Modeling APB energies in multicomponent Ni-base superalloys

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An environment dependent nearest neighbor bond (EDNNB) model was developed to estimate the antiphase boundary (APB) energies in γ′ precipitates (L12 structure) in commercial Ni-base superalloys. In this approach, the most frequent combination of nearest neighbor violations across an APB on the {111} planes in the Al-sublattice were identified. Further, the effect of alloying elements such as Ta, Ti, Nb, W, Mo, Ni, and Cr on seven unique combinations of violations on the APB(111) energies (ΓXYNiNi, X, YAl, Ta, Ti, and Cr in the Al-sublattices) was systematically studied. First-principles calculations were employed to evaluate Γ by substituting Al atoms in the supercells by alloying elements on planes adjacent to the APB(111). The effect of alloying and interaction with a unique violation on APB(111) is captured through an environment strength coefficient, η. Interestingly, Ta and Nb have similar effects on the APB energies. Similarly, the effects are equivalent when the substitution is W or Mo irrespective of the combination of violation on the APB(111). The alloying effect is dramatic when the substitutions are within the vicinity of the APB(111). Ni substitution leads to a reduction of APB energy when the violations are of type Al–Al across the APB(111). All alloying additions increase the APB energy when the violation is Ti–Ti across the APB. Additionally, the magnitude of the strength coefficients is significantly higher than the other type of violations considered in this study. The strength coefficients are negative when the APB(111) has Ti–Cr violations, suggesting a driving force for segregation to APB(111). In conclusion, the creation of more Ti–Ti and Al–Ti violations is beneficial to increase the strength of the precipitate. APB energies in many disk and blade alloys were predicted using strength coefficients. The trends in APB energies are in good agreement with the trends in yield strength within the subsets of blade and disk alloys. The development of the EDNNB model opens avenues for predicting planar fault energies in novel multi-principal element compositions strengthened by L12 were discussed.