Fig. 1 Structure models for the first-principles calculations of this work: a β" unit cell model, b β"/Al interface model along [230]Al, c β"/Al interface model along [$\stackrel{\mathrm{-}}{3}$ 10]Al

Fig. 2 Supercells used for calculating the substitution energy of one solute atom X at the Si1 site in the β"/Al interface along [$\stackrel{\mathrm{-}}{3}$ 10]Al: a Supercell for calculating ${E}_{{{\text{Al}}_{{{52}}} {\text{Mg}}_{{{15}}} {\text{Si}}_{{{12}}} {X}}}^{1}$ with X located at matrix Al, b the same supercell of a with X and Si1 exchanged

Fig. 3 Substitution energies of Type I microalloying elements at the β"/Al interface along [$\stackrel{\mathrm{-}}{3}$ 10]Al

Fig. 4 Substitution energies of Type II microalloying elements at the β"/Al interface along [$\stackrel{\mathrm{-}}{3}$ 10]Al

Fig. 5 Substitution energies of Type III microalloying elements at the β"/Al interface along [$\stackrel{\mathrm{-}}{3}$ 10]Al

Fig. 6 Substitution energies of three types of microalloying elements at the β"/Al interface along [230]Al: a Type I elements, b Type II elements, c Type III elements

Fig. 7 Substitution energies of three types of microalloying elements in the β" bulk: a Type I elements, b Type II elements, c Type III elements

Fig. 8 Atomic-resolution HAADF-STEM images of Zn a and Sc b containing β" precipitates, taken from the Al-Mg-Si-Zn and Al-Mg-Si-Sc alloys, respectively. The green circles and purple triangles indicate the characteristic sub-units of β" and β', respectively. The blue and red arrows indicate the distinct Zn and Sc atomic columns, respectively. The orange dashed ellipses in a indicate the Zn-containing Al sites of the β" phase

Fig. 9 Ideal work of adhesion for the β"/Al interface along [$\stackrel{\mathrm{-}}{3}$ 10]Al with microalloying elements occupying their most preferential atomic sites: a the cases with microalloying elements occupying the interfacial Al sites, b the cases with microalloying elements occupying the interfacial Mg or Si sites, c the cases with microalloying elements occupying the β" bulk sites

Fig. 10 Shear modulus G a, Young's modulus E b, bulk modulus B c, Pugh's rule B/G d, and Poisson's ratio $\nu$ e of the β" phase with microalloying elements occupying their most preferential β" bulk sites