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Many materials and workpieces arise from the melt by solidification. During the solidification process, a microstructure evolves which has major influence on material's properties. Therefore the objective of a large number of investigations in material's sciences is to act in a controlable manner on the microstructural evolution during solidification. To reduce the experimental effort, computer simulation methods are asked for. The phase field method is developed to perform simulations of the microstructural evolution with spatial resolution. In future the method allows computer aided optimization of the solidification process of technical alloys. As a first example, the solidification of pure silicon in a silicon ingot solidification process is presented. Another example is the simulation of a peritectic reaction similar to peritectic reactions in Ti-Al alloys.