Power laws in the growth kinetics of metal clusters on oxide surfaces

The possibility of expressing the growth kinetics of metal on weakly interacting substrates (oxides and insulators) by a power law is examined. By a model taking into account for direct growth and growth by capture of diffusing adatoms it is shown that the growth rate can be locally expressed by a power law. The model is restricted to the growth of three-dimensional clusters. In the case of a strong competition between clusters for the capture of adatoms a single exponent, between 0.33 and 0.35 is obtained before the coalescence stage. In the limit of isolated clusters the exponent increases continually from 1/3-1 during the growth. The model is compared with growth kinetics of Pd clusters on MgO(100) obtained in situ and continuously by diffraction of He atoms. The agreement with the calculations is very good if we take into account for the finite nucleation rate. The present calculations have been also applied satisfactorily to the published data for other systems. (C) 1998 Elsevier Science Ltd. All rights reserved.