“…In order to reduce the number of plane-wave basis vectors, the ultra-soft pseudo-potential (USPP) scheme [29] was used to describe the interaction potential between the real ion and the valence electrons. As shown in Figure 1a,b, the Ni-based single crystal consists of two phases, namely singlecrystal Ni as the matrix phase (γ-phase) and Ni 3 Al (γ'-phase) as the strengthening phase, both of which exhibit the face-centered-cubic structure [30]. For the γ-phase, the kinetic energy cutoff value is 440 eV, and the number of k-point sampling grids is 12 × 12 × 12; for the γ'-phase, the kinetic energy cutoff value is 400 eV, and the number of k-point sampling grids is 8 × 8 × 8.…”