Coupling Evaporation, Chemical Reactions, and Crystallization: A Population-Balance Framework Applied to Two-Step Perovskite Crystallization
A limited understanding of how evaporation couples to crystallization pathways hampers control over the formation of solution-processed perovskite photoactive layers. Identifying these mechanisms-and learning how to select and tune them-is essential for achieving the desired crystal morphology and, ultimately, improving solar-cell performance and stability. To investigate crystallization pathways in evaporating thin films, we develop a simple and general zero-dimensional population-balance model that couples evaporation, chemical reactions, and crystallization. We use the model to explore a range of parameters for a solvent-solute system that follows a two-step crystallization pathway: solvent evaporation first induces formation of a crystalline precursor, which subsequently recrystallizes into the final phase. The model predicts the evolution of the film composition during drying and provides quantitative LaMer curves. Based on these results, we introduce a vocabulary of "supply limitations" and "rate limitations" that enables the interpretation of crystallization kinetics in terms of the governing process conditions.