Study on the structure and energy of the (0001) surface of α-Al2O3 substrate

There are three different structures of the alpha-Al2O3 (0001) Crystal surface because different atoms are terminated on the outermost layer. Our calculations are based on the density functional theory in local density approximation, and on ultra-soft pseudo-potential methods, with the valence orbital expanded in plane-wave by using three-dimensional periodic boundary conditions in kappa-space, firstly, the calculation result is that alpha-Al2O3 (0001) crystal surface structure which the outermost layer is terminated by a single layer of Al atoms is much more stable than the other two structures. Secondly, a rhombohedral primitive cell is employed to perform cell optimizations, with ten atoms in the unit cell. and the calculated equilibrium parameters are: a(0) = 0.48178 nm, gamma = 120.16, which are in excellent agreement with recent experimental values (a(0) = 0.47591 nm), with a difference of less than 1.3%. Moreover, our calculations are performed with a super-cell slab model in vacuum environment, in which the outermost layer is terminated by single Al atoms. By investigating the four-layer relaxation and Al-O atoms population of the surface, we obtain results that the top single Al layer is an inward relaxation of 0.0792 nm-0.098 nm, that is, the second-layer O atoms are turned into the top layer, and the top O and Al atoms population analysis show that the valence electrons are concentrated on the surface oxygen ions with a greater probability, it is obvious that the alpha-Al2O3 (0001) crystal surface appears in the O-surface state, which is discussed from the microstructure of alpha-Al2O3 (0001) crystals in details.