Vacancy Formation Energy in Metallic Nanoparticles under High Temperature and High Pressure

We present an analytic model to address the vacancy formation energy (VFE) of vacancies in metallic nanoparticles under the conditions of high temperature and high pressure based on the size-dependent cohesive energy consideration. It is found that the VFE decreases with the size of metallic nanoparticles and the VFEs on the surface and at the interface are smaller than those in the core interior. The temperature and pressure can effectively influence the VFE. The atomic energy state in the surface shell in the bond imperfection seems to be the physical origin of the anomalous properties of nanoparticles. Theoretical predictions for the size dependency of the VFE are in agreement with the available results from the simulations.