Metastability and Ostwald Step Rule in the Crystallisation of Diamond and Graphite from Molten Carbon

The crystallisation of carbon from the melt under extreme conditions is highly relevant to Earth and planetary science, ^1,2 , materials manufacturing, and nuclear fusion research ³ . The thermodynamic conditions near the graphite-diamond-liquid (GDL) triple point are especially of interest for geological and technological applications, but high-pressure flash heating experiments aiming to resolve this region of the phase diagram of carbon exhibit large discrepancies. ^4-7 Experimental challenges 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 in the region around the GDL triple point and show that liquid carbon crystallises spontaneously upon cooling at constant pressure. Surprisingly, 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 ⁸ where the strong metastability of graphite hinders the transformation to the stable diamond phase. Our results provide a new key to interpreting melting and recrystallisation experiments and shed light on nucleation kinetics in polymorphic materials with deep metastable states.