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

TL;DR

This paper uses statistical-thermodynamic models to analyze the stability of ordered substitutional structures in graphene, revealing the importance of long-range interactions for stability.

Contribution

It introduces a comprehensive thermodynamic framework to determine stability ranges of various superstructures in graphene considering both short- and long-range interactions.

Findings

Short-range interactions stabilize some superstructures.

Long-range interactions are necessary for the stability of all predicted superstructures.

The all-coordination-shell model predicts broader stability ranges than the third-nearest-neighbor model.

Abstract

Ordered distributions of carbon and substitutional dopant (A) atoms over the sites of a graphene lattice 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 the certain values of interatomic-interaction energies. Even short-range interatomic interactions provide a stability of some superstructures, while only long-range interactions stabilize others.