NDLI: Crystallization for a Brenner-like Potential

Content Provider	Springer Nature Link
Author	Farmer, Brittan Esedoḡlu, Selim Smereka, Peter
Copyright Year	2016
Abstract	Graphene is a carbon molecule with the structure of a honeycomb lattice. We show how this structure can arise in two dimensions as the minimizer of an interaction energy with two-body and three-body terms. In the engineering literature, the Brenner potential is commonly used to describe the interactions between carbon atoms. We consider a potential of Stillinger–Weber type that incorporates certain characteristics of the Brenner potential: the preferred bond angles are 180 $${^\circ}$$ and all interactions have finite range. We show that the thermodynamic limit of the ground state energy per particle is the same as that of a honeycomb lattice. We also prove that, subject to periodic boundary conditions, the minimizers are translated versions of the honeycomb lattice.
Starting Page	1029
Ending Page	1061
Page Count	33
File Format	PDF
ISSN	00103616
Journal	Communications in Mathematical Physics
Volume Number	349
Issue Number	3
e-ISSN	14320916
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2016-08-10
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Theoretical, Mathematical and Computational Physics Mathematical Physics Quantum Physics Complex Systems Classical and Quantum Gravitation, Relativity Theory
Content Type	Text
Resource Type	Article
Subject	Statistical and Nonlinear Physics Mathematical Physics

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Crystallization for a Brenner-like Potential