  The competition between crystallization and vitrification in glass-forming
materials manifests as a non-monotonic behavior in the time-temperature
transformation (TTT) diagrams, which quantify the time scales for
crystallization as a function of temperature. We develop a coarse-grained
lattice model, the Arrow-Potts model, to explore the physics behind this
competition. Using Monte Carlo simulations, the model showcases non-monotonic
TTT diagrams resulting in polycrystalline structures, with two distinct regimes
limited by either crystal nucleation or growth. At high temperatures,
crystallization is limited by nucleation and results in the growth of compact
crystal grains. At low temperatures, crystal growth is influenced by glassy
dynamics, and proceeds through dynamically heterogeneous and hierarchical
relaxation pathways producing fractal and ramified crystals. To explain these
phenomena, we combine the Kolmogorov-Johnson-Mehl-Avrami theory with the field
theory of nucleation, a random walk theory for crystal growth, and the
dynamical facilitation theory for glassy dynamics. The unified theory yields an
analytical formula relating crystallization timescale to the nucleation and
growth rates through universal exponents governing glassy dynamics of the
model. We show that the formula with the universal exponents yields excellent
agreement with the Monte Carlo simulation data and thus, it also accounts for
the non-monotonic TTT diagrams produced by the model. Both the model and theory
can be used to understand structural ordering in various glassy systems
including bulk metallic glass alloys, organic molecules, and colloidal
suspensions.
