Insight into Crystal Nucleation Mechanisms and Pathway Coexistence from Advanced Sampling Methods
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Nucleation process in atomistic systems is ubiquitous yet often governed by extraordinarymicroscopic complexity. Rare-event kinetics, strong interfacial effects, and the coexistence of multiple nucleation pathways can all play decisive roles in determining both nucleation rates and pathways, posing significant challenges for quantitative modeling and physical interpretation. This dissertation employs forward flux sampling (FFS) to study nucleation kinetics in heterogeneous and homogeneous systems, with the objectives of establishing reliable methodologies under pathway coexistence and identifying physically meaningful descriptors that govern nucleation efficiency. On the methodological side, we redesign and integrate the FFS framework into the LAMMPS molecular dynamics package, enabling massively parallel sampling of rare nucleation events. An analytical two-path model is developed to relate the apparent FFS rate constant to pathway growth probabilities and the statistical composition of configurations sampled at the initial milestone. This model quantifies finite-sampling bias in the presence of competing pathways and provides a general understanding of convergence behavior in FFS calculations. These methodological insights are first applied to heterogeneous ice nucleation on an FCC (211) surface. We show that the commonly adopted size-based order parameter fails due to the formation of highly anisotropic, disk-like crystalline seeds that do not represent viable ice nuclei. By introducing nucleus shape anisotropy as an additional geometric constraint, we identify two competing nucleation pathways
a primary-prism-planed (PPP) pathway and a secondary-prism-planed (SPP) pathway, both leading to hexagonal ice but with different crystalline orientations. Although the PPP pathway dominates nucleation, the early-stage presence of the less efficient SPP pathway produces large statistical uncertainty in FFS rate estimates, providing a concrete demonstration of convergence issues predicted by the two-path model. Building on this converged sampling framework, we investigate heterogeneous ice nucleation on graphene and demonstrate that lattice match alone does not determine nucleation efficiency. Instead, the nucleation rate correlates strongly with the density difference between interfacial water and ice in the first contact layer. Enhanced surface hydrophilicity induces a negative lattice mismatch that reduces this density difference and maximizes the nucleation rate. The density-based perspective is further extended to homogeneous crystallization of carbon near the graphite–diamond–liquid triple point using machine-learning interatomic potentials, where competing diamond and graphite pathways are selected according to their density proximity to the liquid. Together, these results establish density difference as a unifying physical descriptor of nucleation kinetics and demonstrate the necessity of converged pathway-resolved sampling for quantitative nucleation studies.
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