Elasticity theory of topological defects in carbon nanotubes and graphene

Abstract

We develop elasticity theory to predict the energies of topological defects in carbon nanostructures. The theory is a simple, quantitatively accurate and transferable continuum approach to predicting defect formation energies that obviates the need for computationally expensive quantum mechanical methods. Thus the theory has the potential to serve as the basis for thermodynamic and multi-scale modelling of the structural properties of carbon nanostructures.

Acknowledgements

The authors acknowledge insightful discussions with J. Grossman. EE acknowledges the support of the Intel Corporation. EE and DCC acknowledge the support of the National Science Foundation under contract DMR 0528511. The authors acknowledge the support of the US Department of Energy, Office of Basic Energy Sciences, under Contract No. DE-AC02-05CH11231. Computing resources from the DOE National Energy Research Scientific Computing Center are also acknowledged.

Notes

^†There is a degeneracy with respect to the definition of the orientation angle φ for SW defects. The orientation angle can be chosen in one of two ways, depending on which pentagon–heptagon pair is chosen as the dislocation comprising the dipole. This degeneracy is resolved here by choosing the angle φ to be that which minimizes the continuum energy, and then (for the atomistic calculations) shearing the lattice vectors appropriately for that choice of φ.

^†For brevity, the six results for the (12, 3) nanotube are not shown; the correlation between the continuum and atomistic predictions is typical of results shown here.