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Comprehensive structure exploration and thermodynamics of graphitic heteroatom doped graphene superstructures

Benedict Saunders

Lukas Hörmann* and Reinhard J. Maurer†

  • *Contact author: lukas.hoermann@univie.ac.at
  • †Contact author: reinhard.maurer@univie.ac.at
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Phys. Rev. B 114, 264101 – Published 2 November, 2026

DOI: https://doi.org/10.1103/db9g-7gvs

Abstract

Graphene has been studied in detail due to its mechanical, electrical, and thermal properties. It is well documented that the introduction of dopants or defects in the lattice can be used to tune material properties for a specific application, such as in electronics, sensors, or catalysis. To design graphene with specific properties, one must achieve control over the composition and concentration of defects. This requires a fundamental understanding of the stability of defects and their interaction in a superstructure. We present a comprehensive defect structure determination approach that enables close to exhaustive enumeration of all relevant defect structures. The approach uses a combination of density functional theory and machine learning to build a transferable energy model for defect formation. We show the capabilities of our approach for free-standing graphene with heteroatom defects, establishing a thermodynamic model to investigate how temperature affects the configuration space of doped graphene. Our analysis yields physical insights into defect interactions. A characteristic peak in the heat capacity indicates a structural transition. We provide a mechanistic explanation for this behavior and demonstrate how the transition temperature shifts with different thermodynamic reservoirs.

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Phys. Rev. B 114, 264101– Published 2 November, 2026
  • Received 19 September 2025
  • Revised 5 October 2026
  • Accepted 8 October 2026
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