Thermodynamic modeling of Fe-Nb and Fe-Nb-Ni systems supported by first-principles calculations and diffusion-multiple measurements

The Fe-Nb and Fe-Nb-Ni systems are remodeled using updated sublattice models for the topologically close-packed (TCP) phases of Laves_C14, δ and μ with new experimental data and first-principles and phonon calculations based on density functional theory (DFT). Scanning electron microscopy (SEM) imaging, electron probe micro-analyzer (EPMA), and wavelength-dispersive spectroscopy (WDS) are used to determine phase compositions and tie-lines in the Fe-Nb-Ni system through a diffusion multiple isothermally treated at 1373 K. The three-, three-, and five- sublattice models are used for Laves_C14, δ, and μ phases according to their Wyckoff positions, respectively. DFT calculations are employed to predict thermochemical data as a function of temperature for Laves_C14, δ, and μ phases. The new thermodynamic description of the Fe-Nb-Ni system includes a new hexagonal phase named - hP24 - and the updates for the Fe-Nb system and reproduces better the experimental and computational thermochemical and phase equilibrium data from the present study and the literature. The new results will improve thermodynamic predictions of TCP and other phases in both Fe-based and Ni-based alloy systems.