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Phagraphene [fæ’græfiːn] is a proposed graphene allotrope composed of 5-6-7 carbon rings. Phagraphene was proposed in 2015 based on systematic evolutionary structure searching.[1] Theoretical calculations showed that phagraphene is not only dynamically and thermally stable, but also has distorted Dirac cones. The direction-dependent cones are robust against external strain with tuneable Fermi velocities.[1]

Higher-energy allotropes named Haeckelite contained penta- hexa- and hepta-carbon rings. Three types (rectangular, oblique and hexagonal) were proposed as early as 2000.[2] These metastable allotropes have a trivial intrinsic metallic behavior.

Phagraphene is predicted to have a potential energy of 193.2 kcal/mol.[3] The bond order is 1.33, the same as for graphene.[3]


An unrelated material called PHA/graphene is a polyhydroxyalkanoate graphene composite.


  1. ^ a b Wang, Zhenhai; Zhou, Xiang-Feng; Zhang, Xiaoming; Zhu, Qiang; Dong, Huafeng; Zhao, Mingwen; Oganov, Artem R. (9 September 2015). "Phagraphene: A Low-Energy Graphene Allotrope Composed of 5–6–7 Carbon Rings with Distorted Dirac Cones". Nano Letters. 15 (9): 6182–6186. arXiv:1506.04824. Bibcode:2015NanoL..15.6182W. doi:10.1021/acs.nanolett.5b02512. PMID 26262429. S2CID 8417064.
  2. ^ Terrones, H.; Terrones, M.; Hernández, E.; Grobert, N.; Charlier, J-C.; Ajayan, P. M. (21 February 2000). "New Metallic Allotropes of Planar and Tubular Carbon" (PDF). Physical Review Letters. 84 (8): 1716–1719. Bibcode:2000PhRvL..84.1716T. doi:10.1103/PhysRevLett.84.1716. PMID 11017608.
  3. ^ a b Cranford, S.W. (January 2016). "When is 6 less than 5? Penta- to hexa-graphene transition". Carbon. 96: 421–428. doi:10.1016/j.carbon.2015.09.092.