Thermodynamic evaluation of the Al–V–C system

The Al–V–C system contains the two ternary compounds V₂AlC and V₄AlC₃ which are of considerable interest for high-temperature applications. The system is so far rather sparsely investigated experimentally and melting temperatures are not known, though expected to be high. Using the information available, including energies of the formation of the ternary compounds calculated by ab initio methods, it was possible to model the system thermodynamically using the Calphad method. The results are presented in the form of isothermal sections and a liquidus surface. The congruent melting temperatures of V₂AlC and V₄AlC₃ are predicted to be 2790 and 2834 K, respectively.     

Liquidus projection of the Al–Nb–V system

In the present work, the liquidus projection of the Al–Nb–V system is proposed for the first time. It corresponds to important data for the design of innovative low-density Al-containing refractory high-entropy alloys. Experimental investigation was carried out via microstructural characterization of fifty-six alloys in as-cast state using scanning electron microscopy (SEM), electron dispersive X-ray spectroscopy (EDS) and X-ray diffractometry (XRD). Results showed no signs of ternary phases and only primary precipitation fields from binary phases were observed. The BCC primary precipitation field is dominant, while V₅Al₈ primary precipitation field is restricted to a small region close to Al–V binary. Three class II (U_I, U_II and U_III) ternary invariant reactions were proposed.     

Thermodynamic modeling of the C–Pu system

The thermodynamic modelling of the binary C–Pu system was performed in the framework of the development of a thermodynamic database for nuclear materials, for increasing the knowledge of the physico-chemical behaviour of the fuel and surrounding materials implicated in GFR (gas cooled fast reactor) systems. The critical assessment was carried out using the CALPHAD approach, based on available experimental data on phase diagram and thermodynamic properties of the solid phases.     

Thermodynamic modeling of the Mo–Ni system

Thermodynamic stability of the MoNi₂ and MoNi₈ compounds has been discussed in detail, and decision about their inclusion in thermodynamic assessment of the Mo–Ni system has been made. Enthalpies of formation of all Mo–Ni intermetallic compounds have been determined with the help of DFT calculations whereas enthalpies of mixing in the solid solutions are estimated using special quasi-random structures. Experimental phase equilibria information gathered in our recent partial investigation of the Mo–Ni system has been incorporated and thermodynamic reassessment of the Mo–Ni system has been performed with the help of the CALPHAD method. The calculated Mo–Ni phase diagram showed good agreement with selected experimental information.     

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 modeling of the Co–Fe–O system

As a part of the research project aimed at developing a thermodynamic database of the La–Sr–Co–Fe–O system for applications in Solid Oxide Fuel Cells (SOFCs), the Co–Fe–O subsystem was thermodynamically re-modeled in the present work using the CALPHAD methodology. The solid phases were described using the Compound Energy Formalism (CEF) and the ionized liquid was modeled with the ionic two-sublattice model based on CEF. A set of self-consistent thermodynamic parameters was obtained eventually. Calculated phase diagrams and thermodynamic properties are presented and compared with experimental data. The modeling covers a temperature range from 298 K to 3000 K and oxygen partial pressure from 10⁻¹⁶ to 10² bar. A good agreement with the experimental data was shown. Improvements were made as compared to previous modeling results.     

Thermodynamic re-assessment of the Al–Ir system

The thermodynamic assessment of the Al–Ir binary system was performed using the CALPHAD technique. The B2-AlIr phase was described, using the two sublattice model with the formula (Al,Ir,V a)_1/2(Al,Ir,V a)_1/2, while Al₉Ir₂, Al₃Ir, Al₁₃Ir₄, Al₄₅Ir₁₃, Al₂₈Ir₉, and Al_2.7Ir compounds were treated as stoichiometric compounds. The fcc-based phases (L1₀-AlIr, L1₂-Al₃Ir, L1₂-AlIr₃ and A1) were described using the four sublattice model with the formula, (Al,Ir)_1/4(Al,Ir)_1/4(Al,Ir)_1/4(Al,Ir)_1/4. From ab initio calculations (VASP) the formation enthalpies of the stable/metastable intermetallic phases involved in the Al–Ir system were estimated. The thermodynamic quantities, such as the phase equilibria, invariant reactions, and formation enthalpies of the intermetallic phases, were calculated using the obtained parameter set, and agree well with experimental data.     

Thermodynamic modeling of B–Mo–Nb ternary system with modified B–Nb description

Based on a critical evaluation of the literature data, the B–Mo–Nb ternary system has been assessed by means of the CALPHAD (CALculation of PHAse Diagrams) technique. There is no ternary compound reported in this system. According to their crystal structures, the substitutional solution is adopted to model the ternary liquid, and the sublattice models are used to describe the Mo₂B, αMoB, (Mo,Nb)B, (Mo,Nb)B₂, Mo₂B₅, MoB₄, Nb₃B₂, Nb₅B₆, Nb₃B₄, Nb₂B₃, (Mo,Nb) and (B) phases. The modeling covers the whole composition and temperature ranges. Due to the same crystal structure, the sublattice model of the NbB phase in the B–Nb binary system is adjusted as (Me,Va)_0.5(B,Va)_0.5, in order to be consistent with the βMoB phase in the B–Mo binary system. The obtained thermodynamic parameters of the B–Mo–Nb system are demonstrated to be self-consistent and reasonable by adequately comparing the calculated and reported thermodynamic information and phase diagram. Based on the present thermodynamic parameters, the liquidus projection and reaction scheme of B–Mo–Nb system are presented.     

Thermodynamic description of the Al−Fe−Nb system

The Al−Fe−Nb system was critically assessed by means of the CALPHAD technique. The solution phases (liquid, face-centered cubic and body-centered cubic) were modeled with the Redlich–Kister equation. The thermodynamic models of compounds Al₁₃Fe₄, Al₂Fe and Al₅Fe₂ in the Al–Fe system and Al₃Nb and AlNb₃ in the Al–Nb system kept consistent with ones in the corresponding binary systems. The Fe₂Nb and μ in the Fe–Nb system, Al₈Fe₅ in the Al–Fe system, and AlNb₂ in the Al–Nb system were treated as the formulae (Al,Fe,Nb)₂(Fe,Nb), (Al,Fe,Nb)₁Nb₄(Fe,Nb)₂(Al,Fe,Nb)₆, (Al,Fe,Nb)₈(Al,Fe,Nb)₅ and (Al,Nb)_0.533(Al,Fe,Nb)_0.333Nb_0.134, respectively. B2 phase was treated as the ordered phase of bcc phase with the thermodynamic models (Al,Fe,Nb)_0.5(Al,Fe,Nb)_0.5(Va)₃ and (Al,Fe,Nb)_0.25(Al,Fe,Nb)_0.25(Al,Fe,Nb)_0.25(Al,Fe,Nb)_0.25(Va)₃. On the basis of optimized thermodynamic parameters of Al–Fe, Al–Nb and Fe–Nb systems in literature, the Al–Fe–Nb system was optimized in the present work. One set of self-consistent thermodynamic parameters of the Al–Fe–Nb system was obtained corresponding to B2 ordered phase with two kinds of thermodynamic model. Five experimental isothermal sections at 1073, 1273, 1423, 1573 and 1723 K, and the liquidus surface projection were well reproduced in the present work.     

Thermodynamic modeling of the Ta–Mo–C ternary system

The Ta–Mo–C system was assessed by means of the CALPHAD approach. All of the phase diagram and thermodynamic information available from the literature were critically reviewed. The liquid was modeled as substitutional solution phase, while the carbides including fcc-(Mo,Ta)C_1-x, bcc-(Mo,Ta), hcp-(Mo,Ta)₂C and η-MoC were described by using corresponding sublattice models. The ζ-Ta₄C_3-x was considered as a linear compound with carbon content fixed, while shp-MoC was treated to be a binary stoichiometric phase. There was no ternary compound reported in this system. The modeling of Ta–Mo–C ternary system covers the entire composition and temperature ranges, and a set of self-consistent thermodynamic parameters for the Ta–Mo–C system was systematically optimized. Comprehensive comparisons between the calculated and reported phase diagram and thermodynamic data show that the reliable information is satisfactorily accounted for by the present modeling. The liquidus projection and reaction scheme of the Ta–Mo–C system were also generated by using the present thermodynamic parameters.