Morse function for nanoscaled cubic metals

Relying on our size-dependent cohesive energy and lattice constant functions, we established the Morse function in a unified form for nanoscaled cubic metals, involving metallic nanoparticles (NPs) and nanostructured materials (NSs). At the equilibrium position at 0 K, the depth of the potential well becomes shallow with smaller D especially for NPs, where D denotes the diameter of NPs or the grain size of NSs. This gives rise to the contraction or expansion of the interatomic spacing for NPs or NSs, respectively. The asymmetry of the binding energy curve in NPs is stronger than in NSs. The difference between NPs and NSs is largely associated with the distinction in the coordination imperfection between the surface and the grain boundary. The established function was supported by available experimental and computer simulation results for NPs and NSs.