On Universality in sputtering yields due to cluster bombardment

Molecular dynamics simulations, in which atomic and molecular solids are bombarded by Ar_n(n = 60-2953) clusters, are used to explain the physics that underlie the "universal relation" of the sputtering yield Y per cluster atom versus incident energy E per cluster atom (Y/n vs E/n). We show that a better representation to unify the results is Y/(E/U₀) versus (E/U₀)/n, where U₀is the sample cohesive energy per atom or molecular equivalent, and the yield Y is given in the units of atoms or molecular equivalents for atomistic and molecular solids, respectively. In addition, we identified a synergistic cluster effect. Specifically, for a given (E/U₀)/n value, larger clusters produce larger yields than the yields that are only proportional to the cluster size n or equivalently to the scaled energy E/U₀. This synergistic effect can be described in the high (E/U₀)/n regime as scaling of Y with (E/U₀)^?, where ? > 1.