Thermodynamic reassessment of the Mo–Hf and Mo–Zr systems supported by first-principles calculations

Based on the experimental phase equilibria and thermodynamic data available in the literature and enthalpies of formation computed from first-principles calculations, the thermodynamic reassessment of the Mo–Hf and Mo–Zr systems was carried out by means of the CALPHAD (CALculation of PHAse Diagram) method. The enthalpies of formation for stable and metastable Laves (C15, C36, C14) phases and enthalpy of mixing for the β(bcc) solid solution phase in dilute solution were predicted via first-principles calculations to supply the necessary thermodynamic data for the modeling in order to obtain the thermodynamic parameters with physical sound meaning. The relative stability of Laves C14, C15 and C36 in the systems was discussed. The solution phases, i.e. liquid, β(bcc) and α(hcp) were described by the substitutional solution model, and all the Laves phases in the systems were described using two sublattice model. A set of self-consistent thermodynamic parameters were obtained for these binary systems, which agrees well with the experimental data in the literature. Based on these results, the trend of the site occupancy fraction of Laves phase changing with temperature was predicted. The isothermal section and the liquidus projection of Mo-Hf-Zr system were also predicted by combing with the Zr–Hf system reported in the literature.     

Thermodynamic assessment of the V–Zn system supported by key experiments and first-principles calculations

The V–Zn system was investigated by a combination of CALPHAD modeling with key experiments and first-principles calculations. Based on a critical literature review, one diffusion couple and nine alloys were designed to reinvestigate the stabilities of the phases reported in the literature. The samples were annealed and cooled under different conditions, followed by examination with X-ray diffraction and scanning electron microscopy with energy-dispersive X-ray spectrometry. Four phases ((V), (Zn), V Zn₃ and V ₄Zn₅) were confirmed to exist in the phase diagram, while V Zn₁₆ and V ₃Zn were not observed. By means of first-principles calculations, the enthalpies of formation for V Zn₃ and V ₄Zn₅ were computed to be −4.55 kJ mol-atoms⁻¹ and −4.58 kJ mol-atoms⁻¹, respectively. A set of self-consistent thermodynamic parameters for this system was obtained by considering the reliable experimental phase diagram data and the enthalpies of formation acquired from first-principles calculations. The calculated V–Zn phase diagram agrees well with the experimental data.     

Thermodynamic reassessment of the Cu–V system supported by key experiments

The temperature of the degenerated invariant reaction in the Cu–V system was accurately determined by means of Differential Scanning Calorimetry (DSC) measurements. On the basis of the experimental data from the present work and those critically assessed from the literature, an optimal thermodynamic data set for the Cu–V system was obtained. Significant improvements have been made, compared with the previous assessments.     

Thermodynamic assessment of the Sr–In and Sr–Bi systems supported by first-principles calculations

Based on the available experimental phase equilibria and thermodynamic data, the Sr–In and Sr–Bi systems have been assessed by means of the CALPHAD technique. The solution phases (Liquid, (αSr), (βSr), (In) and (Bi)) were modeled with the Redlich–Kister polynomial. All the intermetallic compounds (SrIn₅, SrIn₃, Sr₂In₅, SrIn₂, Sr₂In₃, SrIn, Sr₅In₃, Sr₃In, SrBi₃, Sr₁₁Bi₁₀, αSr₅Bi₃, βSr₅Bi₃ and Sr₂Bi) were treated as stoichiometric compounds. The enthalpies of formation at 0 K for SrIn₅, SrIn₃, SrIn₂, SrIn, Sr₅In₃, Sr₃In, SrBi₃, αSr₅Bi₃, βSr₅Bi₃ and Sr₂Bi were computed by first-principles calculations in order to assist the thermodynamic modeling. A set of self-consistent thermodynamic parameters for each of the two systems has been obtained, and the present calculations can satisfactorily reproduce the available experimental data.     

Thermodynamic assessment of the Au–Pb system

The Au–Pb system has been thermodynamically assessed by the CALPHAD method. The excess Gibbs energies of the solution phases were modeled assuming random mixing of components, while the three intermetallic phases were described as stoichiometric compounds. Based on the experimental phase diagram and thermochemical data, a set of self-consistent parameters describing all phases in this system has been obtained.     

Thermodynamic modeling of the V–Si system supported by key experiments

The V–Si system is reassessed based on a critical literature review involving recently reported data and the present experimental data. These new data include the thermodynamic stability of V ₆Si₅ and the enthalpies of formation for the compounds calculated by first-principles method. Two alloys were prepared in the region of (Si)+V Si₂ and annealed at 1273 K for 14 days. After X-ray diffraction (XRD) and chemical analysis of these alloys were performed, the eutectic reaction (L⇔(Si)+V Si₂) temperature was determined by differential thermal analysis (DTA). Self-consistent thermodynamic parameters for the V–Si system were obtained by optimization of the selected experimental values. The calculated phase diagram and thermodynamic properties agree well with the experimental ones. Noticeable improvements have been made, compared with the previous assessments.     

Thermodynamic calculations of the Au–Sc and Fe–Sc systems

Thermodynamic optimization of the Au–Sc and Fe–Sc systems was carried out by means of the CALPHAD (CALculation of PHAse Diagram) method on the basis of the available experimental data in literature. Redlich–Kister polynomials were used to describe the excess Gibbs energy of solution phases, and all the compounds are treated as stoichiometric ones. The Au–Sc system was described thermodynamically for the first time, and the Fe–Sc system was re-optimized by considering the new experimental data about enthalpies of mixing of the liquid phase. A set of self-consistent parameters was obtained for each of these two binary systems, respectively.     

Thermodynamic assessment of the Ga–X (X=B,Ca, Sr,Ba) systems supported by first-principles calculations

Thermodynamic modeling of the Ga–X (X=B, Ca, Sr, Ba) systems was performed based on the available experimental information and first-principles calculations. Enthalpies of formation for the compounds (Ca₂₈Ga₁₁, Ca₅Ga₃, Ca₁₁Ga₇, CaGa, Ca₃Ga₅, CaGa₂, Ca₃Ga₈, CaGa₄, Ga₄Sr, Ga₂Sr, Ga₇Sr₈, Ba₈Ga₇, BaGa₂ and BaGa₄) at 0 K were computed by ab initio methods, and were used to improve the accuracy of the present assessment. A set of self-consistent thermodynamic parameters was obtained. The computed phase diagrams and thermodynamic properties of the Ga–X (X=B, Ca, Sr, Ba) systems agree well with the experimental data and first-principles calculations.     

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.