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We modified a multi-phase-field model previously developed by the authors and applied it to investigate the peritectic microstructure formation and corresponding kinetics in an Al–Ni alloy during directional solidification. The model presented uses the parameters derived directly from the free energy functions of individual phases. The thermodynamic driving force is treated as a function of the difference between the current diffusion potential of the solute on an interface and the corresponding equilibrium diffusion potential. The time evolution of the concentration field is simplified and is given by one term. The main advantage of the modified model arises through the reduced number of parameters depending on phase-field variables. The proposal model is then extended to multi-component systems. In this context two methods for the evaluation of the thermodynamic parameters are proposed. The resulting model can be employed for large scale parameter studies even for demanding multi-component systems.