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 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 description of the Ti–H system

Previous thermodynamic assessments of the Ti–H system are reviewed, and a new evaluation is carried out by taking into account the liquid phase in the system using the associate solution model. The sublattice model is utilized to depict the interstitial solution phases with various lattice ratios. The model parameters are optimized in the least square procedure by selecting most reported equilibrium solubility and thermochemical data of the Ti–H system. It is demonstrated that a credible set of thermodynamic parameters well describing the whole Ti–H system is obtained. With these parameters, the behavior of the Ti–H system was predicted at higher pressures of 10, 100 and 370 atm.     

Thermodynamic description of the Cr–Ge system

The Cr–Ge binary system was thermodynamically optimized using the CALPHAD method. The liquid phase was described by means of an associate solution model. The BCC terminal solid solution was described by the substitutional solution model. The two-sublattice model was used to describe the non-stoichiometric compounds Cr₃Ge, αCr₅Ge₃ and βCr₅Ge₃. The Cr₁₁Ge₈, CrGe and Cr₁₁Ge₁₉ phases were modeled as stoichiometric compounds. A set of thermodynamic parameters for the Cr–Ge system was obtained via thermodynamic optimization using assessed experimental data. The calculated phase diagram and thermodynamic properties agree well with most of the experimental data.     

Thermodynamic description of the Ni–Sc system

The Ni–Sc system was thermodynamically assessed by the CALPHAD approach based on the available experimental data including the thermodynamic properties and phase equilibria. The excess term of the Gibbs energy of the solution phases (liquid, b.c.c., f.c.c. and h.c.p.) was assessed with the recent exponential temperature dependence of the interaction energies by Kaptay (Calphad 28–2 (2004) 115–124; Calphad 32–2 (2008) 338–352; Mat. Sci. Eng. A 495 (2008) 19–26) and compared with Redlich and Kister (Ind. Eng. Chem. 40 (1948) 345–348) polynomial equation results. The intermetallic compound Ni₂Sc in this binary system which has a homogeneity range, was treated by a two-sublattice model (Sundman et al., Calphad 9 (1985) 153–190; Hillert and Staffansson, Acta Chem. Scand 24 (1970) 3618). The others compounds were modeled as stoichiometric. A consistent set of thermodynamic parameters was optimized to give account of the available experimental and thermodynamic data.     

Experimental investigation and thermodynamic description of the Fe–Mo–Zr system

The phase relations at 1273 K and liquidus surface projection of the Fe–Mo–Zr system were investigated by means of electron probe micro-analyzer (EPMA), scanning electron microscopy coupled with energy dispersive spectroscopy (SEM-EDS) and X-ray diffraction (XRD) methods. The composition range of C14 Laves phase was determined at 1273 K. The maximum solubility of Mo in C15–Fe₂Zr, Mo in Fe₂₃Zr₆, Fe in C15–Mo₂Zr and Zr in μ phase is about 4.8, 0.6, 17.7 and 4.6 at.% at 1273 K, respectively. The isothermal section at 1273 K of the Fe–Mo–Zr system on the whole composition ranges was constructed using 30 annealed alloys. In the liquidus surface projection, the primary solidification phase regions of bcc(Fe), C15–Fe₂Zr, C14, μ, R, σ, bcc(Zr), C15–Mo₂Zr and bcc(Mo) were experimentally confirmed using 31 as-cast alloys. Based on the experimental data in literature and the present work, the Fe–Mo–Zr system was optimized using CALPHAD method, and a set of self-consistent reliable thermodynamic parameters was obtained.     

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.     

Thermodynamic description of the Mg–Eu binary system

Thermodynamic assessment of the Mg–Eu binary system has been carried out by combining first-principles calculations and Miedema’s theory with CALPHAD method. Firstly, the mixing enthalpy of the liquid alloys was calculated by using Miedema’s theory, and formation enthalpies of the intermetallic compounds were calculated by using the projector augmented-wave (PAW) method within the generalized gradient approximation (GGA). Subsequently, the liquid phase was described employing a simple substitutional model, of which the excess Gibbs energy was formulated with a Redlich-Kister expression. And the solubility of Eu in HCP_(Mg) and Mg in BCC_(Eu) were neglected. While the intermetallic compounds Mg₁₇Eu₂, Mg₅Eu, Mg₄Eu, Mg₂Eu and MgEu, were treated as stoichiometric compounds. Consequently, a set of self-consistent thermodynamic parameters for all stable phases in the Mg–Eu binary system were obtained, which can reproduce most of the thermodynamic and phase boundary data.     

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 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 assessment of the Al–Cu–Er system

The Cu–Er binary system had been thermodynamically assessed with the CALPHAD approach. The solution phases including Liquid, Fcc and Hcp were treated as substitutional solution phases, of which the excess Gibbs energies were formulated with the Redlich–Kister polynomial function. All the binary intermetallic compounds were treated as stoichiometric phases. Combining with the thermodynamic parameters of the Al–Cu and Al–Er binary systems cited from the literature, the Al–Cu–Er ternary system was thermodynamically assessed. The calculated phase equilibria were in good agreement with the experimental data.     

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.     

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.