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 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 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 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 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 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.