Carbon phase diagram with empirical and machine learned interatomic potentials

Abstract

In the present work we detail how the many-body potential energy landscape of interatomic potentials for carbon can be explored by utilising the nested sampling algorithm, allowing the calculation of their pressure-temperature phase diagram up to high pressures. We present a comparison of three interatomic potential models, Tersoff, EDIP and GAP-20, focusing on their macroscopic properties, particularly on their melting transition and on identifying thermodynamically stable solid structures up to at least 100 GPa. The studied models all form graphite structures upon freezing at lower pressure, then the diamond structure as the pressure increases. We were able to locate the transition between these phases in case of the Tersoff and EDIP models. We placed particular focus on the state-of-the-art machine learning (ML) model, GAP-20, and calculated its phase diagram up to 1 TPa to evaluate its predictive capabilities well outside of the model's fitting conditions. The phase diagram showed a remarkably good agreement with the experimental phase diagram up to 200 GPa, despite a variety of unexpected graphite layer spacing. Above that nested sampling identified two novel stable solid structures, a strained diamond structure and above 800 GPa a strained hexagonal-close-packed structure. However, the stability of these two phases were not confirmed by DFT calculations, highlighting potential routes to further improve the ML model.