Decomposition of a solid and surface solutions supersaturated with impurity atoms results in creation of nanoclusters/nanoislands. Descriptions of such decomposition are based on the adiabatic principle which declares that diffusion currents of monomers in the vicinity of clusters adjust themselves to the actual cluster sizes. In this case the probabilities of absorption/desorption of atoms on the cluster interfaces depend only on these sizes and clustering is a Markovian stochastic process completely described by these probabilities.
The thermodynamical approach assumes that forming clusters do not disturb the supersaturated solution and the absorption probability depends on the average monomer concentration in the system. We will consider a more general case, when the absorption/desorption probabilities depend on the kinetics of impurity atoms in the vicinity of the cluster interface including their interaction with this interface, and the difference between the absorption and desorption rates of monomers coincides with the value of the diffusion current at the cluster interface.
This current results from the spatially non-uniform impurity concentration induced by a forming cluster. Having in mind the adiabatic principle the current can be determined from the solution of the steady-state diffusion problem in the vicinity of the selected cluster. The average concentration of monomers in the system and their absorption by other clusters form the boundary conditions for this problem. Thus, the absorption/desorption mechanisms couple the kinetics of impurity atoms at the cluster interface with impurity diffusion which depends on monomer annihilation at other clusters.
We demonstrate that such coupling can result in deviation of the forms of parameters governing clusterization from those predicted by the thermodynamic approach giving additional possibilities for monitoring the kinetics of nanocluster/nanoisland nucleation. For illustration of this effect we choose the steady-state nucleation mode when the nucleation barrier determines the steady-state nucleation rate of 2D and 3D clusters.
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