Soft and hard shells in metallic nanocrystals

The inhomogeneous elastic properties of metallic nanocrystals are studied using semiempirical potentials for Au, Pb, Ag, and Cu. The enhanced low-and high-frequency modes are found to be spatially localized in two shells, a soft surface shell and a hard transition shell. Our analysis shows that the linear frequency dependence of the vibrational density of states is attributed to the two-dimensional nature of the surface shell that is independent of the system size, while the high-frequency tail mainly comes from the transition shell.