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 typica lly is transported through the old phase by diffusion. A recent theory has made quantitative predictions about a morphology diagram which cl assifies 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. Importan t control parameters are the supercooling and the crystalline anisotro py. We confirm the basic predictions for the occurrence of the growth for ms compact and fractal dendrites for anisotropic surface tension a nd compact and fractal seaweed for vanishing anisotropy. More specific ally, we find the following results. For arbitrary driving forces an a verage interface can move at constant growth rate even with fully isot ropic surface tension. At zero anisotropy and small driving force we f ind fractal seaweed with a fractal dimension almost-equal-to 1.7, in a greement with simple Laplacian aggregation. With increasing anisotropy the pattern can be described as fractal dendritic, growing faster tha n 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 transiti on from the compact dendritic to a compact seaweed morphology when ani sotropy is reduced as predicted. The transition appears to be disconti nuous with metastable states. Symmetry-broken double fingers of the gr owing phase seem to be the basic building blocks for the compact-seawe ed morphology.