Theoretical search for possible Au-Si crystal structures using a genetic algorithm

We performed a global search for possible Au-Si crystal structures using a genetic algorithm (GA) combined with density functional theory (DFT) calculations. Two Au-Si structures, $\mathrm{A}{\mathrm{u}}_8\mathrm{S}{\mathrm{i}}_8$ and $\mathrm{A}{\mathrm{u}}_{16}\mathrm{S}{\mathrm{i}}_8$, were found to be energetically stable and have no imaginary frequencies by phonon calculations. The formation energies of all the studied structures gave a convex hull of the Au-Si system, showing that the most stable composition was $\mathrm{Au}-\mathrm{Si}=1:1$ and that the Si-rich structures were much less stable than the Au-rich ones.

Figure 1

Formation energies ($E_{f}s$) of the predicted Au-Si structures at various Au contents. The blue square and purple triangles represent the lowest energy and the second lowest energy structures, respectively.

Figure 2

Lowest energy structure of $\mathrm{A}{\mathrm{u}}_8\mathrm{S}{\mathrm{i}}_8$, plotted by VESTA [41]. (a) and (b) Top and side views of the $\mathrm{A}{\mathrm{u}}_8\mathrm{S}{\mathrm{i}}_8$ structure; (c) and (d) top view of layer No. 1 and No. 2.

Figure 3

(a) and (b) Top and side views of the low-energy structure of $\mathrm{A}{\mathrm{u}}_4\mathrm{S}{\mathrm{i}}_4$, plotted by VESTA [41].

Figure 4

Low-energy structures of $\mathrm{A}{\mathrm{u}}_8\mathrm{S}{\mathrm{i}}_2$ and $\mathrm{A}{\mathrm{u}}_{16}\mathrm{S}{\mathrm{i}}_4$, plotted by VESTA [41]. (a) and (b) Top and side views of the $\mathrm{A}{\mathrm{u}}_8\mathrm{S}{\mathrm{i}}_2$ structure; (c) and (d) top and side views of the $\mathrm{A}{\mathrm{u}}_{16}\mathrm{S}{\mathrm{i}}_4$ structure.

Figure 5

Lowest energy structure of $\mathrm{A}{\mathrm{u}}_{16}\mathrm{S}{\mathrm{i}}_8$, plotted by VESTA [41]. (a) and (b) Top and side views of $\mathrm{A}{\mathrm{u}}_{16}\mathrm{S}{\mathrm{i}}_8$; (c) and (d) top and side views of $\mathrm{A}{\mathrm{u}}_{16}\mathrm{S}{\mathrm{i}}_8$ with normal Au atoms and cross marked Au atoms, which indicates two different $8c$ Wyckoff positions.

Figure 6

(a) and (b) Top and side views of the lowest energy structure of $\mathrm{A}{\mathrm{u}}_8\mathrm{S}{\mathrm{i}}_4$, plotted by VESTA [41].

Figure 7

Lowest energy structures of (a) $\mathrm{A}{\mathrm{u}}_6\mathrm{S}{\mathrm{i}}_4$, (b) $\mathrm{A}{\mathrm{u}}_5\mathrm{S}{\mathrm{i}}_3$, (c) $\mathrm{A}{\mathrm{u}}_7\mathrm{Si}$, and (d) $\mathrm{A}{\mathrm{u}}_2\mathrm{S}{\mathrm{i}}_4$, plotted by VESTA [41].

Figure 8

Lowest energy structures of (a) $\mathrm{A}{\mathrm{u}}_6\mathrm{S}{\mathrm{i}}_2$ and (b) $\mathrm{AuS}{\mathrm{i}}_7$, plotted by VESTA [41].

Figure 9

Phonon band structures of the structures (a) $\mathrm{A}{\mathrm{u}}_8\mathrm{S}{\mathrm{i}}_8$, (b) $\mathrm{A}{\mathrm{u}}_{16}\mathrm{S}{\mathrm{i}}_8$, (c) $\mathrm{A}{\mathrm{u}}_8\mathrm{S}{\mathrm{i}}_2$, and (d) $\mathrm{A}{\mathrm{u}}_{16}\mathrm{S}{\mathrm{i}}_4$.

Figure 10

Electronic band structures of the structures (a) $\mathrm{A}{\mathrm{u}}_8\mathrm{S}{\mathrm{i}}_8$, (b) $\mathrm{A}{\mathrm{u}}_{16}\mathrm{S}{\mathrm{i}}_8$, (c) $\mathrm{A}{\mathrm{u}}_8\mathrm{S}{\mathrm{i}}_2$, and (d) $\mathrm{A}{\mathrm{u}}_{16}\mathrm{S}{\mathrm{i}}_4$.