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Abstract Experimental challenges in determining the phase diagram of carbon at temperatures and pressures near the graphite-diamond-liquid triple point are often related to the persistence of metastable crystalline or glassy phases, superheated crystals, or supercooled liquids. A deeper understanding of the crystallisation kinetics of diamond and graphite is crucial for effectively interpreting the outcomes of these experiments. Here, we reveal the microscopic mechanisms of diamond and graphite nucleation from liquid carbon through molecular simulations with first-principles machine learning potentials. Our simulations accurately reproduce the experimental phase diagram of carbon near the triple point and show that liquid carbon crystallises spontaneously upon cooling. Metastable graphite crystallises in the domain of diamond thermodynamic stability at pressures above the triple point. Furthermore, whereas diamond crystallises through a classical nucleation pathway, graphite follows a two-step process in which low-density fluctuations forego ordering. Calculations of the nucleation rates of the two competing phases confirm this result and reveal a manifestation of Ostwald’s step rule, where the strong metastability of graphite hinders the transformation to the stable diamond phase. Our results provide a key to interpreting melting and recrystallisation experiments and shed light on nucleation kinetics in polymorphic materials with deep metastable states. 

Heterogeneous ice nucleation is ubiquitous but its microscopic mechanisms can be extraordinarily complex even on a simple surface. Such complexity poses a challenge in modeling nucleation using advanced sampling methods. Here, we investigate heterogeneous ice nucleation on an FCC (211) surface by a forward flux sampling (FFS) method to understand how the complexity in nucleation pathways affects the accuracy of FFS. We first show the commonly adopted, size-based order parameter fails to describe heterogeneous ice nucleation on the FCC (211) surface. Inclusion of geometric anisotropy of ice nucleus as an additional descriptor is found to significantly improve the quality of the size-based order parameter for the current system. Subsequent application of this new order parameter in FFS identifies two competing ice nucleation pathways in the system: a primary-prism-planed (PPP) path and a secondary-prism-planed (SPP) path, both leading to the formation of hexagonal ice but with different crystalline orientations. Although the PPP pathway dominates ice nucleation on the FCC (211) surface, the occurrence of the less efficient SPP pathway, particularly its strong presence at the early stage of FFS, is found to yield a significant statistical uncertainty in the calculated FFS rate constant. We develop a two-path model that enables gaining a general, quantitative understanding of the impact of initial finite sampling on the reliability of FFS calculations in the presence of multiple nucleation pathways. Our study also suggests a few general strategies for improving the accuracy of FFS when exploring unknown but complex systems.