CELLULAR STRUCTURES IN 3-DIMENSIONAL DIRECTIONAL SOLIDIFICATION - SIMULATION AND ANALYSIS

The use of an asymptotically valid interface equation for directional solidification allows numerical studies of the evolution of three-dime nsional cellular structures in extended systems. We consider systems t hat are large enough to render a statistical description of disordered structures meaningful and to enable a direct comparison with experime nt. Moreover, it is possible to assess the stability of the observed p atterns on the basis of long-time simulations. In addition to statisti cal methods already employed in the analysis of experiments, new stati stical tools are introduced to follow the dynamics of the system. In g eneral, three growth phases can be distinguished. During the first, sh ort one, the pattern dynamically selects its preferred length scale by a coarsening or a fine-graining process. In the second, much longer p hase, the cells rearrange, evolving towards a polycrystalline, essenti ally ordered structure. In the third phase, a process of gradual elimi nation of defects takes place. For smaller temperature gradients, ther e is an evolution towards oscillating patterns. Oscillations lead to a reduction of the percentage of defects, unless they act as a precurso r to weak turbulence, which happens at even lower values of the temper ature gradient.