Cluster Isomers Growth Probability Theory Predicts

Existence of clusters is very common in nature. Clusters represent the transition state of materials between single atoms and solid form. Cluster research is significant for both the improvement of fundamental physical theory and the guidance of man's practice. Attractive properties of clusters are determined by their special structures. Different from solid materials, structure of clusters will change if adding or reducing even one atom. Moreover, for the cluster of specific number of atoms, there exist many isomers of different structures. Therefore, observing or predicting the structure accurately is very important in the field of cluster research. At present, clusters of various atom numbers have been successfully prepared and separated in experiment, but it is still too difficult to observe accurate structure of small clusters(n<100). Consequently, theoretical work is important. The structure of the most probable isomer (the one appears most often in growth) is of great concern to people in research. However, no theory or criterion for predicting structure of the most probable isomer at room temperature has been proved universal until now.Molecular dynamics (MD) simulations of the whole growth process from isolated atoms (high temperature) to cluster formation (room temperature) are unapproachable because of the expensive computational cost. However, within only hundreds of nanoseconds, the isomerization process can arrive at equilibrium at high temperatures, and the relative abundance of the various isomers can be determined. Hence predicting the probability for each isomer formed in the end of the growth at room temperature comes down to such questions as the following:how do the isomers form at high temperatures transform at room temperature and how long does the transformation last. In this work, we obtain an analytic relationship between temperature and the transformation time taken by a cluster transforming from one isomer to another, and C12 clusters were taken as a specific example to test the analytic relationship, as small carbon clusters are promising for various potential applications. Based on our statistical model and MD simulations, we found that the time for the most probable isomer of C12 formed at 2500 K turning into any other isomer is more than 1012 years at room temperature. The statistical model in this work can be widely used for predicting stability of cluster isomers, lifetime of nano-components, and so on.