BIFURCATIONS IN A SIDEBRANCH SURFACE OF A FREE-GROWING DENDRITE

We consider a model of a free-growing dendrite in a binary dilute syst em solidifying under nonequilibrium conditions. The numerical solution of the model equations was obtained by finite-difference technique on a two-dimensional square lattice. A special case in which the liquid- solid surface tension is zero and a stabilizing action on the dendriti c form is produced by both the surface kinetics and the anisotropic in fluence of the computational lattice was studied.:We find that, depend ing on the initial undercooling and computational lattice scale, an in teresting behavior in the dendrite sidebranch surface is expected. Exc ept for the evolution of the sidebranch surface realized by regularly repeated doubling of the distances between the secondary branches by t he Feigenbaum scenario, there is a clear tendency for the formation of a needlelike dendrite, structured after a Hopf-type bifurcation, chao tic structure with random period of branching, packet structure with t he branching period that is not defined by the Feigenbaum scenario. Si mulation data are correlated with known conclusions of the thermodynam ical approach to phase transformations, marginal stability theory, and analytical treatments of the local model of the boundary layer. Satis factory qualitative agreement with the results given by the continuum diffusion-limited aggregation model and the modeling of three-dimensio nal heat flow dendrites has been found.