Cluster Incorporation and Critical Nucleus Size in Crystal Growth: Particle-Resolved Observations Using Colloidal Crystals

We investigate cluster incorporation and dissolution events in two-dimensional colloidal crystals using particle-resolved imaging and machine learning. Particle positions were identified from microscopy images using an object-detection method. The obtained particle positions were used to track individual particles and identify changes in cluster size. We analyzed the statistics of cluster incorporation and dissolution events as a function of the size change associated with each event. The observed event frequency is well described by the cluster size distribution. These results demonstrate that particle-resolved, machine-learning analysis can provide a quantitative approach to investigating cluster dynamics in colloidal crystallization. Furthermore, the analysis provides an estimate of the kinetic critical nucleus size. Under quasi-equilibrium conditions, we show that the kinetic critical size coincides with the thermodynamic critical size, even in the presence of a cluster-mediated growth pathway. Our experimental estimate of the kinetic critical nucleus size is consistent in order of magnitude with the thermodynamic estimate.