Competition of Crystallization and Vitrification*

The competition between vitrification and crystallization in glass-forming materials manifests as a non-monotonic behavior in the time-temperature transformation (TTT) diagrams. A coarse-grained model, referred to as the Arrow-Potts model, is constructed to explore the physics behind this competition. Using Monte Carlo simulations, the model is shown to produce two regimes of crystal nucleation and coarsening. At high temperatures, crystallization is dominated by the nucleation of compact and fluctuating crystalline clusters. At low temperatures, crystal coarsening proceeds through hierarchical relaxation pathways within the supercooled liquid, producing fractal ramified crystalline clusters. To explain and unify these two regimes, the Kolmogorov-Avrami theory is used as a framework to combine nucleation theory and a random walk theory for crystal coarsening kinetics, both of which govern the high-T and low-T regimes respectively. Finally, we demonstrate how the universal character of low-T crystallization is characterized by scaling exponents which are crucial to accurately account for the timescales observed in the TTT diagram.