Thermodynamic modelling of the Al–Co–Fe system

In the present work, the Al–Co–Fe ternary system is thermodynamically modelled using the Calphad method. Experimental data such as liquidus, tie lines, phase boundaries, magnetic transition and order–disorder data points are included and critically examined. The data that has a better quality has been chosen to optimize the system. An order–disorder model has been used to describe the bcc and B2 phases. Experimental bcc/B2 transition data points were carefully examined and inconsistent data points were weighted less. A four-stage optimization was employed to fit the magnetic and bcc/B2 transitions and phase boundaries. The thermodynamic models of Al₅Fe₂, Al₅Co₂, Al₂Fe, and Al₉Co₂ are adjusted to include the third element to reflect the solubility of this element in the ternary system. Ternary interaction parameters for bcc and fcc were optimized, using all the relevant experimental data in the literature. The calculation of isothermal and vertical sections are performed using the optimized model parameters and compared with the experimental data. A comparison between modelling and experimental measurements showed a good agreement between the present results and experiments.     

Thermodynamic assessment of the Fe–V–O system

The Fe–V–O system over the whole composition range was optimized according to the reliable phase equilibria and thermodynamic data. The modified quasichemical model was used to describe the liquid phase from metal alloy to oxide melt. Based upon the Compound Energy Formalism, the FeV₂O₄–Fe₃O₄ spinel solution was described by a sublattice model considering the cation distribution between tetrahedral and octahedral sites. Wüstite, corundum and (VO₂)_s.s. were described using a simple Bragg-Williams model. A set of self-consistent model parameters was obtained and the available phase diagram and thermodynamic data were reproduced well within experimental error limits. The complex phase relations in the Fe–V–O system at various temperatures and oxygen partial pressures were elucidated.     

Thermodynamic modeling of the ZrO system

In this study, the complete zirconium-oxygen system has been critically assessed at 1 at. from 300°C to liquidus temperatures. Thermochemical measurements and phase diagram data were used to model the Gibbs free energies of seven phases. Additionally, the ordered interstitial HCP-based solutions were included and considered as simple line compounds. By using the PARROT module in Thermo-Calc, it was possible to optimize the parameters of the models used to describe the Gibbs free energies of the HCP, BCC, Liquid, γ ZrO_2−x,β ZrO_2−x and α ZrO_2−x phases. The Gas phase was considered to behave ideally. Although phase diagrams including the stoichiometric zirconia phases have been assessed, this is the first time, to the best of our knowledge that a complete assessment of this system is published.     

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 remodeling of the Co–Ga system

The thermodynamic properties and phase relations of the Co–Ga binary system are remodeled based on the CALPHAD approach. In this work, CoGa(β$\beta$) is considered to be non-stoichiometric and CoGa₃ to be stoichiometric. The β$\beta$ phase is thermodynamically described by a two-sublattice model (Co,Ga)_0.5 (Co,V a)_0.5. The stability of the β$\beta$ phase is restricted in the low-temperature regions by giving necessary driving force constraints. The lattice parameters and enthalpy of formation of the β$\beta$ and CoGa₃ phases have been compared with first-principles calculations based on density functional theory. The calculated Co–Ga phase diagram is compared to previously calculated ones.     

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.     

Thermodynamic description of the Co–Ni–Ta system

The temperatures of two invariant reactions λ₃ → fcc(Co) + Co₃Ta and λ₃ → Co₃Ta + λ₂ in the Co–Ta system were identified to be 1320 and 1303 K, respectively, by Differential thermal analysis (DTA). The Co–Ta, Ni–Ta and Co–Ni–Ta systems were optimized using the CALculation of PHAse Diagram (CALPHAD) method based on the present experimental results and literature data. Three Laves phases λ₁, λ₂ and λ₃ were described using a two-sublattice model (Co,Ni,Ta)_0.6667(Co,Ni,Ta)_0.3333, and compound (Co,Ni)Ta was modeled as (Co,Ni,Ta)₁Ta₄(Co,Ni,Ta)₂(Co,Ni,Ta)₆ by a four-sublattice model. A set of reliable and self-consistent thermodynamic parameters was obtained, which can be used for a variety of thermodynamic calculations and database establishment of the Co–Ni-based superalloys.     

Experimental measurements and thermodynamic modeling of the Ce–Co–Fe ternary system

The experimental determinations of the isothermal section at 823 K and the supplementary measurements of the liquidus projection of the Ce-Co-Fe ternary system were presented in the present study. In the Ce-Co-Fe ternary system, in consideration of the temperature dependent solubilities of the linear phases such as Ce₂(Co,Fe)₁₇ and Ce(Co,Fe)₂, as well as the specific locations of the univariant lines between each two primary solidification surfaces, it is necessary to study more than one isothermal section and some particular as-cast alloys to construct the phase equilibria in the temperature-composition space of the Ce-Co-Fe system. The samples for determining the liquidus projection were prepared by arc-melting method under high purity argon atmosphere in a water-cooled copper hearth, and then those for measuring the isothermal section at 823 K were isothermally treated and quenched in ice water. The microstructures and the phase compositions of samples were measured by means of scanning electron microscopy (SEM), X-ray diffraction (XRD) and electron probe micro-analyzer (EPMA). Some primary solidification regions and univariant lines of the Ce-Co-Fe ternary system were complementally determined, and the reasonability of the liquidus projection reported in previous literature was further confirmed. The phase equilibrium relations at 823 K were determined, including two-phase and three-phase equilibria. No ternary compounds were discovered in the present study. Based on the experimental results of both the previous literature reports (the reported liquidus projection and isothermal sections at 723 and 1173 K) and the present experimental study, the Ce-Co-Fe ternary system was thermodynamically assessed using the CALPHAD method. The isothermal sections, the vertical sections and the liquidus projection were calculated using the present optimized thermodynamic parameters, and a reasonable agreement between the calculated results and the experimental data was obtained.     

Thermodynamic description of the Al–Fe–Zr system

The Fe–Zr and Al–Fe–Zr systems were critically assessed by means of the CALPHAD technique. The solution phases, liquid, face-centered cubic, body-centered cubic and hexagonal close-packed, were described by the substitutional solution model. The compounds with homogeneity ranges, hex.- Fe₂Zr, Fe₂Zr, FeZr₂ and FeZr₃ in the Fe–Zr system, were described by the two-sublattice model in formulas such as hex.- Fe₂(Fe,Zr), (Fe,Zr)₂(Fe,Zr), (Fe,Zr)Zr₂ and (Fe,Zr)(Fe,Zr)₃ respectively. The compounds Al_mZr_n except Al₂Zr in the Al–Zr system were treated as line compounds (Al,Fe)_mZr_n in the Al–Fe–Zr system. The compounds FeZr₂ and FeZr₃ in the Fe–Zr system were treated as (Al,Fe,Zr)Zr₂ and (Al,Fe,Zr)(Fe,Zr)₃ in the Al–Fe–Zr system, respectively. All compounds in the Al–Fe system and hex.- Fe₂Zr in the Fe–Zr system have no solubilities of the third components Zr or Al, respectively, in the Al–Fe–Zr system. The ternary compounds _λ1${\lambda }_1$ with C14 structure and _λ2${\lambda }_2$ with C15 structure in the Al–Fe–Zr system were treated as _λ1${\lambda }_1$- (Al,Fe,Zr)₂(Fe,Zr) with Al₂Zr in the Al–Zr system and _λ2${\lambda }_2$- (Al,Fe,Zr)₂(Fe,Zr) with Fe₂Zr in the Fe–Zr system, respectively. And the ternary compounds _τ1${\tau }_1$, _τ2${\tau }_2$ and _τ3${\tau }_3$ in the Al–Fe–Zr system were treated as (Al,Fe)₁₂Zr, Fe(Al,Zr)₂Zr₆ and Fe₇Al₆₇Zr₂₆, respectively. A set of self-consistent thermodynamic parameters of the Al–Fe–Zr system was obtained.