Shape and energetics of TiN nanoparticles

The properties of titanium nitride films have previously been found to be dependent upon the surface structure and crystallite orientation. Presented here are results of density functional theory calculations and a thermodynamic model that are used to predict the shape of isolated faceted TiN nanoparticles as a function of size. The model takes as input the surface free energies of the TiN (001) and (111) surfaces and compressibility of bulk TiN, which are be shown to in good agreement with experimental results and the results of other theoretical investigations. The optimization of the TiN nanocrystal shape resulted in a truncated cubic morphology which differs considerably from the truncated octahedral morphology for macroscopic crystals predicted by the Wulff construction. This study concludes that the Wulff construction is not satisfactory for predicting shapes at the nanoscale.