Ab initio study of $\mathrm{Ag}∕{\mathrm{Al}}_2{\mathrm{O}}_3$ and $\mathrm{Au}∕{\mathrm{Al}}_2{\mathrm{O}}_3$ interfaces

Structural stability, adhesion, and chemical bonding of the $\mathrm{Ag}\left(111\right)∕\alpha \text{−}{\mathrm{Al}}_2{\mathrm{O}}_3$ (0001) and $\mathrm{Au}\left(111\right)∕\alpha \text{−}{\mathrm{Al}}_2{\mathrm{O}}_3$ (0001) interfaces are investigated by an ab initio approach based on density functional theory. The interfaces are shown to have different stable structures of ${\mathrm{Al}}_2$, Al, or O termination depending on the chemical potential of aluminum or oxygen atom. A link to thermodynamic factors, i.e., the partial pressure of oxygen gas or the activity of aluminum, is established based on the ab initio thermodynamics developed recently. For condition applicable to sessile drop experiments, the O-terminated interface could exist for the $\mathrm{Ag}∕{\mathrm{Al}}_2{\mathrm{O}}_3$ system but be hard to observe for the $\mathrm{Au}∕{\mathrm{Al}}_2{\mathrm{O}}_3$ interfaces, consistent with the known experiments. The ${\mathrm{Al}}_2$ termination is possible for the $\mathrm{Au}∕{\mathrm{Al}}_2{\mathrm{O}}_3$ interface at relatively low ${\mathrm{O}}_2$ pressure or high Al activity but may be hard to form for the $\mathrm{Ag}∕{\mathrm{Al}}_2{\mathrm{O}}_3$ interface. Works of adhesion $W_{\mathrm{ad}}$ of the stoichiometric interfaces are calculated to be $0.33\mathrm{J}∕{\mathrm{m}}^2$ in generalized gradient approximation (GGA) and $0.59\mathrm{J}∕{\mathrm{m}}^2$ in local density approximation (LDA) for the $\mathrm{Ag}∕{\mathrm{Al}}_2{\mathrm{O}}_3$ interface, $0.29\mathrm{J}∕{\mathrm{m}}^2$ in GGA and $0.58\mathrm{J}∕{\mathrm{m}}^2$ in LDA for the $\mathrm{Au}∕{\mathrm{Al}}_2{\mathrm{O}}_3$ interface, in reasonable agreement with measured data.

Figure 1

Schema of the sandwiched interface supercell used in calculations. The central part of the interface is $\alpha \text{−}{\mathrm{Al}}_2{\mathrm{O}}_3$. Ball models of the upper parts of the interfaces with different terminations are shown in Figs. 3a, 3b, 3c.

Figure 2

(Color online). Ball models of three interfacial configurations before relaxation (top view). Small black (blue in color) balls represent metal (Ag or Au) atoms; small gray (green in color) balls represent Al atoms; big black (red in color) balls represent the first-layer O atoms close to the interface plane; big gray (orange in color) balls represent the second layer O atoms. Dark lined parallelograms show the surface unit cell used in calculations. (a) Metal atoms on top of Al atoms (Al top); (b) Metal atoms on top of O atoms (O top); (c) Metal atoms on top of the threefold oxygen hollow sites (hollow top).

Figure 3

(Color online). Ball model of the relaxed type-I $\mathrm{Ag}∕{\mathrm{Al}}_2{\mathrm{O}}_3$ interfaces (upper half of the symmetric slabs). Big black (blue in color) balls represent Ag atoms, smaller gray (green in color) balls represent Al atoms, and less dark (red in color) balls represent O atoms. Only the most stable configurations are presented. (a) Al-terminated interface of Al top; (b) O-terminated interface of Al-top; (c) ${\mathrm{Al}}_2$-terminated interface of hollow top.

Figure 4

Electron-density difference contour plots of $\left(11\overline{2}0\right)$ plane through interfacial Al and Ag atoms for (a) Al-terminated $\mathrm{Ag}∕{\mathrm{Al}}_2{\mathrm{O}}_3$ interface, (b) O-terminated $\mathrm{Ag}∕{\mathrm{Al}}_2{\mathrm{O}}_3$ interface, and (c) ${\mathrm{Al}}_2$-terminated $\mathrm{Ag}∕{\mathrm{Al}}_2{\mathrm{O}}_3$ interface. This plot represents the difference between the self-consistent electron density distribution of the solid interface and the sum of the overlapping atomic density distributions. The relatively black area with solid lines indicates electron accumulation, and the relatively white area with dashed lines indicates charge depletion.

Figure 5

(a) Projected density of states of interfacial atoms at the Al-terminated $\mathrm{Ag}∕{\mathrm{Al}}_2{\mathrm{O}}_3$ interface. Ag1 and Ag2 correspond to the atoms as labeled in Fig. 3a. Oxygen and Al atoms at the interface have similar DOS distribution to the corresponding atoms in ${\mathrm{Al}}_2{\mathrm{O}}_3$ bulk. (b) Projected density of states of interfacial atoms at the O-terminated $\mathrm{Ag}∕{\mathrm{Al}}_2{\mathrm{O}}_3$ interface. Ag1 and Ag2 correspond to the atoms in Fig. 3b. (c) Projected density of states of interfacial atoms at the ${\mathrm{Al}}_2$-terminated $\mathrm{Ag}∕{\mathrm{Al}}_2{\mathrm{O}}_3$ interface. The DOS of the three Ag atoms at the interface is similar to the DOS of a Ag atom in its bulk state.

Figure 6

Interfacial energies ${\gamma }_I$ of type-I and type-II interfaces for (a) $\mathrm{Ag}∕{\mathrm{Al}}_2{\mathrm{O}}_3$ and (b) $\mathrm{Au}∕{\mathrm{Al}}_2{\mathrm{O}}_3$. The oxygen partial pressure are inferred from the $\Delta {\mu }_{\mathrm{Al}}$ by the combination of Eqs. (2, 3) at a experimental temperature 1300 K for $\mathrm{Ag}∕{\mathrm{Al}}_2{\mathrm{O}}_3$ and at 1400 K for $\mathrm{Au}∕{\mathrm{Al}}_2{\mathrm{O}}_3$. The left vertical dotted line represents the limit that aluminum activity should be less than 1 at the experimental temperature. The right vertical dotted lines are defined by $\Delta {\mu }_{\mathrm{O}}<5.79\mathrm{eV}$.

Figure 7

Works of adhesion for (a) $\mathrm{Ag}∕{\mathrm{Al}}_2{\mathrm{O}}_3$ interfaces at 1300 K and (b) $\mathrm{Au}∕{\mathrm{Al}}_2{\mathrm{O}}_3$ interfaces at 1400 K. Only the results in GGA are plotted.

Figure 8

Heats of solution for a substituional Al atom in the strained Ag and Au bulk.