Hierarchical modeling of C and Si nano-cluster nucleation utilizing quantum and statistical mechanics

A hierarchical, multi-scale computer model for the nucleation of nano-phase materials from the vapor phase is presented. The model utilizes full solutions to quantum mechanics cluster energy equations for sizes up to 10 atoms, and statistical rate theory for larger cluster sizes. Ab initio and semi-empirical quantum mechanics methods are used to investigate the energetics of Si and C clusters. The results of binding energy and most stable configurations show significant differences between C and Si nano-clusters. Atomic cluster size distributions are obtained from reaction rate theory on the basis of collision frequencies in the vapor phase. Cluster reaction rates are determined from the energetics and vibrational modes, as investigated by quantum mechanics for small sizes. The nucleation and further evolution of the cluster size distribution is modeled by solutions to detailed kinetic equations. This multi-scale model is shown to be a useful computer simulation tool, which can be utilized to design experiments on nano-phase materials with minimum adjustable parameters.