Abstract

While experimental realization of crystalline two–dimensional materials has been common in recent years, there are limited examples of amorphous counterparts. Amorphous graphene, a two-dimensional extended carbon system with disorder, is a prototype for studying 2D disorder due to its complex and rich configurational space, which is not yet fully understood. Here we report on an atomistic modelling study of amorphous graphene using a machine learning (ML) based force field. ML force fields are typically “trained” on data from computationally expensive density functional theory (DFT) calculations but can achieve near DFT accuracy with significantly reduced computational cost. One key assumption in many of these methods is that the global energy can be separated into sums of local contributions. The extent to which these “machine-learned” local energies are physically meaningful is an interesting research question. We create structural models by introducing defects into ordered graphene through Monte-Carlo bond switching, defining acceptance criteria using the machine-learned local, atomic energies associated with a defect, as well as the nearest-neighbour (NN) environments. We find that physically meaningful structural models arise from ML atomic energies, ranging from continuous random networks to paracrystalline structures. Our results show that ML atomic energies can be used to guide Monte-Carlo structural searches in principle, and that their predictions of local stability can be linked to short- and medium-range order in amorphous graphene. We expect that the former point will be relevant more generally to the study of amorphous materials, and that the latter has wider implications for the interpretation of ML potential models.

Acknowledgements: The authors would like to acknowledge the use of the University of Oxford Advanced Research Computing (ARC) facility in carrying out this work. This work was supported by the Engineering and Physical Sciences Research Council [grant number EP/L015722/1].