Periodic DFT calculations coupled to a first-principle thermodynamic approach have allowed us to establish a surface phase diagram for the different terminations of the alpha-Al2O3 (1 (1) over bar 02) surface in various temperature and water pressure conditions. Theoretical results are compared with previous experimental data from the literature. Under a wide range of temperature and water pressure (including ambient conditions) the most stable surface (denoted C2_1H(2)O in this work) is terminated with singly coordinated hydroxyls on four-fold coordinated aluminium (Al-4C-mu(1)-OH) while most existing surface models are only considering six-fold coordinated surface Al atoms as in the bulk structure of alumina. The presence of more acidic Al-4C-mu(1)-OH sites helps explain the low Point of Zero Charge (PZC) (between 5 and 6) determined from the onset of Mo oxoanions adsorption on (1 (1) over bar 02) single crystal wafers. It is also postulated that another termination (corresponding to the hydration of the non-polar, stoichiometric surface, stable in dehydrated conditions) may be observed in aqueous solution depending on the surface preparation conditions.