Fig. 1. The [110] (001) dislocation of the γ / γ′ interface. The red balls and blue balls denote Al atoms and Ni atoms, respectively.

Fig. 2. The model of the [110] (001) dislocation core in γ / γ′ interface. The color atoms in the figure correspond to Al and Ni atoms in Fig. 1, respectively.

Fig. 3. The planes A, B, C, and D stack along [−110] direction. Eight substitution sites are: 1^γ′-Al, 2^γ′-Ni1, 3^γ′-Ni2, 4^γ′-Ni3, 5^γ-Ni1, 6^γ-Ni2, 7^γ-Ni3, and 8^γ-Ni4. The color atoms in the figure correspond to Al and Ni atoms in Fig. 1, respectively.

Fig. 4. The atomic distribution around the doped atom. The green ball denotes the doped atom and the blue balls denote Ni atoms. Ni152, Ni141, Ni140, Ni139, Ni138, Ni137, Ni136, Ni135, Ni134, Ni133, and Ni43 are the NN Ni atoms of the doped atom.

Fig. 5. The DCD of the dislocation core doped with Re, Ta, and W. Panel (a) is for the case where Re substitutes for the γ′-Al site; panel (b) is for the case where Ta substitutes for the γ′-Al site; panel (c) is for the case where W substitutes for the γ′-Al site. The blue and yellow regions denote charge loss and accumulation, respectively. The isosurface is 0.0045 e/ų. Ni152, Ni141, Ni140, Ni139, Ni138, Ni137, Ni136, Ni135, Ni134, Ni133, and Ni43 are the NN Ni atoms of the doped atom.

Fig. 6. Charge density contour plots of the dislocation core on the (001) plane and (120) plane. Panels (a), (c), and (e) are the charge density contour plots of the (001) plane that the Re, Ta, and W substitute for γ′-Al site, respectively; panels (b), (d) and (f) are the charge density contour plots of the (120) plane that the Re, Ta, and W substitute for γ′-Al site, respectively. Dashed and solid lines denote the decreased and the increased charge density, respectively. The contour spacing is 0.002 e/a.u.³.

Fig. 7. The PDOSs of the doped atoms and their NN Ni atoms in the dislocation core. The Fermi energies are shifted to zero. The dashed lines and solid lines represent the PDOSs without and with (a) Re, (b) Ta, and (c) W, respectively.

Table 1. The substitution formation energies (in unit eV) of the doped atoms which substitute for 1^γ′-Al, 2^γ′-Ni1, 3^γ′-Ni2, 4^γ′-Ni3, 5^γ-Ni1, 6^γ-Ni2, 7^γ-Ni3, and 8^γ-Ni4, respectively.

Table 2. The vacancy formation energies (in unit eV) for the inequivalent Ni atoms around the doped atoms and the Al atom.

Table 3. The migration energies (in unit eV) of the doped atoms and the Al atom in the dislocation core.

Table 4. The average distance (in unit Å) between X-NN Ni (X = Re, Ta, and W).