  We report that calculating the Gibbs free energy of the alpha-Al_2O_3 (0001)
surfaces in equilibrium with a realistic environment containing both oxygen and
hydrogen species is essential for obtaining theoretical predictions consistent
with experimental observations. Using density-functional theory we find that
even under conditions of high oxygen partial pressure, the metal terminated
surface is surprisingly stable. An oxygen terminated alpha-Al_2O_3 (0001)
surface becomes stable only if hydrogen is present on the surface. In addition,
including hydrogen on the surface resolves discrepancies between previous
theoretical work and experimental results with respect to the magnitude and
direction of surface relaxations.
