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 assessments of the Er–Sb and Sb–Tm systems

By using the calculation of phase diagrams (CALPHAD) method, thermodynamic assessments of the Er–Sb and Sb–Tm systems were carried out based on the available experimental data including thermodynamic properties and phase equilibria. The Gibbs free energies of the liquid, hcp, and rhombohedral phases in the Er–Sb and Sb–Tm systems were modeled by the substitutional solution model with the Redlich–Kister formula, and the intermetallic compounds (Er₅Sb₃, αErSb, βErSb, ErSb₂, Sb₂Tm, αSbTm, βSbTm, α Sb₃Tm₅, and β Sb₃Tm₅ phases) in these two binary systems were described by the sublattice model. An agreement between the present calculated results and experimental data was obtained.     

Modelling of interstitials in the bcc phase

There are several widespread thermodynamic datasets which produce a spurious bcc interstitial solution at high temperature and high X content (X is an interstitally dissolved element). The reason for this is the standard model for bcc interstitial solutions (M(V a,X)₃), which requires careful selection of optimising parameters to minimise spurious appearances of the bcc phase. In this work the model M(V a,X)₁ is suggested as an alternative. This model is much easier to handle and its parameters can be directly compared with those of the fcc phase. The two models are compared for the Fe–C and Nb–N systems. In the Fe–C system almost identical results are achieved. In Nb–N there are some differences for high N content, but there is no experimental data to clearly support any model.     

Experimental investigation and thermodynamic modeling of the Cu–Mn–Ni system

The phase equilibria of the ternary Cu–Mn–Ni system in the region above 40 at.% Mn at 600 ^°C were investigated by means of optical microscopy, X-ray diffraction, scanning electron microscopy with energy dispersive X-ray spectroscopy and electron probe microanalysis. The isothermal section of the Cu–Mn–Ni system at 600 ^°C consists of 4 two-phase regions (cbcc_A12 +fcc_A1, cub_A13 +fcc_A1, cbcc_A12 + cub_A13, L₁₀$L{1}_0$ +fcc_A1) and 1 three-phase region (cbcc_A12 +cub_A13 +fcc_A1). The disordered fcc_A1 phase exhibits a large continuous solution between γ$\gamma$(Cu,Ni) and γ$\gamma$(Mn). The L₁₀$L{1}_0$ phase only equilibrates with fcc_A1 phase, and the solubility of Cu in L₁₀$L{1}_0$ phase is up to 16 at.%. A thermodynamic modeling for this system was performed by considering reliable literature data and incorporating the current experimental results. A self-consistent set of thermodynamic parameters was obtained, and the calculated results show a general agreement with the experimental data.     

Ab initio calculation of the BCC Fe–Al–Mo (Iron–Aluminum–Molybdenum) phase diagram: Implications for the nature of the phase

The metastable phase diagram of the BCC-based ordering equilibria in the Fe–Al–Mo system has been calculated via a truncated cluster expansion, through the combination of Full-Potential-Linear augmented Plane Wave (FP-LAPW) electronic structure calculations and of Cluster Variation Method (CVM) thermodynamic calculations in the irregular tetrahedron approximation. Four isothermal sections at 1750 K, 2000 K, 2250 K and 2500 K are calculated and correlated with recently published experimental data on the system. The results confirm that the critical temperature for the order–disorder equilibrium between Fe₃Al–D0₃ and FeAl–B2 is increased by Mo additions, while the critical temperature for the FeAl–B2/A2 equilibrium is kept approximately invariant with increasing Mo contents. The stabilization of the Al-rich A2 phase in equilibrium with overstoichiometric B2–(Fe,Mo)Al is also consistent with the attribution of the A2 structure to the τ₂ phase, stable at high temperatures in overstoichiometric B2–FeAl.     

Experimental investigation and thermodynamic reassessment of the Fe–Si–Zn system

Based on the critical evaluation of the experimental data available in the literature, the isothermal section of the Fe–Si–Zn system at 873 K was measured using a combination of X-ray analysis and scanning electron microscopy with energy-dispersive X-ray analysis. No ternary phase is observed at 873 K. A thermodynamic modeling for the Fe–Si–Zn system was then conducted by considering the reliable experimental data from the literature and the present work. All the calculated phase equilibria agree well with the experimental ones. It is noteworthy that a stable liquid miscibility gap appears in the computed ternary phase diagrams although it is metastable in the three boundary binaries.     

First-principles calculation of L10 -disorder phase equilibria for Fe–Ni system

By combining Cluster Variation Method with FLAPW electronic structure total energy calculations and the Debye–Grüneisen theory within quasi-harmonic approximation, L1₀-disorder phase equilibria for Fe–Ni system are calculated. The transition temperature, 483 K, determined in the present calculation is lower than that obtained in the previous calculation without thermal vibration effects. The decrease of the transition temperature is ascribed to the enhanced phase stability of a disordered phase due to the thermal softening of a lattice.     

Phase equilibria in the Au–In–Sn ternary system

Phase equilibria of the Au–In–Sn system have been investigated by Differential Scanning Calorimetry (DSC), metallographic examination, Scanning Electron Microscopy (SEM) and Energy Dispersive X-ray Spectroscopy (EDS) measurements. The 130 ^°C isothermal section of the phase diagram was studied. The ternary diagram shows six three-phase fields, and one ternary Au₄In₃Sn₃ phase, which melts incongruently at 382 ^°C and shows a homogeneity range between 21 and about 30 at.% In, at constant Au/Sn ratio.     

Experimental study and thermodynamic remodeling of the Bi–Cu–Ni system

Phase equilibria in the Bi–Cu–Ni ternary system have been studied using differential thermal analysis (DTA) as well as by using the calculation of the phase diagram (CALPHAD) method. Literature experimental phase equilibria data and DTA results from this study were used for thermodynamic modeling of the Bi–Cu–Ni ternary system. Isothermal sections at 300, 400, and 500 °C, vertical sections from bismuth corner with molar ratio Cu:Ni=1/3, 1/1 and 3/1 and vertical section at 40 at.% Cu were calculated and compared with corresponding experimental results. Reasonable agreement between the calculated and experimental data was observed in all cases.