Application of the maximal entropy production principle to rapid solidification: A multi-phase-field model

Because the Cahn-Hillard and Allen-Cahn equations cannot deal with the additional constraints in the multi-phase-field models, several approximate treatments, e.g. a specific partition relation and the condition of equal or unequal diffusion potentials, were proposed. In this paper, the problem is solved successfully by the maximal entropy production principle and a model is developed for rapid solidification of a binary alloy system. Due to the mixture law used to define the free energy density, solute concentration and chemical potential jumps happen at an "imaginary" sharp interface between solid and liquid. The solute diffusions in solid and liquid are described by two independent equations and additional non-linear equations do not need to be employed to fix the solute concentrations of solid and liquid. Application to solute trapping during rapid solidification of Si-9 at.% As alloy shows that a good agreement between the model predictions and the experimental results is obtained. The interface and bulk contributions are decoupled at very low and very high interface velocities and in other cases the interaction between them depends weakly on the interface velocity.