Aggregation and Crystallization: Contemporary View Based on Cellular Automata

In the large field of growth (crystal and aggregate formation) phenomena, the distinction between aggregation and crystallization is rarely emphasized. However, the average coordination number, symmetry, roughness, and fractal dimension of the resulting structure can be meaningfully different. This difference in overall structure has major implications when these aggregates/crystals later serve for nuclei in the heterogeneous phase formation.

In our presentation, we start by outlining the formal difference between the growth mechanisms in both cases. From those, we formulate the update rules for two Cellular Automata - A2A (attachment to any) and A2K (attachment to kink) to investigate the above-mentioned differences between the resulting structures, with the crystallization case expanding on the aggregation one by adding the “attachment to kink (A2K) position” rule.

A pivotal aspect of our exploration involves the correlation between the symmetry observed in the final structures and, specifically, the replication of the underlying lattice symmetry with another notable parameter - the relative fraction of atoms with a given coordination number and the implicit existence of the “attachment to kink” rule in the aggregation case.