First-principles calculations are performed on the stable $\alpha -{\mathrm{Al}}_2{\mathrm{O}}_3$ and metastable $\kappa -{\mathrm{Al}}_2{\mathrm{O}}_3$ phases to understand the stability and bonding of the flexible alumina surfaces. The (001) and $\left(001\mathrm{}¯\right)$ surfaces of $\kappa -{\mathrm{Al}}_2{\mathrm{O}}_3$ are investigated and compared to $\alpha -{\mathrm{Al}}_2{\mathrm{O}}_3\mathrm{}\left(0001\right).$ A needed extension of the original formulation of the Tasker’s rule for the stability of low-symmetry ion-crystal surfaces is found. Also, use of extended Pauling’s rules makes the results applicable to other metastable alumina phases. The most stable termination of $\kappa \mathrm{}\left(001\right)/\left(001\mathrm{}¯\right)$ is found to be in the middle of an Al layer, similarly to $\alpha -{\mathrm{Al}}_2{\mathrm{O}}_3\mathrm{}\left(0001\right).$ This surface is shown to be nonpolar, even though a Tasker point-charge description implies a polar classification. The asymmetry in atomic and electronic structures introduced by the tetrahedrally coordinated Al $\left({\mathrm{Al}}^T\right)$ ions is found to have important consequences for the surface properties. The bulk cation-vacancy lines caused by the ${\mathrm{Al}}^T$ make the $\kappa \mathrm{}\left(001\right)/\left(001\mathrm{}¯\right)$ surfaces more open than $\alpha \mathrm{}\left(0001\right),$ thus allowing a huge inward relaxation $(-117\%)$ at $\kappa \mathrm{}\left(001\right),$ making this surface O terminated. The charge asymmetry in bulk $\kappa -{\mathrm{Al}}_2{\mathrm{O}}_3$ causes an excess of electrons at $\kappa \left(001\mathrm{}¯\right),$ yielding a one-dimensional metallic surface state. Also, the presence of ${\mathrm{Al}}^T$ in the near-surface layer is found to be destabilizing.

• Received 6 August 2002

DOI:https://doi.org/10.1103/PhysRevB.67.195412