Fig. 1 SU models of a group of low-Σ symmetric tilt Al GBs with the [110] or [001] tilt axes. The dark blue and light blue balls denote Al atoms on different (110) or (001) planes, respectively. Along the GB planes, three different types of SUs can be identified using yellow, green, and blue shadows

Fig. 2 Calculated GB vacancy formation energies versus GB formation energies of all the low-Σ Al STGBs. The red dotted line denotes the bulk vacancy formation energy in Al. The layer numbers in parentheses locate the most energy-favored vacancy sites at these GBs

Fig. 3 Calculated segregation energies of alloying elements at low-Σ Al STGBs. A total of twelve elements are considered, including under-sized elements Ni, Co, Fe and Cu, similar-sized elements Si, Zn, Ag, and Ti, and over-sized elements Mg, Zr, Sc, and Er

Fig. 4 Calculated segregation energies (${\Delta E}_{\mathrm{seg}}$ and ${\Delta E}_{\mathrm{seg}}^{\mathrm{vac}}$) for various solute elements at different Al STGBs without and with GB vacancies, $\mathrm{as}$ marked using blue and red bars, respectively. Right next to the bars are the corresponding segregation sites, including substitutional sites (L0 to L2), interstitial sites (Int), vacancy sites (Vac), as well as the first and second nearest-neighboring sites to the vacancy (1NN and 2NN). The horizontal dashed lines mark the zero segregation energy, above which GB segregation is energetically forbidden

Fig. 5 Predicted vacancy segregation effects on the GB binding strength

Fig. 6 Predicted solute segregation effects on the work of separation of clean GBs: (a) solute segregation only, (b) vacancy and solute co-segregation

Fig. 7 Valence electron charge density distributions of Σ5(210) GBs: (a) clean GB, (b-d) solute-segregated GBs, (e) vacancy-containing GB, (f-h) solute-segregated vacancy-containing GBs