Crystallization of Glasses: A Theoretical Analysis of the Role of Fragility and Polymorphism in Crystals.

Abstract

Here we develop an elasticity-based theory of crystallization in glasses that incorporates structural heterogeneity, fictive temperature, and polymorph-mediated pathways. In a glass, structural degrees of freedom are effectively frozen, so that the fictive temperature Tf remains higher than the ambient temperature T, rendering the system intrinsically out of equilibrium. A central result is that the crystal-glass interfacial penalty is renormalized in fragile systems by soft, liquid-like regions, leading to a subquadratic mismatch energy scaling as ΣR3/2 rather than the classical R2 form. Applying this framework to ethanol, we show that nucleation proceeds preferentially via a two-step route through a plastic crystalline polymorph. The associated barriers are dramatically reduced: the glass-to-plastic step exhibits barriers of only  ∼5 kBT, compared to  ∼102 kBT for the direct glass-to-crystal transition. This large separation explains the dominance of the Ostwald pathway and the emergence of a pronounced time-temperature-transformation (TTT) nose. In contrast, silica retains the classical R2 scaling due to its rigid network, leading to very large barriers and suppressed bulk nucleation.