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Ana Carpio, Applied Mathematics - Graphene defects
In two dimensional graphene the atoms are arranged forming a honeycomb crystal lattice. Distortions in the lattice are commonly observed and have a well defined geometry. They happen to be the cores of dislocations. In the continuum limit, a planar graphene sheet would deform according to isotropic elasticity equations. Some deformations produce singular solutions, with singularities located at dislocations. When the lattice structure is restored, the singularity is regularized and takes the form of a defect in the hexagonal lattice. These defects interact with each other through their elastic fields, which allows to predict their stability and interactions. Heptagon-pentagon pairs are stable cores of edge dislocations. Edge dislocations can also appear as octogons, which are reactive due to a dangling bond and tend to catch adatoms. Opposite pairs of edge dislocations create dipoles. Well known Stone-Wales defects are dipoles which anhilate and disappear in finite time, unless a force splits them in two opposite heptagon-pentagon pairs moving in opposite directions. Stable dipoles take the form of vacancies or divacancies.
Heptagon-pentagon Stone-Wales defect
(stable) (unstable)
Vacancy Divacancy
(stable) (stable)
The stability of simple defects is studied in Phys. Rev. B 78, 085406, 2008. Defect groupings are analyzed in Cont. Mech. Therm., 23, 337-346, 2011. See New J. Physics 10, 053021, 2008 for possible effects on electromagnetic properties. Nucleation of defects is discussed in EPS, 81, 36001, 2008 and CSF 42, 1623-1630, 2009. Formation of rippled domains due to coupling of the lattice equations with stochastic effects is discussed in Phys. Rev. B, 86, 195402, 2012 and J. of Stat. Mech., P09015, 2012. Recent work in collaboration with J.H Warner studies out of plane deformations at the core of defects by Von Karman models and hyperstress theories, see Phys Rev B 92, 155417, 2015.
In two dimensional graphene the atoms are arranged forming a honeycomb crystal lattice. Distortions in the lattice are commonly observed and have a well defined geometry. They happen to be the cores of dislocations. In the continuum limit, a planar graphene sheet would deform according to isotropic elasticity equations. Some deformations produce singular solutions, with singularities located at dislocations. When the lattice structure is restored, the singularity is regularized and takes the form of a defect in the hexagonal lattice. These defects interact with each other through their elastic fields, which allows to predict their stability and interactions. Heptagon-pentagon pairs are stable cores of edge dislocations. Edge dislocations can also appear as octogons, which are reactive due to a dangling bond and tend to catch adatoms. Opposite pairs of edge dislocations create dipoles. Well known Stone-Wales defects are dipoles which anhilate and disappear in finite time, unless a force splits them in two opposite heptagon-pentagon pairs moving in opposite directions. Stable dipoles take the form of vacancies or divacancies.
Heptagon-pentagon Stone-Wales defect
(stable) (unstable)
Vacancy Divacancy
(stable) (stable)
In addition to the
presence of dislocation cores, there seems to be
evidence of the formation of 3D ripples in planar
graphene sheets.
Ripples
2D
projection
The stability of simple defects is studied in Phys. Rev. B 78, 085406, 2008. Defect groupings are analyzed in Cont. Mech. Therm., 23, 337-346, 2011. See New J. Physics 10, 053021, 2008 for possible effects on electromagnetic properties. Nucleation of defects is discussed in EPS, 81, 36001, 2008 and CSF 42, 1623-1630, 2009. Formation of rippled domains due to coupling of the lattice equations with stochastic effects is discussed in Phys. Rev. B, 86, 195402, 2012 and J. of Stat. Mech., P09015, 2012. Recent work in collaboration with J.H Warner studies out of plane deformations at the core of defects by Von Karman models and hyperstress theories, see Phys Rev B 92, 155417, 2015.
