First-principles study of $\gamma {\text{-Al}}_2{\text{O}}_3$ (100) surface

The atomic and electronic structures of the $\gamma {\text{-Al}}_2{\text{O}}_3$ (001) surface are studied using the density-functional theory approach. From calculated surface energies for different surface terminations, we identified a mixed dense Al-O (001) layer, containing both octahedral aluminum and oxygen atoms, as the most stable $\gamma {\text{-Al}}_2{\text{O}}_3$ (001) surface. We found that environmental ${\text{O}}_2$ gas does not affect the surface stoichiometry. Comparison of the electronic structure of the surface and the bulk $\gamma {\text{-Al}}_2{\text{O}}_3$ shows that the band gap at the surface is slightly smaller than that of the bulk $\gamma$ alumina due to the contributions of the surface $\text{O}2p$ states.

Figure 1

Total density of states of bulk $\gamma {\text{-Al}}_2{\text{O}}_3$ calculated with (a) B1 configuration, (b) B1 configuration after removing two electrons from the system, and (c) the optimized $1\times 1\times 3$ supercell. The Fermi level is aligned to 0 and a Gaussian broadening width of 0.05 eV was used.

Figure 2

(Color online) The energetically most favorable configuration of the $1\times 1\times 3$ supercell. The red (large, marked with “O”) atoms are O, the green (small, marked with “Al-Tet”) atoms are tetrahedral site Al, the purple (small, marked with “Al-Oct”) atoms are octahedral site Al, and the blue (small, marked with “Al-Vac”) ones are the vacant octahedral sites.

Figure 3

(Color online) (a) The slab model of S3 configuration of $\gamma {\text{-Al}}_2{\text{O}}_3$ (001) surface and (b) the schematical picture of cleaving surfaces along the low-density plane. The size and color of atoms are the same as in Fig. 2.

Figure 4

(Color online) Energy barrier for one Al atom filling into the vacant site on the surface. The images start from the relaxed structure of the surface and end at the final position. The cycles are the energy differences to the starting image for each image along the reaction path. The insets are the initial, transition, and final states viewing from the [110] direction of the lattice. The color and size of atoms and vacancies are the same as in Fig. 2

Figure 5

(Color online) Surface free energy of different $\gamma {\text{-Al}}_2{\text{O}}_3$ (001) surfaces as a function of temperature at given oxygen-partial pressure $P=0.2\text{bar}$.

Figure 6

(Color online) Surface free energy of different $\gamma {\text{-Al}}_2{\text{O}}_3$ (001) surfaces as a function of oxygen-partial pressure at a room temperature $T=300\text{K}$.

Figure 7

Total density of states of the S3 $\gamma {\text{-Al}}_2{\text{O}}_3$ (001) surface. The Fermi level is aligned to 0 and a Gaussian broadening width of 0.05 eV was used.

Figure 8

(Color online) Atomic-projected DOS on O and Al atoms at the $\gamma {\text{-Al}}_2{\text{O}}_3$ (001) surface of S3 configuration. Solid and dashed lines for $p$ and $s$ states, respectively. Note the different scales in the plots.

Figure 9

(Color online) (a) Top view and (b) side view of the wave functions corresponding to the states at the top of the valence band marked by stars in Fig. 7. The gray (middle sized) and red (small sized) spheres are Al and O atoms, respectively; the large dumbbell is the shape of the wave function. For each dumbbell, different colors at each side represent different phases of the wave function.