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 thixoformability of Al–Si–Cu alloys

The aim of this work was to evaluate the thixoformability of Al-(2 to 7 wt%) Si–Cu alloys by differential thermal analysis (DTA), differential scanning calorimetry (DSC) and CALPHAD simulation. Thermoanalytical data were generated for exothermic (rheocasting) and endothermic (thixoforming) cycles under different kinetic conditions (heating and cooling rates of 5, 10, 15, 20 and 25 °C/min). The findings indicate that the SSM critical temperatures and liquid fractions are directly affected by the kinetic conditions, chemical composition and heat-flow direction and that the measured values of these critical temperatures and liquid fractions vary according to the thermodynamic evaluation technique used (Calphad simulation, DSC or DTA). The SSM working window (a) became smaller as the heating/cooling rates and Si content increased; (b) was larger for rheocasting (solidification) than for thixoforming (melting) operations; (c) was on average approximately 12 °C wider and covered a range of mass fractions approximately 0.12 greater for DSC measurements than for DTA measurements; and (d) had a low sensitivity for all the conditions analyzed, indicating the thermodynamic stability of the Al–Si–Cu system. CALPHAD simulation successfully predicted several transformations and the thermodynamic behavior of the temperatures and liquid fractions analyzed. The DTA and DSC techniques yielded discrepant results for some of the critical points investigated, such as the limits of the SSM working window. The majority of the DSC cycles were more sensitive to variations in kinetic conditions, heat-flow direction and chemical composition than the corresponding DTA cycles. Furthermore, the tertiary Al₂Cu phase transformation could not be identified in many of the DTA cycles. For these reasons, DTA should be used with caution when predicting the thermodynamic behavior of potential raw materials for SSM processing.     

Thermodynamic optimization of the Ni–Al–Nd ternary system

Thermodynamic optimization of the Ni-Al-Nd ternary system and Al-Nd binary systems have been conducted in the present work. A self-consistent set of thermodynamic parameters for the Al-Nd binary system and Ni-Al-Nd ternary system have been optimized using CALPHAD method. Isothermal sections at 600 and 700 °C as well as the liquidus projection have been reproduced. Isopleths with 93 at% Al, 9 at% Ni and 3 at% Nd, have been calculated also. The calculated thermodynamic and phase equilibria data for both the binary and the ternary systems agree fairly well with the experimental data. This work can be used as multi-component thermodynamic database for Ni-based alloys.     

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.     

Modelling the thermodynamic data for hcp Zn and Cu–Zn alloys– an ab initio and calphad approach

The phase diagrams of systems between zinc and elements such as Cu, Ag and Au show two distinct hcp phases on the Zn side of the system. Because of this, it is difficult to model the thermodynamic properties of these phases within a single dataset. As a result it is common to assess the data for these systems with two hexagonal phases, a phase HCP_A3 with a near ideal c/a ratio and the terminal solid solution of Zn with an anomalously high value for this ratio designated as HCP_ZN. We have examined the effect of additions of Cu on the enthalpy of mixing and lattice parameters of HCP_ZN in order to verify, using ab initio calculations, the origin of the above mentioned thermodynamic model for the alloy. The analysis of the calculations allows us to suggest a possible alternative to the state-of-the-art two hcp phases approach akin to the magnetic model used with success within the CALPHAD modelling.     

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 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 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 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.