Fractal and compact growth morphologies in phase transitions with diffusion transport

First-order phase transitions take place when a supercritical nucleus of the new phase grows into the old phase. A conserved quantity typically is transported through the old phase by diffusion. A recent theory has made quantitative predictions about a morphology diagram which classifies the various resulting patterns formed by the growing nucleus at long times. In this paper we present detailed numerical studies on the advancement of an interface due to diffusional transport. Important control parameters are the supercooling and the crystalline anisotropy. We confirm the basic predictions for the occurrence of the growth forms compact and fractal dendrites for anisotropic surface tension and compact and fractal seaweed for vanishing anisotropy. More specifically, we find the following results. For arbitrary driving forces an average interface can move at constant growth rate even with fully isotropic surface tension. At zero anisotropy and small driving force we find fractal seaweed with a fractal dimension 1. 7, in agreement with simple Laplacian aggregation. With increasing anisotropy the pattern can be described as fractal dendritic, growing faster than a compact dendrite, which finally is obtained at larger anisotropy. This is in agreement with the prediction for noisy dendrites. At large driving forces, but still below unit supercooling, we find a transition from the compact dendritic to a compact seaweed morphology when anisotropy is reduced as predicted. The transition appears to be discontinuous with metastable states. Symmetry-broken double fingers of the growing phase seem to be the basic building blocks for the compact-seaweed morphology.