Anatomy of a complex crystallization pathway

Crystallization is ubiquitous in nature. For example, it occurs in cloud formation and precipitation, and the Earth's crust is a tapestry of crystalline structures, shaping landscapes and ecosystems. Despite its ubiquity, however, our understanding of crystallization remains incomplete, especially for complex crystals, which exist in a plethora of systems spanning many length scales, including intermetallic compounds and colloidal assemblies. To investigate and compare the crystallization pathways among disparate systems that form the same complex crystal, we study two prototype systems with molecular dynamics simulations, one of which is governed solely by entropy, the other by both entropy and enthalpy. Remarkably, we find that both systems are polymorphic and share the same crystal polymorphs. Using local structure metrics, we demonstrate how we can use simple machine learning tools strategically and agnostically to dissect the complex crystallization pathways down to the single particle level, examine closely the transitions among the various polymorphs along the crystallization pathway, and compare these pathways across systems. Our findings advance fundamental understanding of crystallization processes in complex crystals.