The paper was published in JETP Letters.
In this paper we employed computer simulation to study how diamond forms in multilayer graphene under pressure induced by indentation. We utilized machine-learning potentials to describe the interactions between atoms in the system.
Our simulations revealed that the initially formed diamond nucleus originates near the indenter and does not penetrate the entire thickness of the graphene film. The structure of the diamond seed is highly sensitive to the stacking pattern of the graphene layers and the size of the indenter.
We examined two specific graphene stacking patterns: ABC and AA', which could potentially lead to diamond formation. We hypothesized that these stacking patterns would form spontaneously due to layer shifting during indentation.
For the ABC stacking pattern, a cubic diamond embryo with a threefold rotational axis surrounded by regions of hexagonal diamond (lonsdaleite) emerged first. As indentation proceeded, both cubic diamond and lonsdaleite regions grew in size, see Fig. (a).
a,b) atomic structure of multilayer graphene with ABC (a) and AA' (b) stacking with the formed diamond region caused by indentation. Left: a slice of the structure, side view. Right: a top view of the film, where red lines show the slice area. The atomic environment of the structure is analyzed, and atoms belonging to the cubic diamond structure are highlighted in blue, and hexagonal diamond atoms are highlighted in orange; c) phase transition pressure dependence of the number of layers in graphene for the case of an indenter of infinite size (plane).
The AA' stacking pattern exhibited different behavior. Initially, a layer of hexagonal diamond with mirror symmetry appeared, followed by the formation of cubic diamond regions around it, see Fig. (b). The thickness of the lonsdaleite layer remained constant as indentation pressure increased, while the fraction of cubic diamond increased significantly. At small indenter sizes, hexagonal diamond acted as a twinning defect precursor within the cubic diamond regions, ultimately transforming into the cubic diamond phase.
Another crucial finding was the substantially lower pressure required for the phase transition from AA' stacked multilayer graphene to lonsdaleite compared to ABC stacked multilayer graphene transforming into cubic diamond for thin films indented by a flat surface (representing the limit of an infinitely large indenter), see Fig. (c).
Using ab initio analysis, we demonstrated that this difference arises from the redistribution of electrons on the lonsdaleite surface, leading to a lower surface energy for hexagonal diamond compared to cubic diamond.
Currently, scientists possess techniques for measuring Raman spectra during the indentation process using an optically transparent indenter objective. The spectra of cubic and hexagonal diamond can be distinguished. Samples containing mixed lonsdaleite and diamond phases exhibit a shift in the broad main peak from 1332 cm-1 to lower frequencies (down to 1320 cm-1).
Therefore, the possibility of experimentally verifying our predictions exists, which we hope to achieve in the near future.