Kinetic approach Becker and Doering

The formation of nuclei of a new phase can be considered as a sequence of bimolecular reactions in which every cluster of one class (size N atoms) transforms into the next higher Qf + 1) or lower N -1) class by attachment or detachment of one atom Ai [4.12]  

If a supersaturation, or overpotential is applied, a net flux of clusters to higher classes is induced. In the steady state, the flux 

The attachment probability iVatt.iV increases with size of the cluster, because more and more sites per cluster for attachment are offered. The detachment probability. w et.N I in contrast, decreases with increasing N, because the atoms get bound to the cluster more and more strongly. Hence, with increasing N, the transformation rate to lower classes decreases, so that for a sufficiently large value of N, e.g., S, the rate of 

Beginning with the second equation, each one of these S equations can be multiplied by the factor, 

This is a quite general equation. It does not depend on type (two- or three-dimensional), on state (solid or liquid), or on form (including non-equilibrium forms) or size of the cluster. K the clusters are crystalline, however, there are different ways of obtaining the final arbitrary shape with size S. Each one of these different paths is possible and, depending on the probabilities and Wau contribute independently to the overall flux rate. 

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