M1 Solidification: Nucleation and Growth

Topic

Allowing the molten metal to cool below its equilibrium melting temperature without yet solidifying creates a state of undercooling, which serves as the precise driving force for the metal's solidification. This undercooling determines the free energy change associated with the nucleation of a solid nucleus within the melt—specifically, the difference in free energy between forming that solid nucleus and leaving the liquid melt as it is. Greater undercooling makes the free energy change associated with nucleation more favorable to the formation of the solid nucleus, thereby increasing the driving force available for the metal's solidification to proceed.

However, this free energy change associated with nucleation does not favor every solid nucleus equally, as it competes with the surface energy required to create the interface between the solid nucleus and the surrounding liquid melt. This competition gives rise to a critical nucleus radius—the minimum size a solid nucleus must reach so that further growth reduces rather than increases its total free energy—and a critical energy barrier, representing the energy the nucleus must overcome to reach that critical radius. Greater undercooling reduces both the critical nucleus radius and the critical energy barrier, making it easier for a solid nucleus to overcome the barrier and continue growing.

This critical energy barrier, in conjunction with the melt temperature, determines the nucleation rate—the frequency at which new solid nuclei appear per unit of time and volume. This nucleation rate, in turn, determines the resulting cast microstructure of the metal, including both its initial grain size and its dendritic morphology. A higher nucleation rate results in a greater number of solid nuclei competing for the same volume of melt, thereby leading to a smaller initial grain size in the resulting cast microstructure. Thus, this model—characterized by the nucleation and growth processes with which it began—feeds into another model within the same set (the one describing the metal's grain size) by providing the initial grain size of the casting microstructure, a value already determined by that very nucleation rate. The fact that this same nucleation rate—along with the Avrami equation describing the time-evolution of the solidified fraction derived from it—is reused for an analogous purpose in a model for a different class of materials (describing glass formation via vitrification) means that both models share the same mathematical framework to describe two opposite outcomes: the controlled crystallization of the metal and the avoidance of crystallization in the glass.

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