A statistical-thermodynamic analysis of stably ordered substitutional structures in graphene

Ordered distributions of carbon and substitutional dopant (A) atoms over the sites of a graphene lattice, i.e. CmA superstructures with dopant contents c=1/(m+1), and problem of their stability are considered theoretically. The ranges of values of interatomic-interaction parameters providing the low-temperature stability of the graphene-based C7A, C3A, and CA superstructures are determined within the framework of both the third-nearest-neighbor Ising model and, more realistically, the all-coordination-shell interaction model. The first model results in the “omission” (instability) of some predicted superstructures, while the second model shows that all predicted superstructures are stable at certain values of interatomic-interaction energies. Even short-range interatomic interactions provide a stability of some superstructures, while only long-range interactions stabilize others.