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

Abstract

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.

Crystallization Instability in Glass-Forming Mixtures

“…In the case of the KA system, we note that if the liquid approaches a 1∶1 composition, then crystallization, not of the one-component fcc, but of the 1∶1 composition bcc crystal, may be expected. We noted in the Introduction that the Ostwald rule of stages, generalized to mixtures, would provide pathways by which the nuclei may grow [20].…”

“…Thus the compositional fluctuations we consider are distinct from enhanced crystal nucleation rates due, for example, to density fluctuations related to a nearby critical point [18,19]. Clearly, our analysis falls within the concept of the Ostwald rule of stages, suitably generalized to mixtures [20]. In this context, we emphasize that the crystals formed through such compositional fluctuations will in general not be thermodynamically stable.…”

Crystallization of Glass: What We Know, What We Need to Know

“…The parameters of the critical clusters have to be determined here based on appropriate sets of equations as derived in the framework of the generalized Gibbs approach. 5,35,36 For small undercoolings, the denominator in Eq. (17) is reduced to the classical expression, again; however, it can result in quite different values for higher undercooling (low temperatures).…”

Nucleation in Glasses – New Experimental Findings and Recent Theories

“…However, CNT fails by several orders of magnitude for a quantitative description of nucleation, resulting in severe underestimation of the nucleation rates (Sen and Mukerji, 1999). Various developments or alternative theories have been proposed mainly based on phenomenological or density functional methods (Granasy and James, 1999;Schmelzer et al, 2010;Schmelzer et al, 2004;Sen and Mukerji, 1999;Weinberg, 2002). They resolved some of the limits of CNT such as the use of the capillarity approximation, a sharp interface, a lack of temperature or size-dependencies for the interface or the surface energy.…”