Deterministic lattice model for diffusion-controlled crystal growth

An efficient lattice model is developed to study the stages of diffusion-controlled crystal growth. We establish the existence of a dense branching morphology and its relation to diffusion-limited aggregation. We find a clear morphological transition from kinetic-effect-dominated growth to surface-tension-dominated growth, marked by a difference in the way growth velocity scales with undercooling. We also study the evolution of interfacial instability and find a scaling behaviour for the interface power spectra, indicating the non-linear selection of a unique length scale.