Structure formation and the morphology diagram of possible structures in two-dimensional diffusional growth

The morphology diagram of possible structures in two-dimensional diffusional growth is given in the parameter space of undercooling Delta versus anisotropy of surface tension epsilon. The building block of the dendritic structure is a dendrite with parabolic lip, and the basic element of the seaweed structure is a doublon. The transition between these structures shows a jump in the growth velocity. We also describe the structures and velocities of fractal dendrites and doublons destroyed by noise. We introduce a renormalized capillary length and density of the solid phase and use scaling arguments to describe the fractal dendrites and doublons. The resulting scaling exponents for the growth velocity and the different length scales are expressed in terms of the fractal dimensions for surface and bulk of these fractal structures. All the considered structures are compact on length scales larger than the diffusion length and they show fractal behavior on intermediate length scales between the diffusion length and a small size cutoff which depends on the strength of noise.