title: Breaking of symmetry in graphene growth on metal substrates.
abstract: In graphene growth, island symmetry can become lower than the intrinsic symmetries of both graphene and the substrate. First-principles calculations and Monte Carlo modeling explain the shapes observed in our experiments and earlier studies for various metal surface symmetries. For equilibrium shape, edge energy variations δE manifest in distorted hexagons with different ground-state edge structures. In growth or nucleation, energy variation enters exponentially as ∼e(δE/k(B)T), strongly amplifying the symmetry breaking, up to completely changing the shapes to triangular, ribbonlike, or rhombic.
authors.affiliation: Department of Materials Science and NanoEngineering, Rice University, Houston, Texas 77005, USA.
authors.forename: Vasilii I
authors.initials: VI
authors.lastname: Artyukhov
authors.affiliation: Department of Mechanical Engineering, Columbia University, New York, New York 10027, USA.
authors.forename: Yufeng
authors.initials: Y
authors.lastname: Hao
authors.affiliation: Center for Multidimensional Carbon Materials, Institute for Basic Science (IBS), Ulsan 689-798, Republic of Korea.|Department of Chemistry, Ulsan National Institute of Science and Technology (UNIST), Ulsan 689-798, Republic of Korea.
authors.forename: Rodney S
authors.initials: RS
authors.lastname: Ruoff
authors.affiliation: Department of Materials Science and NanoEngineering, Rice University, Houston, Texas 77005, USA.
authors.forename: Boris I
authors.initials: BI
authors.lastname: Yakobson