Computer simulation of sapphire nitridation used to obtain nitride-based heterostructures (GaN) on an Al2O3 substrate has been performed. The adhesion of atomic nitrogen to the sapphire (0001) surface is investigated ab initio. The possibility of replacing surface-layer oxygen atoms with nitrogen atoms has been examined. The calculated results indicate that adsorbed nitrogen atoms occupy the most stable positions above surface oxygen atoms at different nitrogen concentrations. The changes in the total system energy after replacement of surface oxygen atoms with nitrogen atoms have been calculated. It turns out that oxygen replacement is energetically unfavorable for a single nitrogen adatom. However, this process becomes energetically favorable if the concentration of nitrogen atoms increases. This outcome, obtained for the first time, enables better understanding of the atomic-scale mechanism of sapphire nitridation.