How Do Crystals Nucleate and Grow: Ostwald’s Rule of Stages and Beyond

Abstract

W. Ostwald predicted with the “rule of stages” formulated by him that phase formation processes in complex condensed matter systems may proceed step by step via different evolution paths involving 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. Advancing this idea, it was shown in recent years by us that in condensation and boiling, as well as in segregation and crystallization processes in multi-component liquid and solid solutions, critical clusters may be formed and evolve via a continuous sequence of states with properties which may differ from the properties of any of the macroscopic phases present in the respective phase diagram. The kinetics of nucleation proceeds hereby via a scenario similar to spinodal decomposition, i.e., via a continuous amplification of density and/or composition differences accompanied eventually by sequential discrete changes of the structure of the system. The basic ideas and results of this theoretical approach developed by us are described in the present chapter. Recently published experimental results on crystal nucleation are discussed in detail giving additional confirmation of these conclusions. As a second man topic devoted also to the theoretical description of crystal nucleation, the relevance of the concepts of fragility of the liquid for the understanding of crystal nucleation and growth in glass-forming liquids is explored. Finally, a number of directions of research are discussed which may lead to new insights into the complex phenomena of crystal formation and growth processes.