Metastability and Ostwald Step Rule in the Crystallisation of Diamond and Graphite from Molten Carbon (2503.02069v2)

Abstract: The crystallisation of carbon from the melt under extreme conditions is highly relevant to earth and planetary science, materials manufacturing, and nuclear fusion research. 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. 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 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.

Analyzing Crystallization Dynamics in Carbon through a Microscopic Lens

The paper "Metastability and Ostwald Step Rule in the Crystallisation of Diamond and Graphite from Molten Carbon," explores the dynamics of carbon crystallization under extreme thermodynamic conditions, highlighting implications in earth and planetary science, materials manufacturing, and nuclear fusion research. The research employs molecular simulations with first-principles machine learning potentials to decipher the mechanisms of diamond and graphite nucleation from liquid carbon near the graphite-diamond-liquid (GDL) triple point, which is critical for interpreting the carbon phase diagram discrepancies reported in experimental studies.

Key Findings

The authors report a thorough investigation of the phase diagram of carbon around the GDL triple point, demonstrating accurate simulation outcomes consistent with experimental data. The results underscore that liquid carbon exhibits spontaneous crystallization when cooled at constant pressure, with metastable graphite forming above the diamond's thermodynamic stability region. This is attributed to liquid carbon's density being higher than that of graphite at pressures exceeding 2 GPa, promoting spontaneous nucleation of graphite up to approximately 15 GPa due to Ostwald's step rule.

Nucleation Rates: The research employs forward flux sampling molecular dynamics to compute nucleation rates of graphite and diamond. The paper unveils that at pressures below 15 GPa, graphite nucleation is favored, while at higher pressures, diamond becomes predominant. These findings are supported by the validated classical nucleation theory (CNT) model that characterizes the nucleation rates, highlighting distinct mechanisms for the nucleation of graphite and diamond which support Ostwald’s step rule predictions.

Implications and Theoretical Developments

This paper is a significant contribution to understanding phase transition kinetics in polymorphic materials, providing insights into carbon's crystallization routes under varying pressure conditions. It challenges previous assumptions that liquid carbon is a strong glass former by demonstrating spontaneous crystallization, particularly of metastable graphite, at pressures where diamond is more thermodynamically stable. This implies significant barriers exist that hinder the direct transition from metastable graphite to stable diamond.

Structured Crystallization Pathways: The paper describes distinct crystallization pathways where graphite follows a two-step process with preliminary low-density fluctuations, differing from the typical nucleation path of diamond which does not precede crystalline ordering with density fluctuations. These findings showcase a non-classical, density-driven crystallization mechanism that could reshape current theoretical models in crystallization science.

Practical Applications and Future Directions

For materials science, understanding these crystallization kinetics is crucial for optimizing the manufacturing conditions of carbon-based materials, including synthetic diamonds. This research could influence the design of high-pressure, high-temperature synthesis protocols by delineating the conditions favorable for specific types of carbon crystallization.

Future Developments in AI and Simulations: The use of first-principles machine learning potentials in this research highlights the potential for AI-driven advancements in simulating complex molecular dynamics over extended time scales and large systems. These techniques can be further refined to explore other monoatomic and polymorphic systems, potentially unveiling novel crystallization dynamics in related materials.

In summary, this paper provides substantial insights into carbon's crystalline transitions under extreme conditions, substantiated by numerical models that corroborate a complex interplay of density-driven metastability and kinetic nucleation phenomena. The structural elucidation of these processes not only clarifies previously ambiguous experimental observations but also sets the stage for more refined investigations into metastable phase transformations in other polymorphic and monoatomic systems.