Abstract
We interpret the crystallization of several glass-forming systems in which fresnoite crystals are formed in terms of the rigidity percolation theory. The structure of glass-forming melts can be described as a network with some rigid and some floppy regions. A jump of some properties of the system is expected when the average number of constraints per molecule exceeds a threshold value. In particular, we observed a drastic change in the critical undercooling at which crystallization begins. Above the rigidity threshold, nucleation takes place predominantly in some small floppy regions. This is the reason why the condition for the start of crystallization can be reformulated: the threshold undercooling is so large that the size of the critical nucleus does not exceed the size of the floppy regions.
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