Exploring the Morphology of Two, Three and Four-Atom Removed Hole Defects in 2D B₂C Monolayers Using a Machine Learning-Enhanced Process

Graphene’s success in advancing battery technology, sensors, medical devices, and composite materials, has prompted the exploration of other nanostructures for broader applications, with B2C among them. The B2C monolayer is a promising 2D structure for next-generation batteries and catalysis, and numerous research teams have extensively studied its structural, thermal, and mechanical stability. Creating antidot structures or introducing periodic physical hole defects allows for the fine-tuning of material properties and significantly increases the number of catalytically active sites by introducing more edges, which are known to be more reactive. However, to our knowledge, there has been no systematic study into the physical structures of hole defects in B2C monolayers, which would confirm if antidots could also tune their properties. This research aims to understand the structures of two-atom, three-atom, and four-atom hole defects in B2C monolayers, and the bonding mechanisms around these defects in the most favorable cases. Our primary approach accounted for all permutations up to four atom-removed defects and relaxed the structures using DFT by GPAW. To thoroughly search the configuration space, we adopted a global search scheme using a neural network (NN) trained on the fly in a genetic algorithm (GA) and relaxed the structures generated by the GA with DFT. We identified several structures resembling those proposed by Luo et al. using a particle swarm optimization (PSO) search but our NN-GA-DFT scheme generally did not yield hole structures with lower formation energies than those generated by manually removing atoms. The lowest antidot structure formation energies resulted from permutations of asymmetrical rings, which were obtained by altering the locations of atoms along a favorable hole. This gave energies of -3.727 eV, -5.177 eV, and -9.763 eV for 2, 3, and 4 atoms removed defects respectively. However, the permuted structures might be in different phases, so we also included the lowest three without permutations: -3.123 eV, -5.060 eV, and -8.555 eV for 2, 3, and 4 atoms removed defects, respectively. When more carbons were removed, hole edges tended to over-fill with borons, while when more borons were removed, hole edges maintained the intact B2C motif.