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Boundaries determine the formation energies of lattice defects in two-dimensional buckled materials

Sandeep K. Jain, Vladimir Juričić, and Gerard T. Barkema
Phys. Rev. B 94, 020102(R) – Published 19 July 2016
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Abstract

Lattice defects are inevitably present in two-dimensional materials, with direct implications on their physical and chemical properties. We show that the formation energy of a lattice defect in buckled two-dimensional crystals is not uniquely defined as it takes different values for different boundary conditions even in the thermodynamic limit, as opposed to their perfectly planar counterparts. Also, the approach to the thermodynamic limit follows a different scaling: inversely proportional to the logarithm of the system size for buckled materials, rather than the usual power-law approach. In graphene samples of 1000 atoms, different boundary conditions can cause differences exceeding 10 eV. Besides presenting numerical evidence in simulations, we show that the universal features in this behavior can be understood with simple bead-spring models. Fundamentally, our findings imply that it is necessary to specify the boundary conditions for the energy of the lattice defects in the buckled two-dimensional crystals to be uniquely defined, and this may explain the lack of agreement in the reported values of formation energies in graphene. We argue that boundary conditions may also have an impact on other physical observables such as the melting temperature.

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  • Received 4 March 2016
  • Revised 25 June 2016

DOI:https://doi.org/10.1103/PhysRevB.94.020102

©2016 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Sandeep K. Jain1,*, Vladimir Juričić1,2,†, and Gerard T. Barkema1,3

  • 1Institute for Theoretical Physics, Universiteit Utrecht, Leuvenlaan 4, 3584 CE Utrecht, The Netherlands
  • 2Nordita, Center for Quantum Materials, KTH Royal Institute of Technology, and Stockholm University, Roslagstullsbacken 23, S-106 91 Stockholm, Sweden
  • 3Instituut-Lorentz, Universiteit Leiden, Niels Bohrweg 2, 2333 CA Leiden, The Netherlands

  • *S.K.Jain@uu.nl
  • juricic@nordita.org

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Issue

Vol. 94, Iss. 2 — 1 July 2016

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