Parallel pathway mechanism describing crystal nucleation in glass-forming materials

This work introduces a general parallel pathway mechanism (PPM) for crystal nucleation, combining traditional three-dimensional (3D) classical nucleation theory (CNT) with a two-dimensional (2D) nucleation framework. This approach offers enhanced flexibility in describing diverse nucleation kinetics observed across various systems, addressing limitations of existing models like the Turnbull-Fisher (T-F) equation. Unlike the T-F equation, which predicts maximal nucleation near the glass transition temperature ( T g ), the PPM relates a maximum nucleation rate that can occur over a wide temperature range, from T g to near the melting point ( T m ). That is because the peak nucleation rate can be precisely tuned by adjusting the relative activation energies of the two parallel routes. At higher temperatures, the 2D mechanism dominates, forming nuclei that rapidly convert to 3D clusters. Conversely, the traditional 3D mechanism, leading directly to spherical crystallites, is favored at lower temperatures. The PPM provides a more robust description of experimental data, particularly for systems exhibiting "U-shaped" activation energy profiles, thereby resolving the challenge with modeling the apparent "CNT breakdown" region often observed at temperatures below where the maximum nucleation rate occurs. While this region has been characterized by incomplete glass relaxation due to dramatically slowing system dynamics, the PPM provides a mechanistic explanation for the difference in nucleation kinetics observed on either side of the maximum.