@phdthesis{Rasin2006, author = {Rasin, Igor}, title = {Numerical simulation of microstructure of the GeSi alloy}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus-474}, school = {BTU Cottbus - Senftenberg}, year = {2006}, abstract = {The goal of this work is to investigate pattern formation processes on the solid-liquid interface during the crystal growth of GeSi. GeSi crystals with cellular structure have great potential for applications in gamma-ray and neutron optics. The interface patterns induce small quasi-periodic distortions of the microstructure called mosaicity. Existence and properties of this mosaicity are important for the application of the crystals. The properties depend on many factors; this dependence, is currently not known even not qualitatively. A better understanding of the physics near the crystal surface is therefore required, in order to optimise the growth process. There are three main physical processes in this system: phasetransition, diffusion and melt flow. Every process is described by its own set of equations. Finite difference methods and lattice kinetic methods are taken for solving these governing equations. We have developed a modification of the kinetic methods for the advectiondiffusion and extended this method for simulations of non-linear reaction diffusion equations. The phase-field method was chosen as a tool for describing the phase-transition. There are numerous works applied for different metallic alloys. An attempt to apply the method directly to simulation GeSi crystal growth showed that this method is unstable. This instability has not been observed in previous works due to the much smaller scale of simulations. We introduced a modified phase-field scheme, which enables to simulate pattern formation with the scale observed in experiment. A flow in the melt was taken in to account in the numerical model. The developed numerical model allows us to investigate pattern formation in GeSi crystals. Modelling shows that the flow near the crystal surface has impact on the patterns. The obtained patterns reproduce qualitatively and in some cases quantitatively the experimental results.}, subject = {Germanium; Silicium; Legierung; Kristallwachstum; Kristallz{\"u}chtung; Gitter-Boltzmann; Phasenfeld; Erstarrung; Strukturbildung; Crystal growth; Lattice Boltzmann; Phase field; Solidification; Pattern formation}, language = {en} }