M1 Glass Formation: Cooling Kinetics

Topic

As the glass melt cools from its liquid state, the cooling rate—the speed at which the melt loses temperature—competes at every moment against the kinetics of nucleation and crystal growth; given sufficient time, these kinetics would transform the melt into a crystalline solid rather than the glass in question. A higher cooling rate means the melt has less time within each temperature interval for these nucleation and crystal growth kinetics to produce crystals.

There exists a specific critical cooling rate—as described by Uhlmann's criterion—above which the kinetics of nucleation and crystal growth fail to produce a detectable crystallized fraction before the melt becomes too cold and too viscous to continue crystallizing. If the melt's cooling rate exceeds this critical value, crystallization is avoided, and the melt—instead of solidifying as a crystalline solid—freezes into the disordered structure of the glass; conversely, if the cooling rate falls below this critical value, crystallization does occur before the melt freezes.

The nucleation and crystal growth kinetics competing against the cooling rate are determined at any given moment by the melt's nucleation rate: the more crystallization nuclei that appear per unit of time and volume, the faster the crystallized fraction grows (according to the Avrami equation) for a given holding time. A higher nucleation rate—for a constant cooling rate—makes it more difficult for that cooling rate to exceed the critical speed required to prevent crystallization. Thus, this model—framed by the interplay between cooling rate and the kinetics of nucleation and crystal growth—defines vitrification precisely as the avoidance of crystallization: the melt transforms into glass not because of some additional transformative process, but because the cooling rate prevents the nucleation rate and the crystallized fraction—both governed by the Avrami equation—from producing any crystals before the melt freezes. The fact that this same nucleation rate and crystallized fraction (governed by Avrami) *do* manifest when the formed glass is reheated or remains in service at high temperatures for an extended period leads another model in this set to repurpose these same equations to describe a pathology—devitrification—rather than the controlled glass-formation process itself.

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