Analysis of rippling in incommensurate one-dimensional coupled chains

Paul Cazeaux; Mitchell Luskin; Ellad B. Tadmor

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arXiv · 1606.02619

Analysis of rippling in incommensurate one-dimensional coupled chains

Paul Cazeaux·Mitchell Luskin·Ellad B. Tadmor

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Abstract

Graphene and other recently developed 2D materials exhibit exceptionally strong in-plane stiffness. Relaxation of few-layer structures, either free-standing or on slightly mismatched substrates occurs mostly through out-of-plane bending and the creation of large-scale ripples. In this work, we present a novel double chain model, where we allow relaxation to occur by bending of the incommensurate coupled system of chains. As we will see, this model can be seen as a new application of the well-known Frenkel-Kontorova model for a one-dimensional atomic chain lying in a periodic potential. We focus in particular on modeling and analyzing ripples occurring in ground state configurations, as well as their numerical simulation.

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Paul Cazeaux, Mitchell Luskin, Ellad B. Tadmor. 2016-06-08. Analysis of rippling in incommensurate one-dimensional coupled chains. https://arxiv.org/abs/1606.02619

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