Nucleation is the activated process that controls the kinetics of first order phase transitions. Classical nucleation theory (CNT) describes the fluctuations responsible for nucleation as small clusters of the stable phase that need to overcome a single free energy barrier before they spontaneously grow. However, two-step nucleation, where the clusters appear to cross one barrier to sample states associated with an intermediate, metastable phase, before finally transforming to the stable state in a second step, have been observed in a growing number of systems, including nucleation in protein solutions [1] and in biomineralization [2].

This raises important questions concerning the nature of the 'intermediate' state clusters, their actual role in the nucleation mechanism, and how they may influence the nucleation rate. Using a simple lattice model, we show [3] that two-step nucleation can be understood in terms of a small system, first order phase transition that occurs within the fluctuation that is then superimposed on the nucleation of the bulk phases. The cluster size at which the fluctuation phase transition occurs is controlled by the thermodynamic state of the system. As a result, the nucleation mechanism evolves from a CNT-like, one-step process, to a two-step process as the system moves through the metastable phase diagram. We also find [4] that the nucleation free energy surface for the system is accurately described by a capillarity model originally developed by Iwamatsu [5]. Finally, a master equation approach is used to study how the microscopic kinetics of the fluctuation phase transition and cluster growth affect the transient and steady state nucleation rates on a simple model free energy surface [6].

[1] Yamazaki, T. et al. Two types of amorphous protein particles facilitate crystal nucleation. Proc. National Acad. Sci. 114, 2154–2159 (2017). [2] Gebauer, D., Völkel, A. & Cölfen, H. Stable Prenucleation Calcium Carbonate Clusters. Science 322, 1819–1822 (2008). [3] James, D. et al. Phase transitions in fluctuations and their role in two-step nucleation. J Chem Phys 150, 074501 (2019). [4] Eaton, D., Saika-Voivod, I., Bowles, R. K. & Poole, P. H. Free energy surface of two-step nucleation. J Chem Phys 154, 234507 (2021). [5] Iwamatsu, M. Free-energy landscape of nucleation with an intermediate metastable phase studied using capillarity approximation. J. Chem. Phys. 134, 164508 (2011). [6] Bowles, R. K. & Harrowell, P. The influence on crystal nucleation of an order-disorder transition among the subcritical clusters, arXiv preprint: 2109.12226 (2021).