Regensburg 2007 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 30: Poster II

DY 30.50: Poster

Donnerstag, 29. März 2007, 16:00–18:00, Poster D

Dendritic melting along a grain boundary — •Claas Hueter, Efim Brener, and Dmitri Temkin — Institut für Festkörperforschung, Forschungszentrum Jülich, D-52425 Jülich, Germany

Dendritic growth is a process which is very important in materials science. It can occur not only in solidification, but also in melting processes. Specifically, we discuss the melting of an overheated crystal along a grain boundary, in the framework of the symmetric model of diffusion-limited growth.

In contrast to the conventional dendritic growth, which requires the consideration of the anisotropy of the surface tension to provide a selection of the characteristic length scale of the appearing pattern and the growth velocity, the situation is here rather different: The presence of the triple junction at the tip allows a steady growth even for isotropic surface tension. This pattern formation problem is solved entirely analytically for specific parameter ranges. To our best knowledge, this is the first case of an entirely analytical solution in dendritic growth. In other cases, the corresponding nonlinear eigenvalue problem is solved numerically.