We have investigated the influence of the surface tension anisotropy on the dynamics of pattern selection during the directional solidification of a binary alloy. Whereas the importance of this anisotropy is well documented for free dendritic growth, its role in directional solidification was recognized only recently. In particular, it was shown that recently discovered multiple cells can be dynamically selected if the initial perturbation has a fixed periodicity. These results are in excellent agreement with recent experiments where a perturbation of fixed wavelength is imposed at the beginning of the solidification process, using a modulated laser beam. We have also developed a phase-field model for the directional solidification of eutectic alloys with an additional ternary impurity.
Simulations show the development of large two-phase eutectic cells, in agreement with experiments.
The step dynamics in epitaxial thin-film growth are governed by the interplay of the flux of deposited atoms, the surface diffusion, and the desorption from the surface. In particular, we have investigated the dynamics of spiral ridges around screw dislocations. Whereas these spirals are well understood in the regime where desorption is dominant, our method enables us to investigate the opposite case, relevant for molecular beam epitaxy, where surface diffusion is dominant. Both directional solidification and epitaxial growth are important industrial methods for advanced materials fabrication. Many properties of the final material are largely influenced by the microstructure of the material, which in turn is determined by the dynamics of the growth front.