Prediction of vacancy formation energies in Ni-based superalloys by density functional theory calculations and machine learning

Thermal vacancies play a critical role in high-temperature Ni-based superalloys, influencing elastic constants, creep resistance, oxidation resistance, etc. Local chemical variations in multicomponent alloys generate a broad distribution of vacancy formation energies, producing low-energy states that increase vacancy concentrations. This study investigates the impact of transition (Cr/Co/Fe), refractory (Nb/Ta/Mo/W) and other alloying elements (Al/Cu/Ti/Mn) on vacancy thermodynamics in 79 FCC Ni-based alloys containing 2–6 elements. Density functional theory-based studies show that Cr/Nb/Ta/Al/Ti introduce significant lattice distortions, partially donate electrons which reduces their self-consistent chemical potentials, and broaden vacancy formation energy distributions (standard deviation up to 0.15 eV). In contrast, Co/Fe/Mo/W show lower charge localization. At typical operational temperatures of 1000 K, calculated vacancy concentrations in Ni96-X12 vary as: Nb > Ti > Ta > Al > Cu > Cr > Fe > Co ~ Ni > Mn ~ Mo > W. Multielement alloys show similar trends, where Cr/Nb/Ta-rich compositions have low-energy states (~0.5 eV) and higher vacancy concentrations. Finally, graph neural networks screened ~5500 virtual compositions, identifying eleven compositions with mean vacancy formation energy >1.75 eV and ~100 times lower vacancy concentration than pure Ni at 1000 K. These results provide valuable guidelines for defect engineering in high-temperature alloys.