First-principles calculations of step formation energies and step interactions on TiN(0Â 0Â 1)

We study the formation energies and repulsive interactions of monatomic steps on the TiN(0 0 1) surface, using density functional total-energy calculations. The calculated formation energy of [1 0 0] oriented steps agree well with recently reported experimental values; these steps are shown to have a rumpled structure, with the Ti atoms undergoing larger displacements than the N atoms. For steps that are parallel to [1 1 0], our calculations predict a nitrogen (N) termination, as the corresponding formation energy is several hundred meV/Å smaller than that of Ti-terminated steps.