Generic features of late-stage crystal growth

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Abstract
A cell dynamical system model, which realistically incorporates diffusion, is developed to study various aspects of late-stage crystal growth. The algorithm is computationally efficient, allowing the development of complex spatial structures to be studied, and is motivated by renormalization group considerations. We establish the existence of an asymptotic dense branching morphology and relate it to diffusion-limited aggregation. Our findings indicate that the radius of a dense-branching structure grows linearly with time, despite being diffusion controlled, in agreement with experimental observations of the growth of spherulites. A clear morphological transition from kinetic-effect-dominated growth to surface-tension-dominated growth is observed, marked by a difference in the way growth velocity scales with undercooling. We also study the evolution of interfacial instability and find scaling behavior for the interface power spectra, indicating the nonlinear selection of a unique length scale, insensitive to short length-scale fluctuations.