Solution-based thermodynamic modeling of the Ni–Al–Mo system using first-principles calculations

A solution-based thermodynamic description of the ternary Ni–Al–Mo system is developed here, incorporating first-principles calculations and reported modeling of the binary Ni–Al, Ni–Mo and Al–Mo systems. To search for the configurations with the lowest energies of the N phase, the Alloy Theoretic Automated Toolkit (ATAT) was employed and combined with VASP. The liquid, bcc and γ-fcc phases are modeled as random atomic solutions, and the γʹ-Ni3Al phase is modeled by describing the ordering within the fcc structure using two sublattices, summarized as (Al,Mo,Ni)0.75(Al,Mo,Ni)0.25. Thus, γ-fcc and γʹ-Ni3Al are modeled with a single Gibbs free energy function with appropriate treatment of the chemical ordering contribution. In addition, notable improvements are the following: first, the ternary effects of Mo and Al in the B2-NiAl and D0a-Ni3Mo phases, respectively, are considered; second, the N-NiAl8Mo3 phase is described as a solid solution using a three-sublattice model; third, the X-Ni14Al75Mo11 phase is treated as a stoichiometric compound. Model parameters are evaluated using first-principles calculations of zero-Kelvin formation enthalpies and reported experimental data. In comparison with the enthalpies of formation for the compounds ψ-AlMo, θ-Al8Mo3 and B2-NiAl, the first-principles results indicate that the N-NiAl8Mo3 phase, which is stable at high temperatures, decomposes into other phases at low temperature. Resulting phase equilibria are summarized in the form of isothermal sections and liquidus projections. To clearly identify the relationship between the γ-fcc and γʹ-Ni3Al phases in the ternary Ni–Al–Mo system, the specific γ-fcc and γʹ-Ni3Al phase fields are plotted in x(Al)–x(Mo)–T space for a temperature range 1200–1800 K.