Nano-crystalline films of pure cubic ZrO2 have been produced by ion beam assisted deposition (IBAD) processes which combine physical vapor deposition with the concurrent ion beam bombardment in a high vacuum environment and exhibit superior properties and strong adhesion to the substrate. Oxygen and argon gases are used as source materials to generate energetic ions to produce these coatings with differential nanoscale (7 to 70 nm grain size) characteristics that affect the wettability, roughness, mechanical and optical properties of the coating. The nanostructurally stabilized chemically pure cubic phase has been shown to possess hardness as high as 16 GPa and a bulk modulus of 235 GPa. We examine the mechanical properties and the phase stability in zirconia nanoparticles using first principle electronic structure method. The elastic constants of the bulk systems were calculated for monoclinic, tetragonal and cubic phases. We find that calculated bulk modulus of cubic phase (237GPa) agrees well with the measured values, while that of monoclinic (189GPa) or tetragonal (155GPa) are considerably lower. We observe considerable relaxation of lattice in the monoclinic phase near the surface. This effect combined with surface tension and possibly vacancies in nanostructures are sources of stability of cubic zirconia at nanoscale.