Thermal collision rate constants for small nickel clusters of size 2–14 atoms
Authors: Venkatesh R. , Lucchese R. R. , Marlow W. H. , Schulte J. 
Published: July 2002

The collisions of small nickel clusters of size 2–14 atoms were studied using the classical trajectory method. Three cases were considered: cluster–monomer, cluster–dimer, and cluster–cluster collisions. The interaction between the nickel atoms was modeled by a semiempirical many-body potential based on the second moment approximation of the tight-binding scheme. This potential, which previously has been shown to reproduce a wide range of bulk properties including finite temperature behavior for nickel, was also found to describe the cluster properties very well. Both the internal temperatures of the colliding clusters and the collision temperature were set equal to 1200 K. In each of the cases studied, sticking was the dominant channel of reaction for clusters other than dimer and trimer. The sticking cross section was further found to be well approximated by the geometric cross section obtained using a simple hard sphere model for clusters larger than pentamer in the case of cluster–monomer and cluster–dimer collisions. For cluster–cluster collisions, the hard sphere approximation overestimates the sticking cross section by about 40% for even the largest clusters considered.
However in this case also, the observed trend suggests a better agreement for cluster sizes somewhat larger than the sizes considered in this study. The other significant reaction channel observed was monomer evaporation which becomes more frequent and persists for larger target cluster sizes as the size of the projectile cluster is increased. The cross section results in all three cases do not exhibit any dramatic dependence on cluster size, consistent with the experimental observation of smooth and featureless size distributions for nickel and other transition metal clusters. The cluster–monomer collision calculations were repeated by setting the internal temperature of the cluster to 0 K. The lowering of temperature did not lead to any dramatic size dependence. For the 0 K case, the sticking cross section is underestimated by the hard sphere cross section even for the larger clusters. However, the observed trend indicates a better agreement between the two cross sections for cluster sizes outside the size regime considered. For all of the above cases considered, the hard sphere cross section appears to be easily parametrizable in terms of the cluster size. For a limited number of cluster sizes, the collision calculations were repeated using different integration times and from these calculations it appears that the collisionally formed clusters decay roughly in an exponential manner. This suggests that the cluster decay rates may be obtained using a simple statistical theory such as the RRK theory. Also, these calculations suggest that even the smallest of the collisionally formed clusters survives long enough to be cooled by collisions with background gas molecules. As a consequence, cluster growth may be determined by coagulation-type reactions, unless monomer is supplied continuously. The implications of the results of this study to cluster growth models are discussed. The results of this study may be improved by the inclusion of two factors, directional bonding and (particularly) long range interactions in the potential.