Theoretical analytical model of vacancy formation energy with simultaneous dependence on surface orientation, temperature, and material size

Abstract From the perspectives of bond energy theory, the bond–order–length–strength correlation mechanism, and the core–surface configuration for nanomaterials, a physics-based model, free of any adjustable parameters and simultaneously considering the coupling effects of surface orientation, temperature, and size on the vacancy formation energy of metal materials is developed. To confirm our present model, the temperature-dependent vacancy formation energies of six face-centered cubic metals and the size-dependent vacancy formation energies of gold particles are predicted, which are in reasonable agreement with the simulation results. In particular, the model can provide a convenient method to predict the temperature-dependent vacancy formation energy of nanomaterials with different surface orientations, and also can provide a new method to study the structural relaxation. The study shows that the size effect on the vacancy formation energy depends on the stronger bond energy in the surface layers compared with those in the core interior, and the temperature-dependent vacancy formation energy arises from cohesive energy weakening, with the opposite trend to that induced by size reduction.