How Do Crystals Form and Grow in Glass-Forming Liquids: Ostwald's Rule of Stages and Beyond

More than 100 years ago, W. Ostwald formulated his rule of stages. He predicted that phase formation processes in complex systems proceed via a discrete series of metastable states, which can be formed in a macroscopic form at the given thermodynamic conditions, until finally the most stable phase will be reached. We show here that in segregation and crystallization processes in multicomponent solutions, critical clusters may be formed and evolve via a continuous sequence of states with properties that may differ from the properties of the corresponding macroscopic phases of the equilibrium phase diagram. The pathways of nucleation resemble hereby a scenario similar to spinodal decomposition, that is, the process proceeds via a continuous amplification of density and/or composition differences, which are eventually accompanied by sequential discrete changes of the structure of the system. This way of analysis restores the ability of the classical nucleation theory-modified in the described proper way-to describe crystal nucleation in super-cooled liquids not only qualitatively but even in a quantitatively correct way.