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Article: On the crystallization of 2D hexagonal lattices
Title | On the crystallization of 2D hexagonal lattices |
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Authors | |
Issue Date | 2009 |
Citation | Communications in Mathematical Physics, 2009, v. 286, n. 3, p. 1099-1140 How to Cite? |
Abstract | It is a fundamental problem to understand why solids form crystals at zero temperature and how atomic interaction determines the particular crystal structure that a material selects. In this paper we focus on the zero temperature case and consider a class of atomic potentials V = V 2 + V 3, where V 2 is a pair potential of Lennard-Jones type and V 3 is a three-body potential of Stillinger-Weber type. For this class of potentials we prove that the ground state energy per particle converges to a finite value as the number of particles tends to infinity. This value is given by the corresponding value for a optimal hexagonal lattice, optimized with respect to the lattice spacing. Furthermore, under suitable periodic or Dirichlet boundary condition, we show that the minimizers do form a hexagonal lattice. © 2008 Springer-Verlag. |
Persistent Identifier | http://hdl.handle.net/10722/327492 |
ISSN | 2023 Impact Factor: 2.2 2023 SCImago Journal Rankings: 1.612 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Weinan, E. | - |
dc.contributor.author | Li, Dong | - |
dc.date.accessioned | 2023-03-31T05:31:45Z | - |
dc.date.available | 2023-03-31T05:31:45Z | - |
dc.date.issued | 2009 | - |
dc.identifier.citation | Communications in Mathematical Physics, 2009, v. 286, n. 3, p. 1099-1140 | - |
dc.identifier.issn | 0010-3616 | - |
dc.identifier.uri | http://hdl.handle.net/10722/327492 | - |
dc.description.abstract | It is a fundamental problem to understand why solids form crystals at zero temperature and how atomic interaction determines the particular crystal structure that a material selects. In this paper we focus on the zero temperature case and consider a class of atomic potentials V = V 2 + V 3, where V 2 is a pair potential of Lennard-Jones type and V 3 is a three-body potential of Stillinger-Weber type. For this class of potentials we prove that the ground state energy per particle converges to a finite value as the number of particles tends to infinity. This value is given by the corresponding value for a optimal hexagonal lattice, optimized with respect to the lattice spacing. Furthermore, under suitable periodic or Dirichlet boundary condition, we show that the minimizers do form a hexagonal lattice. © 2008 Springer-Verlag. | - |
dc.language | eng | - |
dc.relation.ispartof | Communications in Mathematical Physics | - |
dc.title | On the crystallization of 2D hexagonal lattices | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1007/s00220-008-0586-2 | - |
dc.identifier.scopus | eid_2-s2.0-59449106896 | - |
dc.identifier.volume | 286 | - |
dc.identifier.issue | 3 | - |
dc.identifier.spage | 1099 | - |
dc.identifier.epage | 1140 | - |
dc.identifier.eissn | 1432-0916 | - |
dc.identifier.isi | WOS:000263059600010 | - |