Kinetics of cluster formation in the laser vaporization source: Carbon clusters

Abstract

A general model of cluster formation in the laser vaporization source starting from the atomic vapor is developed and applied to carbon clusters. Two limiting cases of cluster growth exist: the diffusion-limited regime, in which the cluster distribution is essentially featureless, and the reaction-limited regime, in which the most stable clusters show as magic numbers in the cluster distribution. An approximate theory of the aggregation kernel allows for calculation of the cluster distribution in the reaction-limited regime from the formation energies of the reacting clusters. Heat released in cluster fusion allows small and medium size clusters to attain their lowest or almost lowest energy configurations in both the diffusion- and reaction-limited regimes. For larger clusters, crystalline structures are expected for transition metals, while network-forming materials are likely to exibit a multitude of structures. An application to carbon clusters in the n=1–25 range reproduce the experimentally observed cluster distributions and the magic numbers in the n=10–25 regime. The equilibrium structures of the small carbon clusters formed in the nozzle are found to be chains and monocyclic rings. At the reaction temperature, the transition between the chain and ring structures occurs around n=10 for the neutral and the positively charged clusters.