Casting a bright light on Ostwald’s rule of stages

Abstract

Crystallization, which is a ubiquitous process in both natural and technological settings, follows a rich set of pathways as crystallizing systems evolve from dispersed monomers to condensed solids in their equilibrium, ordered state. While sound theoretical frameworks for both nucleation (1) and subsequent growth (2) via direct assembly of monomers into ordered phases were established in the 19th and 20th centuries, over the past two decades the advent of experimental methods capable of probing the atomic structure of crystals during the early stages of formation have placed the limitations of those frameworks in stark relief (3). In particular, initial appearance of poorly ordered, amorphous, or liquid precursors that then (re)crystallize to form the final phase is now recognized as widespread. Ostwald’s rule of stages (4), which states that the phase that nucleates is not necessarily the most thermodynamically stable, rather it is the one closest in free energy to the mother phase, is often invoked to explain the appearance of these precursors. However, an a priori rationale for the universal validity of this rule does not exist (5). Moreover, the structural pathways by which disordered phases transform to well-ordered crystals and the relative roles of kinetic and thermodynamic controls over both their appearance and conversion remain poorly understood. In PNAS, Niozu et al. (6) exploit the brightness of X-ray free electron laser pulses to probe the structure of more than a million individual Xe nanoparticles formed in supercooled jets within the timescale required for initial disordered precursors to transform to the ordered, equilibrium phase. In doing so, the authors reveal an unexpected structural state composed of hexagonally close packed (hcp) layers that are randomly stacked. They attribute the appearance of this random hcp (rhcp) phase to a size-dependent free energy that initially favors random stacking, before eventually shifting to favor the … [↵][1] 1Email: james.deyoreo{at}pnnl.gov. [1]: #xref-corresp-1-1

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