Ab initio molecular dynamics and elastic properties of TiC and TiN nanoparticles

The results of first-principles simulations of relaxed ground-state structure and vibrational modes are presented for titanium carbide and titanium nitride clusters of nearly stoichiometric composition and compared to frozen phonon and molecular dynamics calculations for crystalline TiC and TiN. The calculations have been done with the SIESTA method, using norm-conserving pseudopotentials and the basis of strictly localized numerical pseudoatomic orbitals. The dominant vibration mode corresponding to the zone-center TO phonon (14 THz) persists and gets hardened (21 THz) in the small Ti4C4 cluster. The increase of the cluster size to Ti14C13 leads to an enhancement of vibrational density of states in the intermediate range of frequencies, including the phonon band gap of pure crystalline TiC (near 15 THz). Similar trends can be noted for the Ti-N system, with the vibration spectrum slightly scaled upwards but otherwise very close to that of TiC. The clusters studied are yet too small to perform a reliable analysis of acoustic modes.