (L). Ten compounds, Dy₃Ni, Dy₃Ni₂, DyNi, DyNi₂, DyNi₃, Dy₂Ni₇, DyNi₄, Dy₄Ni₁₇, DyNi₅ and Dy₂Ni₇, were treated as stoichiometric phases. The parameters of the Gibbs energy expressions were optimized according to all the available experimental information of both the equilibrium data and the thermodynamic results. A set of self-consistent thermodynamic parameters of the Dy–Ni system has been obtained. The calculations agree well with the respective experimental data.     

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.     

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 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.     

Thermodynamic assessment of the Ce-Pt system

The thermodynamic assessment of the Ce-Pt binary system has been carried out by using the CALPHAD (Calculation of Phase Diagrams) method based on the available literature data including the phase equilibria and thermodynamic properties. The Gibbs free energies of the liquid, bcc_A2 and fcc_A1 phases were described by the subregular solution model with the Redlich-Kister formula, and those of the intermetallic compounds (Ce₇Pt₃, Ce₃Pt₂, Ce₅Pt₄, CePt, Ce₃Pt₄, CePt_x and CePt₅) in the Ce-Pt binary system were described by the sublattice model, and two intermetallic compounds (Ce₅Pt₃,CePt₂) in the Ce-Pt binary system were described by the two-sublattice model. A consistent set of thermodynamic parameters leading to a reasonable agreement between the calculated results and literature data was obtained.     

Thermodynamic reassessment of the Au–Dy system supported by first-principles calculations

Based on the available experimental phase equilibria and thermodynamic data and enthalpies of formation computed via first-principles calculations, thermodynamic reassessment of the Au–Dy system was carried out by means of the CALPHAD method. The enthalpies of formation at 0 K for AuDy₂, αAuDy, βAuDy, Au₂Dy, Au₃Dy, Au₅₁Dy₁₄ and Au₆Dy were computed via first-principles calculations to supply the necessary thermodynamic data for the modeling in order to obtain the thermodynamic parameters with sound physical meaning. The solution phases, i.e. liquid, (Au), (αDy) and (βDy), were described by the substitutional solution model, and all the intermetallic compounds in the Au–Dy system were treated as stoichiometric phases. A set of self-consistent thermodynamic parameters for the Au–Dy system was finally obtained. The calculated phase diagram and thermodynamic properties agree reasonably with the literature experimental data and the present first-principles calculations.     

Thermodynamic assessments of the Er–Sb and Sb–Tm systems

By using the calculation of phase diagrams (CALPHAD) method, thermodynamic assessments of the Er–Sb and Sb–Tm systems were carried out based on the available experimental data including thermodynamic properties and phase equilibria. The Gibbs free energies of the liquid, hcp, and rhombohedral phases in the Er–Sb and Sb–Tm systems were modeled by the substitutional solution model with the Redlich–Kister formula, and the intermetallic compounds (Er₅Sb₃, αErSb, βErSb, ErSb₂, Sb₂Tm, αSbTm, βSbTm, α Sb₃Tm₅, and β Sb₃Tm₅ phases) in these two binary systems were described by the sublattice model. An agreement between the present calculated results and experimental data was obtained.     

Thermodynamic assessment of the B–Ce and B–Pr systems

By using the Calculation of Phase Diagrams (CALPHAD) technique, the thermodynamic assessments of the B–Re (Re: Ce, Pr) binary system were carried out based on the experimental data including thermodynamic properties and phase equilibria. Gibbs free energies of the solution phases (liquid, fcc, bcc, dhcp) were modeled by the subregular solution model with the Redlich–Kister equation, and those of the intermediate compounds (B₄Ce, B₆Ce, B₅Pr₂, B₄Pr, B₆Pr) were described by the two-sublattice model. A consistent set of thermodynamic parameters leading to reasonable agreement between the present calculated results and experimental data was obtained.     

Thermodynamic assessment of the Eu–Pb and Lu–Pb systems

The thermodynamic assessment of the Eu–Pb and Lu–Pb binary systems has been carried out by using the Calculation of Phase Diagrams (CALPHAD) method 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 (Eu₂Pb, Eu₅Pb₃, βEuPb, αEuPb, EuPb₃, Lu₅Pb₃, βLu₅Pb₄, αLu₅Pb₄, Lu₆Pb₅, and LuPb₂) in the binary systems were described by the two-sublattice model. A consistent set of the thermodynamic parameters leading to a reasonable agreement between the calculated results and literature data was obtained.     

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 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 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.