A thermodynamic description and phase relationships of the FeCr system: Part I the BCC phase and the sigma phase

A generalized approach which was applied successfully to account for the magnetic contribution to the thermodynamic properties of FeNi is applied to FeCr. The predicted magnetic specific heats for two bcc alloys at x_Cr = 0.16 and 0.21 are in good agreement with the experimental data available in the literature. The magnetic Gihbs energy, enthalpy and entropy for the bcc phase are obtained accordingly. The nonmagnetic thermodynamic properties of the bcc phase are obtained primarily from thermochemical data as well as those for the sigma phase. The calculated stable and metastable equilibria involving the bcc and sigma phases are in reasonable agreement with data reported in the literature. The calculated metastable miscibility gap of the bcc phase is highly asymmetric and the calculated spinodals show unusual features.     

Thermodynamic assessment of the Co–Cr–Fe system and atomic mobility study of its fcc phase

In the present work, the Co–Cr–Fe system was thermodynamically assessed by using the CALPHAD approach coupled with first-principles calculations and experimental data from the literature. Subsequently, the fcc Co–Cr–Fe ternary diffusion couples annealed at 1273 and 1473K were scanned by using electron probe microanalysis (EPMA) to obtain the composition profiles, from which the interdiffusion coefficients were extracted by the Whittle-Green method. Based on these interdiffusion coefficients and present thermodynamic parameters, the atomic mobilities of Co, Cr, and Fe in the fcc Co–Cr–Fe alloys were assessed by means of DICTRA software. The calculated interdiffusion coefficients, composition profiles and diffusion paths of the fcc Co–Cr–Fe alloys were consistent with the experimental data, which verifies the accuracy of the assessed atomic mobilities.     

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 assessment of the Ni–Co–Cr system and Diffusion Study of its fcc phase

In the present work, the liquidus and solidus for a series of Ni_xCo_1-2xCr_x alloys were measured by means of differential scanning calorimetry, and the first-principles calculations were performed to obtain total energies for all solid solutions and end-members of the intermediate phases in the Ni–Co–Cr ternary system. Various types of data from the present work and the literature were used in the assessments of the Ni–Co–Cr ternary system and sub-binary systems by the CALPHAD method, and were well reproduced by the present thermodynamic database. In addition, diffusion couples of fcc Co–Cr and Ni–Co–Cr alloys were assembled and annealed at different temperatures to extract interdiffusion coefficients. Experimental diffusion data from the present work and the literature, in conjunction with thermodynamic parameters, were adopted to assess the atomic mobilities of the fcc phase in the Ni–Co–Cr system. The calculated and experimental diffusion coefficients reach a satisfactory agreement. The diffusional kinetic database developed was further validated by appropriate predictions of composition profiles and diffusion paths.     

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.     

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.     

A thermodynamic evaluation of the FeMoC system

A new evaluation of the Fe-Mo-C system has been made using a sublattice model and including the magnetic effect. A set of parameter values describing the Gibbs energy of each individual phase was determined with a computerized optimization technique. It gives satisfactory agreement with the experimental information over a wide temperature range. Several diagrams and tables concerning phase equilibria are presented.     

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.     

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 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 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 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.