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.     

Thermodynamic assessment of the Ni–Sc binary system

On the basis of the experimental data of the phase equilibria and the thermochemical properties, a critical evaluation for the Ni–Sc binary system has been carried out using the CALPHAD (Calculation of Phase Diagrams) method. The associated model is used for the liquid phase containing the constituent species Ni, Sc and ScNi. The terminal solid solutions Fcc_A1 (Ni), Hcp_A3 (Sc), and Bcc_A2 (Sc) are described by the solution model with the Redlich–Kister polynomial. The intermetallic compounds, ScNi₅, Sc₂Ni₇, ScNi and Sc₂Ni, are treated as strict stoichiometric compounds. The compound with a homogeneity range, (ScNi₂), is modeled using two sublattices as (Sc,Ni)_0.333(Sc,Ni)_0.667. A set of self-consistent thermodynamic parameters for the Ni–Sc binary system is obtained. The calculated results agree well with the available experimental data from literatures.     

Experimental investigation and thermodynamic modeling of the Ni–Ti–V system

The liquidus surface projection and isothermal section at 1273 K of the Ni–Ti–V system were established using X-ray diffraction (XRD), scanning electron microscopy (SEM) coupled with energy dispersion spectroscopy (EDS), electron probe micro-analyzer (EPMA) and differential thermal analysis (DTA) techniques. Six primary solidification regions and four invariant reactions were deduced in the liquidus surface projection, and six three-phase regions were derived in the isothermal section at 1273 K. No ternary compound was observed. According to the experimental results in the present work and literatures, the Ni–Ti–V system was modeled by means of the CALPHAD (CALculation of PHAse Diagram) method. Two-sublattice model (Ni,Ti)₁₀(Ni,Ti)₂₀ for binary σ phase was used, and the thermodynamic parameters of the σ and NiV₃ phases in the Ni–V system was reassessed. Solution phases (liquid, fcc, bcc and hcp) were modeled with the substitutional solution model in the Ni–Ti–V system. The compounds, Ni₃Ti, NiTi₂, Ni₃V and σ, were treated as (Ni,Ti,V)_m(Ni,Ti,V)_n, and B2 were treated as (Ni,Ti,V)_0.5(Ni,Ti,V) _0.5Va₃. A set of self-consistent thermodynamic parameters of individual phases was obtained.     

Reinvestigation of the phase diagram of the Dy–Ga binary system

The phase diagram of the Dy–Ga binary system was reinvestigated by differential scanning calorimetry (DSC) and X-ray diffraction (XRD) analysis. The existence of the compounds Dy₅Ga₃, DyGa, DyGa₂, DyGa₃ and DyGa₆ was confirmed at low temperature in this system. A new high temperature intermetallic compound may exist between DyGa and DyGa₂ at a temperature range between 1217 and 1295 ^°C. No polymorphic transition was found for DyGa₃. The phase diagram of the Dy–Ga binary system was constructed and modified.     

A thermodynamic assessment of Ni–Sb system

The Ni–Sb system was critically assessed by means of the CALculation of PHAse Diagram (CALPHAD) technique. The solution phases, Liq and (αNi), were modelled as the substitutional solutions with the Redlich–Kister equation. The intermediate phases, (γNiSb) and (βNi₃Sb), with homogeneity ranges were described respectively using three-sublattices (Sb)_1/3(Ni%,V a)_1/3(V a%,Ni)_1/3 and (Sb)_1/4(Ni%,V a)_1/2(Ni%,V a)_1/4 based on their structure features. Corresponding to the phase (βNi₃Sb), the two low-temperature phases of (δNi₃Sb) and (θNi₅Sb₂) with narrow homogeneity ranges were modelled as two-sublattice, (Ni)_3/4(Sb,Ni)_1/4 and (Ni)_5/7(Sb,Ni)_2/7. The intermetallic compound ζNiSb₂ with no homogeneity ranges was treated as stoichiometric compound. The phase ε$\epsilon$Sb was considered as pure Sb for the solubility of Ni in ε$\epsilon$Sb is very low. A set of self-consistent thermodynamic parameters of the Ni–Sb system was obtained. The optimized phase diagram and thermodynamic properties were presented and compared with experimental data.     

Elastic and thermodynamic properties of the Ni–B system studied by first-principles calculations and experimental measurements

The elastic and thermodynamic properties of NiB, Ni₂B, Ni₃B, orthorhombic Ni₄B₃(O–Ni₄B₃), monoclinic Ni₄B₃(M–Ni₄B₃), and Ni₂₃B₆, are calculated via first-principles method for the Ni–B system. The ground state energies, the full sets of elastic constants and the associated macroscopic elastic parameters of these Ni–B alloys are computed for the first time. Taking contributions from lattice vibrations and thermally excited electrons into account, thermodynamic properties at finite temperatures are then predicted. In addition, we measure the molar heat capacity at constant pressure for NiB and compare the results with the theoretical predictions. Various calculations demonstrate that the first-principles calculation can be used to clarify the diverse experimental data, and provide reliable thermodynamic data.     

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.     

Refinement of the thermodynamic modeling of the Nb–Ni system

The Nb–Ni system is reassessed on the basis of a critical literature review involving recent experimental data. These newly published experimental data include the phase relation associated with the NbNi₈ phase, phase transition temperatures resulting from selected alloys, all invariant reaction temperatures, and enthalpies of mixing of liquid, as well as the crystallographic data on the μ$\mu$ (Nb₇Ni₆) phase. A consistent thermodynamic data set for the Nb–Ni system is obtained by optimization of the selected experimental values. The calculated phase diagram, crystallographic properties and thermodynamic properties agree reasonably with the experimental data. Noticeable improvements have been made, compared with the previous thermodynamic optimizations.     

Experimental investigation and thermodynamic description of the Ni–Ti–W system

The liquidus surface projection and isothermal sections at 1173 and 1373 K of the Ni–Ti–W system were constructed on the basis of microstructure and phase constituents of as-cast and annealed alloys, which were obtained by means of scanning electron microscopy (SEM) coupled with energy dispersion spectroscopy (EDS), X–ray diffraction (XRD). Six primary solidification regions were determined in the liquidus surface projection. Five and six three-phase regions were derived in the isothermal sections at 1173 and 1373 K, respectively. No new ternary compounds were found. Based on the present experimental data, the Ni–Ti–W system was optimized using CALPHAD (CALculation of PHase Diagram) method. The solution phases, liquid, fcc, bcc, and hcp, were treated as substitutional solution. Two compounds Ni₃Ti and NiTi₂ were treated as (Ni,Ti,W)_m(Ni,Ti,W)_n, and Ni₄W was treated as (Ni,Ti)₄W₁ by a two-sublattice model. NiTi with B2 crystal structure was treated as the ordered phase of bcc solution, and model was (Ni,Ti,W)_0.5(Ni,Ti,W)_0.5(Va)₃. A set of self-consistent thermodynamic parameters was obtained.     

Thermodynamic re-assessment of the Fe-Dy and Fe-Tb binary systems

In this work, based on the critical evaluation of previous optimizations and available experimental data in the published literature, the Fe-Dy and Fe-Tb binary systems were re-assessed thermodynamically using the CALPHAD method. The solution phases including liquid, fcc-Fe, bcc-Fe, bcc-Dy, bcc-Tb, hcp-Dy and hcp-Tb, were described by the substitutional solution model and their excess Gibbs energies were expressed with the Redlich-Kister polynomial. Due to their narrow homogeneity ranges, the intermetallic compounds, Fe₁₇Dy₂, Fe₂₃Dy₆, Fe₃Dy, Fe₂Dy, Fe₁₇Tb₂, Fe₂₃Tb₆, Fe₃Tb and Fe₂Tb, were modeled as stoichiometric compounds. Self-consistent thermodynamic parameters to describe the Gibbs energies of various phases in the Fe-Dy and Fe-Tb binary systems were obtained finally. The calculated results are in good agreement with the reported phase equilibria and thermodynamic properties.     

Thermodynamic modeling of the C–Pu–U system

The ternary C–Pu–U system is thermodynamically assessed to pursue the development of a thermodynamic database for future nuclear fuels. The substitution model was used for the liquid phase, and a two-sublattice model for the PuC–UC monocarbide, PuC₂–UC₂ dicarbide and Pu₂C₃–U₂C₃ sesquicarbide phases. Ternary interaction parameters were adjusted on the experimental information for the phase relationships. Isoplethal and isothermal ternary sections, as well as some liquidus temperatures are calculated and compared with the experimental data. The overall agreement is discussed, and shows that experimental uncertainties still remain.