Evolution of cluster size-distributions in nucleation-growth and spinodal decomposition processes in a regular solution

Nucleation-growth and spinodal decomposition processes are two of the basic mechanisms first-order phase transitions – like condensation and boiling, segregation or crystallization and melting – may proceed. Their adequate theoretical description is essential in order to understand the basis mechanisms of self-structuring of matter at nano-scale dimensions. The basic features of evolution of cluster size-distributions are discussed in detail both for meta-stable (nucleation) and unstable (spinodal decomposition) initial states for a simple model of a binary mixture. The results are obtained by the numerical solution of a set of kinetic equations where the thermodynamics of cluster formation is formulated based on the generalized Gibbs' method. It is shown, that nucleation will not proceed, in general (especially in meta-stable initial states near to the spinodal curve), via the saddle point but in trajectories of evolution by-passing the saddle point. For systems in unstable initial states, spinodal decomposition can proceed similarly to nucleation forming clusters evolving to the new phase via the ridge of the thermodynamic potential hyper-surface.