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Numerical modelling of the growth of superconducting materials is beneficial with respect to both process control and the understanding of growth phenomena. The phase field method can be used to treat the evolution of a solid-liquid interface and has been extended to describe aspects of the multiphase system YBaCuO. The method is appropriate to simulate the faceted growth of both the properitectic and peritectic phases and its dependence upon Y-diffusion in the liquid phase. Numerical results show qualitative agreement with microstructures being experimentally observed in a transparent organic model system of YBaCuO and the YBaCuO system itself.