Publication:
Dislocations and defects in graphene

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2017-06
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Abstract
Graphene is a two dimensional material whose surprising properties have arisen promising expectatives. Mathematically, it is described by an hexagonal lattice. This lattice exhibits geometrical defects: heptagon-pentagon pairs, Stone-Wales defects, vacancies, divacancies. These defects can be described as cores of edge dislocations and dislocation groupings. Their long time stability is then understood analyzing the response of isolated defects to applied forces. In simpler two dimensional lattice models, we argue that the onsets of both dislocation motion and dislocation nucleation correspond to different types of bifurcations. Dislocation motion is associated to global bifurcations in a branch of stationary dislocation solutions to give raise to traveling wave solutions. Homogeneous dislocation nucleation may be described by pitchfork bifurcations in simple geometries. As the way forces are applied changes, the bifurcation diagram varies. In real graphene lattices, curvature effects are important, specially at the core of defects. These effects are captured by discrete versions of Foppl-Von Karman equations in hexagonal lattices.
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Física-Modelos matemáticos , Física de materiales , Matemáticas (Matemáticas) , Análisis numérico
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12 Matemáticas , 1206 Análisis Numérico
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[1] A. Carpio, L.L. Bonilla, Periodized discrete elasticity models for defects in graphene, Physical Review B 78, 085406, 2008. [2] LL Bonilla, A Carpio, Theory of defect dynamics in graphene: defect groupings and their stability, Continuum Mechanics and Thermodynamics, 23, 337-346, 2011. [3] LL Bonilla, A Carpio, Driving dislocations in graphene, Science 337, 161-162, 2012. [4] A. Carpio, Wavefront solutions for discrete two dimensional nonlinear diffusion equations, Applied Mathematics Letters, 15(4), 415-421, 2002. [5] A. Carpio, L.L. Bonilla, Edge dislocations in crystal structures considered as traveling waves of discrete models, Physical Review Letters, 90(13), 135502, 1-4, 2003; 91(2), 029901-1, 2003. [6] A. Carpio, L.L. Bonilla, Oscillatory wave fronts in chains of coupled nonlinear oscillators, Physical Review E., 67, 056621, 1-11, 2003. [7] A. Carpio, Nonlinear stability of oscillatory wave fronts in chains of coupled oscillators, Physical Review E, 69, 046601, 1-13, 2004. [8] A. Carpio, Wave trains, self-oscillations and synchronization in discrete media, Physica D-Nonlinear Phenomena 207(1-2), 117-136, 2005 [9] I. Plans, A. Carpio, L.L. Bonilla, Homogeneous nucleation of dislocations in a periodized discrete elasticity model, Europhysics Letters, 81, 36001, 1-6, 2008. [10] I. Plans, A. Carpio, L.L. Bonilla, Toy nanoindentation model and incipient plasticity, Chaos, solitons and fractals 42, 1623-1630, 2009. [11] LL Bonilla, A Carpio, C. Gong, J Warner, Measuring strain and rotation fields at the dislocation core in graphene, Physical Review B 92, 155417, 2015. [12] A. Carpio, SJ Chapman, JJL Velazquez, Pile-up solutions for some systems of conservation laws modelling dislocation interaction in crystals, SIAM Journal on Applied Mathematics 61(6), 2168-2199, 2001
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https://hdl.handle.net/20.500.14352/19724
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