## 3 Results and Discussion
### Sputtering Yield Evaluations
The binding energy of an atom is the energy required to remove an atom from the surface of a material, and its value correlates with the sublimation energy. The sputtering yield depends on the surface binding energy (\(E\)) as following \(Y\)-1/\(E\). It is believed that the higher the binding energy, the lower the sputtering yield. In particular, the binding energies in pure Al and Mg metals are 3.19 and 1.42 eV, respectively [51]. Following the AFM measurements presented above, the sputtering yield of Al was less than that of Mg. In the case of the intermetallic phases, the differences in their sputtering yields were most likely also due to differences in their binding energies. The binding energies for the Al\({}_{12}\)Mg\({}_{17}\) intermetallic phase were calculated using the DFT method. The binding energies of pure Al and Mg were calculated for comparison purposes. The calculation of the atoms' binding energies was also planned for the Al\({}_{3}\)Mg\({}_{2}\) phase; however, it could not be carried out because of the large number of atoms in the lattice, as was the case for the WF calculation. Therefore, the Al\({}_{30}\)Mg\({}_{23}\) phase was subjected to calculation. The surface binding energy [52] was defined as  
\[E_{SSE}=E_{atom}+E_{SV}-E_{S}, \tag{3}\]  
where \(E_{S}\) is the total energy of the slab with a clean surface, and \(E_{SV}\) denotes the total energy of the surface slab with a single surface vacancy. The surfaces with and without vacancy are relaxed. \(E_{atom}\) is the atomic energy of the removed species. The calculated values of the binding energy of atoms are presented in Table 4.  
The binding energy of atoms in pure Al was found to be higher than that of pure Mg, which was consistent with the known data. In the case of the Al\({}_{12}\)Mg\({}_{17}\) intermetallic phase, the removal of an Al atom from its surface requires an energy of 3.90-4.02 eV, which is, on average, higher than the binding energy of pure Al atoms of 3.40-3.84 eV. To remove Mg atoms from the surface of the same phase, an energy of 1.53-1.71 eV is required, which also \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Structure** & **Vacancy Type** & **Surface Binding Energy, eV** \\ \hline \multirow{2}{*}{Al} & (001) & & 3.84 \\ \cline{2-3}  & (111) & & 3.40 \\ \hline \multirow{2}{*}{Mg} & (001)\(\rightarrow\)(0001) & & 1.56 \\ \cline{2-3}  & (111)\(\rightarrow\)(11-21) & & 1.57 \\ \hline \multirow{4}{*}{Al\({}_{12}\)Mg\({}_{17}\)} & (001)\(\rightarrow\)(0001) & & 4.02 \\ \cline{2-3}  & (001)\(\rightarrow\)(0001) & & 1.53 \\ \cline{2-3}  & (111)\(\rightarrow\)(11-21) & & 3.90 \\ \cline{2-3}  & (001)\(\rightarrow\)(0001) & & 1.71 \\ \cline{2-3}  & (001)\(\rightarrow\)(0001) & & 2.86 \\ \cline{2-3}  & (111)\(\rightarrow\)(11-21) & & 3.10 \\ \cline{2-3}  & (111)\(\rightarrow\)(11-21) & & 3.65 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The values of the binding energies in Al, Mg and the intermetallic phases Al\({}_{12}\)Mg\({}_{17}\) and Al\({}_{30}\)Mg\({}_{23}\) (close to Al\({}_{3}\)Mg\({}_{2}\)), calculated via the DFT method. exceeds, on average, the binding energy of atoms in pure Mg, 1.56-1.57 eV. In the case of the Al\({}_{30}\)Mg\({}_{23}\) phase, the energy required to remove Al atoms from its surface was 2.86-3.10 eV, which is, on average, less than the binding energies of pure Al and the Al\({}_{12}\)Mg\({}_{17}\) phase. The binding energy of Mg for the same phase was 1.85 eV, which exceeded the binding energy of pure Mg, as well as the binding energy of Mg atoms for the Al\({}_{12}\)Mg\({}_{17}\) phase. Therefore, it can be concluded that the binding energy of the atoms in the Al\({}_{12}\)Mg\({}_{17}\) phase slightly exceeded the binding energy of atoms in Al, which was consistent with the estimated values of the sputtering yield.