A simplified model based upon cohesive energy was proposed to estimate the formation energy of Schottky vacancies in free-standing metal nanoparticles with body-centered cubic and face-centered cubic crystal structures. To study the effect of particle size and shape, the surface energy, elastic contraction and average coordination number of particles at the surface and core was considered. It was shown that the energy of vacancy formation in face-centered cubic nanoparticles increased with decreasing the size while the effect of particle shape (sphere, cubic and icosahedral) was marginal. In spite of this behaviour, body-centered cubic nanoparticles exhibited a critical particle size at around 25Å, at which a minimum Schottky vacancies was attained. Additionally, the energy of vacancy formation was notably lower for body-centered cubic nanoparticles with cubic shape than spherical ones. The application of the developed model was shown for free-standing Fe and Cu nanoparticles.

Effects of Particle Size, Shape and Crystal Structure on the Formation Energy of Schottky Vacancies in Free-Standing Metal Nanoparticles: a Model Study. H.Delavari, H.R.Madaah Hosseini, A.Simchi: Physica B, 2011, 406[20], 3777-80