Induction time of a polymorphic transformation

When a solution is supersaturated with respect to multiple polymorphs, the polymorph with the lowest nucleation barrier will form first. If this is a metastable polymorph, it will persist until the induction of nuclei of a lower free-energy phase, marking the onset of a polymorphic transformation. Induction of a more stable polymorph can occur under two conditions: a.) during steady-state nucleation, or b.) after complete crystal growth of the metastable phase. Using the theory of competing stochastic processes, we derive the rare probability of forming a higher-barrier, more-stable polymorph during steady-state nucleation, and use this to explain variations in crystallization products between repeat experiments, which may underlie the phenomenon of "Disappearing Polymorphs". We also derive the induction time of a stable phase from a solution equilibrated with a metastable phase, and show that once the stable phase nucleates, bulk metastable crystals will spontaneously ripen onto nanoscale nuclei or seeds of a more stable phase, thermodynamically driving dissolution-reprecipitation processes. Existing strategies to prolong or shorten the lifetimes of transient metastable phases are reviewed and interpreted within the context of polymorphic induction. The analyses in this work are conducted from classical nucleation and crystal growth theories, suggesting that paradigms shifts to 'non-classical' nucleation theories may not be necessary to rationalize multistage crystallization