Topological defects in graphene
Pilar Ariza (University of Seville), Juan Mendez (University of Seville), Michael Ortiz (Caltech)
Synthesis, Characterization, and Modeling of Low-Dimensional Nanomaterials
Tue 2:40 - 4:00
Salomon 202
We present an application of the theory of discrete dislocations developed by Ariza and Ortiz (2005) to the analysis of defects in graphene based on discrete crystal elasticity. The mechanics of crystal lattices containing dislocations can be expressed in terms of fields that are supported on the lattice itself, e.g., the displacement field and the energy density; and fields that are defined on certain ancillary lattices, e.g., the eigendeformation fields which describe the dislocations. A mechanics of discrete lattices is built using ideas from discrete differential calculus and algebraic topology. We discuss the specialization of the theory to graphene and its further specialization to the force-constant model developed by Aizawa in 1990, the AIREBO potential and a tight binding potential described by Xu in 1992. The ability of the discrete dislocation theory to predict defect core structures and energies is critically assessed for periodic arrangements of dipoles and quadrupoles. We show that, with the aid of the discrete Fourier transform, these problems are amenable to exact solution within the framework of discrete dislocation theory, which confers the theory a distinct advantage over conventional atomistic models. In particular, the discrete dislocation theory predicts 5-7 ring core structures that are consistent with observation and dislocation energies that fall within the range of prediction of other models. We also present an assessment of the finite-temperature dynamical stability of discrete dislocations in graphene. In order to ascertain stability, we insert discrete dislocation quadrupole configurations into molecular dynamics calculations as initial conditions. In calculations we use LAMMPS and the AIREBO potential. The analysis shows that the core structures predicted by discrete dislocation theory are dynamically stable up to high temperatures, though they tend to relax somewhat in the course of molecular dynamics.