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A Multi-Phase-Field model is applied to predict microstructure evolution and microsegregation during directional solidification of Ni-Al-Cr as the most important ternary in single crystal Ni-base superalloys. The model addresses both the dendritic growth of the primary γ phase and the subsequent interdendritic precipitation of the γ phase. Calculators of multicomponent phase equilibria are obtained using Thermo-Calc and a realistic thermodynamic database, either as a preprocessing tool or on-line by means of the TQ-interface. Multicomponent diffusion is calculated according to the Fick-Onsager relations using kinetic databases of the software DICTRA. A 1-D-benchmark on solidification of a Ni-Al-Cr alloy will be presented which compares an on-line coupled phase field calculation to a sharp-interface calculation using the software DICTRA. A cut-down version of the phase field model is then applied to simulate dendritic growth. The precipitation of interdendritic γ for different cooling rates is simulated I a shape constrained version of the model.