Modeling of Nucleation Processes

Nucleation is the onset of a first-order phase transition by which a metastable phase transforms into a more stable one. Such a phase transition occurs when an initial system initially in equilibrium is destabilized by the change of an external parameter like the temperature or the pressure. If the perturbation is small enough, the system does not become unstable but rather stays metastable. In diffusive transformations, the system then evolves through the nucleation, the growth and the coarsening of a second phase. Such a phase transformation is found in a lot of situations in materials science like condensation of liquid droplets from a supersaturated vapor, solidification, precipitation from a supersaturated solid solution, ... The initial stage of all these different processes can be well described within the same framework. Since its initial formulation in 1927 by Volmer, Weber and Farkas and its modification in 1935 by Becker and D\"oring the classical nucleation theory has been a suitable tool to model the nucleation stage in phase transformations. In this article, we first describe this theory. A kinetic approach, the cluster dynamics, can also be used to describe nucleation. This constitutes the second part of this article. The links as well as the difference between both descriptions are emphasized. Since its initial formulation, the classical nucleation theory has been enriched, so as to take into account the fact that clusters other than monomers can migrate and react. It has been also extended to multi-component systems. These generalizations of the initial formalism are also presented.