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Crystallization in Carbon Nanostructures

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Abstract

We investigate ground state configurations for atomic potentials including both two- and three-body nearest-neighbor interaction terms. The aim is to prove that such potentials may describe crystallization in carbon nanostructures such as graphene, nanotubes, and fullerenes. We give conditions in order to prove that planar energy minimizers are necessarily honeycomb, namely graphene patches. Moreover, we provide an explicit formula for the ground state energy which exactly quantifies the lower-order surface energy contribution. This allows us to give some description of the geometry of ground states. By recasting the minimization problem in three-space dimensions, we prove that ground states are necessarily nonplanar and, in particular, rolled-up structures like nanotubes are energetically favorable. Eventually, we check that the C20 and C60 fullerenes are strict local minimizers, hence stable.

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Authors and Affiliations

  1. Dipartimento di Ingegneria meccanica, energetica, gestionale e dei trasporti (DIME)-sezione MAT, Università degli Studi di Genova, p.le Kennedy 1, 16129, Genoa, Italy

    Edoardo Mainini

  2. Istituto di Matematica Applicata e Tecnologie Informatiche “E. Magenes”-CNR, v. Ferrata 1, 27100, Pavia, Italy

    Ulisse Stefanelli

  3. Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Vienna, Austria

    Ulisse Stefanelli

Authors
  1. Edoardo Mainini
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  2. Ulisse Stefanelli
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Correspondence to Ulisse Stefanelli.

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Communicated by M. Salmhofer

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Mainini, E., Stefanelli, U. Crystallization in Carbon Nanostructures. Commun. Math. Phys. 328, 545–571 (2014). https://doi.org/10.1007/s00220-014-1981-5

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  • DOI: https://doi.org/10.1007/s00220-014-1981-5

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