There's a reason why engagement rings are more expensive than wooden pencils. Diamond and graphite are both made of crystallized carbon, but diamond is much rarer.
In a study published in Nature Communications, researchers including Margaret Berrens at Lawrence Livermore National Laboratory (LLNL) created molecular dynamics simulations to explain what material forms when carbon crystallizes. Their work reveals that graphite can spontaneously nucleate, despite diamond being the stable phase under the studied conditions, offering insight into why natural diamonds are so rare.
Experiments to understand carbon crystallization have been inconsistent, with large discrepancies. The harsh conditions in which carbon crystallizes (pressures consistent with the Earth's interior) are difficult to achieve in the laboratory, and the transition happens very quickly.
To address that challenge, the authors developed accurate and efficient machine-learning potentials. They trained their model on density functional theory, which is a state-of-the-art quantum mechanical method used in condensed-matter physics.
With this model, the team could study thousands of atoms over the course of microseconds - well beyond the reach of conventional quantum simulations.
When liquid molten carbon was cooled at constant pressure, they expected to see glassy carbon as a result. Surprisingly, they instead saw spontaneous crystallization. At higher pressures, diamond formed. At lower pressures, some of which should also form diamond, they instead saw graphite.
"Graphite crystallized even within the domain where diamond is most stable," said Berrens.
This counterintuitive result arises from the distinct nucleation pathways of graphite and diamond, with graphite's metastability and lower interfacial free energy favoring its formation even in the stability domain of diamond.
More simply put: picture the diamond phase at the top of a shorter staircase and the graphite phase at the top of a taller staircase. The graphite is more difficult to get to. But now imagine the diamond staircase has huge steps, while the graphite staircase has steps that are more manageable. Because those intermediate steps are easier to get to, the carbon takes the path of least resistance, crystallizing into graphite instead of diamond under certain conditions.
Understanding the fine lines that separate graphite from diamond from liquid molten carbon is critical for modeling the interior of giant planets and achieving fusion ignition at LLNL's National Ignition Facility (NIF).
"In experiments such as those at NIF, diamond is commonly used as the surface of the target capsule. During the initial phase of implosion, it is driven to melt and blow off, or ablate, as evenly as possible," said Berrens. "Understanding carbon crystallization near the graphite-diamond-liquid triple point is essential to ensure the transition remains controlled rather than chaotic to obtain high-yield shots."
With this knowledge of carbon's behavior, the team also aims to help lay the correct mathematical foundations for hydrodynamic simulations of NIF capsule performance.
This work was a collaboration with researchers at the University of California Davis and George Washington University.
