What's beyond diamond ?
where diamond ends and something else starts
Diamond and graphite look very different at first glance. Diamond is superhard, transparent, shiny and expensive (because it is rare), graphite is instead soft, black and cheap (because it is abundant). Nevertheless, both are forms of the same element carbon but they have very different arrangement and bonding of atoms. Graphite is stable at atmospheric pressure and diamond at high pressure. Since 1956, high pressure has been used to transform graphite to diamond, enabling production of artificial diamonds.
On the pressure scale, graphite is thus before diamond. What the then beyond diamond? Is there anything at all? If so, what does it look like and how far is it? And most importantly, how to get there if we want to observe it?
In other words, we have two questions to answer. The theoretical one is how much we have to compress diamond in order to rearrange its atoms, and what does the new arrangement look like. The experimental one is how to reach such pressure, even if for a short time, and how to detect whether the atoms have changed their arrangement.
The theoretical question has interested people for a long time. The first (and we still believe correct) prediction was provided in 1984 [1] - at the pressure of about 1 TPa (1012 Pa, 10 million times higher than the normal atmospheric pressure, three times higher than the pressure at the center of the Earth) diamond should transform to the so called BC8 phase. The prediction was based on analogy with silicon but later atudies employing advanced systematic crystal structure prediction methods confirmed it entirely. BC8 is a complicated structure (figure - red atoms) which still maintains the preferred number of four bonds per carbon atom but their arrangement is more complicated, allowing a volume reduction of about 3%.
The experimental problem is serious. We need a pressure of at least 1 TPa, which is an extreme pressure that cannot be reached in a static terrestrial experiment. Currently the only possibility is the so called ramp compression which can reach pressure in the TPa range, however, only for a short time of about 10 ns.
But even reaching such pressure for a very short time might not be enough since diamond does not yield easily. Few years ago, the experiment [2] reached a pressure of 2 TPa, but surprisingly, no transition was observed. Diamond was only compressed but its structure did not change. The BC8 phase in carbon thus has not yet been experimentally observed.
Since the experiment is very challenging and costly, it is useful to perform a computer simulation. It could discover how exactly should the transformation proceed and test various possibilities that might be useful for the design of the experiment.
Currently computer simulations as well as many other branches of science and everyday life are heavily influenced by the revolution related to the application of machine learning (ML) methods. The simulations are based on the ability to compute the energy of the system (so-called potential) if we know the positions of all atoms. This can be calculated by means of quantum mechanics, but the calculation is complicated and lengthy and for systems with more than few thousands of atoms practically impossible. And here ML comes to help - it can learn e.g. the potential for carbon from a large number of examples and then compute it fast and with high accuracy even for millions of atoms. This progress allows to substantially push the frontiers of what we can simulate.
In our work we employed the ML potential for carbon [3] developed by the group of Prof. I. Oleynik at the University of South Florida, Tampa, USA. By means of metadynamics [4] and molecular dynamics we first simulated transitions induced by high pressure from the cubic diamond phase. We observed that in the initial stage a disordered droplet is formed, representing supercooled liquid. Within a short time the droplet crystallizes to BC8 which subsequently gradually grows and finally fills the whole system. Cubic diamond, however, is not the only diamond phase of carbon. Another phase, hexagonal diamond (lonsdaleite) is found in Nature, albeit quite rarely. In our work we simulated for the first time also the transition from this phase (figure). The result was surprising - the transition proceeded similarly to the case of cubic diamond, but substantially faster. Since time plays in the ramp compression method a crucial role, because the high pressure is reached only for a very short time, using hexagonal diamond as initial material might be a better choice. We also simulated decompression of BC8 to atmospheric pressure and found that this exotic phase could possibly survive quenching to ambient conditions and exist as a metastable phase.
The work [5] which is the result of a collaboration with the group of Prof. I. Oleynik, was on 1 June 2026 published in the journal Phys. Rev. B Letters (belongs to Nature index) and will be useful for the design of future experiments aiming at the synthesis of BC8. The research at the Comenius University was supported by the grants APVV-19-0371 and APVV-23-0515.
References
[1] M. T. Yin, Si-III (BC-8) crystal phase of Si and C: Structural properties, phase stabilities, and phase transitions, Phys. Rev. B 30, 1773 (1984).
[2] A. Lazicki, D. McGonegle, J. R. Rygg, D. G. Braun, D. C. Swift, M. G. Gorman, R. F. Smith, P. G. Heighway, A. Higginbotham, M. J. Suggit, et al., Metastability of diamond ramp-compressed to 2 terapascals, Nature (London) 589, 532 (2021).
[3] J. T. Willman, K. Nguyen-Cong, A. S. Williams, A. B. Belonoshko, S. G. Moore, A. P. Thompson, M. A. Wood, and I. I. Oleynik, Machine learning interatomic potential for simulations of carbon at extreme conditions, Phys. Rev. B 106, L180101 (2022).
[4] A. Laio and M. Parrinello, Escaping free-energy minima, Proc. Natl. Acad. Sci. USA 99, 12562 (2002).
[5] Roman Martoňák, Sergey Galitskiy, Azat Tipeev, Joseph M. Gonzalez, and Ivan I. Oleynik, From diamond to BC8 to simple cubic and back: Kinetic pathways to post-diamond carbon phases from metadynamics, Phys. Rev. B 113, L220101 (2026).