Demonstration of Avrami's kinetics: Connection with rate equations for clustering on surfaces

Through an appropriate analogy with the scattering problem a demonstration of Avrami's kinetic theory has been worked out. This approach has been successfully used for obtaining the general solution of the kinetics of the instantaneous growth of multiple phases. It is shown that even in the case of clustering on surfaces, when the nucleation process does not occur at preexisting active sites and Avrami's formula could not hold, the proposed method allows the kinetics of the transformed surface to be computed. The connection between Avrami's theory and the atomistic model for nucleation at solid surfaces has been also discussed in light of the rate equation formalism.