Development of a metastable phase diagram to describe solidification in undercooled Fe–Co melts

Droplets of Fe–0.3Co and Fe–0.5Co (at. fraction) alloys were undercooled using the electromagnetic levitation technique. Temperature–time profiles revealed that above a critical undercooling, a metastable phase formed on solidification which transformed back to the equilibrium phase during recalescence. A metastable phase diagram for Fe–Co was calculated by extending the liquidus and solidus lines of the δ$\delta$-ferrite (bcc) phase beyond the equilibrium composition range. Two parameters in the thermodynamic database were then altered so that the metastable solidus line fitted well to the metastable solidus temperature measured from the levitation experiments. The adjusted database was shown to have good agreement with both equilibrium and metastable experimental data and the parameters for bcc Co were shown to be reasonable. The activation energy for formation of a spherical nucleus was calculated using values of free energy and entropy from the adjusted database. The results showed that the metastable bcc phase has a lower activation energy for nucleation than the stable fcc phase below a critical level of undercooling. The experimentally measured critical undercooling was in good agreement with the calculated value.     

Study of diffusion mobilities of Nb and Zr in bcc Nb–Zr alloys

On the basis of the available thermodynamic parameters, the atomic mobilities of Nb and Zr in bcc Nb–Zr alloys are critically assessed as functions of temperatures and compositions by the CALPHAD method, where self-diffusion coefficients, impurity diffusion coefficients, tracer diffusion coefficients, interdiffusion coefficients and concentration curves are simultaneously optimized. Comparisons between the calculated and experimentally measured diffusion coefficients are made, where good agreement is evident. In addition, the obtained mobility parameters can reproduce a reasonable concentration profile for the Nb/Zr diffusion couple annealed at 1868 K for 5400 s.     

Refinement of the thermodynamic modeling of the Nb–Ni system

The Nb–Ni system is reassessed on the basis of a critical literature review involving recent experimental data. These newly published experimental data include the phase relation associated with the NbNi₈ phase, phase transition temperatures resulting from selected alloys, all invariant reaction temperatures, and enthalpies of mixing of liquid, as well as the crystallographic data on the μ$\mu$ (Nb₇Ni₆) phase. A consistent thermodynamic data set for the Nb–Ni system is obtained by optimization of the selected experimental values. The calculated phase diagram, crystallographic properties and thermodynamic properties agree reasonably with the experimental data. Noticeable improvements have been made, compared with the previous thermodynamic optimizations.     

A thermodynamic description of the Gd–Mg–Sm system

The Mg–Sm, Gd–Sm and Gd–Mg–Sm systems were thermodynamically optimized using the CALPHAD technique. The solution phases, liquid, bcc, hcp and rhombohedral, were described by the substitutional solution model. The isostructural compounds, MgGd in the Gd–Mg system and MgSm in the Mg–Sm system with a B2 structure was assumed to form a continuous range of solid solutions in the Gd–Mg–Sm system. The order–disorder transition between the bcc solution with an A2 structure and compound Mg(Gd, Sm) with a B2 structure in the system has been taken into account and thermodynamically modeled. The other isostructural compounds Mg₅Gd and Mg₅Sm, Mg₃Gd and Mg₃Sm, Mg₂Gd and Mg₂Sm in the Gd–Mg–Sm system were described according to the formulae Mg₅(Gd,Sm), Mg₃(Gd,Sm), and Mg₂(Gd,Sm), respectively. The compound Mg₄₁Sm₅ with a homogeneity range was treated as a line compound Mg₄₁(Gd,Sm)₅ in the Gd–Mg–Sm system. Based on the experimental data in the Mg-rich corner of the Gd–Mg–Sm system, a set of thermodynamic parameters describing the Gibbs energies of individual phases of the Gd–Mg–Sm system as functions of composition and temperature was obtained. In addition, the complete ternary phase diagram of the Gd–Mg–Sm system were predicted.     

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.     

Re-modeling of Laves phases in the Cr–Nb and Cr–Ta systems using first-principles results

Total energies of Laves phases Cr₂X, CrX₂, CrCr₂ and XX₂ (X=Nb,Ta) in all three structural forms C14, C15 and C36 have been calculated ab initio by pseudopotential VASP code with a complete relaxation of structural parameters. The calculated values were used in a two-sublattice model for re-modeling of Gibbs energies of Laves phases and subsequently for calculation of phase diagrams of Cr–Nb and Cr–Ta systems by CALPHAD method. It turns out that application of ab initio calculated values of total energy of hypothetical “end-members” in a two-sublattice model substantially simplifies the modeling and lowers the number of necessary parameters. Comparison of phase diagrams obtained by a model using first-principles results with previous empirical approach as well as relative stability of Cr₂X polytypes is presented.     

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.     

A thermodynamic modeling of the Cu–Pd system

The phase equilibria and thermodynamic properties of the Cu–Pd system are optimized using the CALPHAD (CALculation of PHAse Diagram) technique. In the present work, the liquid and face-centered cubic (fcc) solution phases are modeled with the substitutional solution model. A two-sublattice model (Cu,Pd)_0.75(Cu,Pd)_0.25 is applied to describe the ordered Cu₃Pd phase, the one-dimensional long-period superlattice (1D-LPS) and two-dimensional long-period superlattice (2D-LPS) structures, in order to cope with the order–disorder transition between three intermetallic compounds (Cu₃Pd, 1D-LPS and 2D-LPS) and fcc solution (A1) in the Cu–Pd system. A two-sublattice model (Cu, Pd)(Cu, Pd) is used to describe the homogeneity range of CuPd phase. A set of self-consistent thermodynamic parameters is obtained and the calculated phase diagram and thermodynamic properties are presented and compared with the experimental data.