This paper proposes a mathematical model of solidification dynamics of binary alloys. We express the state of an alloy by the phase parameter and the concentration, and describe the dynamics as a free energy minimizing process. The most advantageous feature of the model is that the interaction energy is directly given to each pair of atoms according to types of alloys. Thus, we can easily know the conditions to let the model correspond to all basic kind of alloys including eutectic, peritectic alloys, for example. We also perform some numerical simulations and reproduce typical structures observed in real alloys.
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Sakai, K. A mathematical model of solidification dynamics of binary alloys. Japan J. Indust. Appl. Math. 17, 43 (2000). https://doi.org/10.1007/BF03167335
- binary alloys
- isothermal solidification dynamics
- mathematical model using phase parameter