Elastic theory of defects in toroidal crystals
Department of Physics, Syracuse University, 13244-1130, Syracuse, New York, USA
Published online: 4 November 2008
We report a comprehensive analysis of the ground-state properties of axisymmetric toroidal crystals based on the elastic theory of defects on curved substrates. The ground state is analyzed as a function of the aspect ratio of the torus, which provides a non-local measure of the underlying Gaussian curvature, and the ratio of the defect core energy to the Young modulus. Several structural features are discussed, including a spectacular example of curvature-driven amorphization in the limit of the aspect ratio approaching one. The outcome of the elastic theory is then compared with the results of a numerical study of a system of point-like particles constrained on the surface of a torus and interacting via a short-range potential.
PACS: 81.10.Aj Theory and models of crystal growth; physics of crystal growth, crystal morphology, and orientation – / 61.72.Bb Theories and models of crystal defects – / 61.48.De Structure of carbon nanotubes, boron nanotubes, and closely related graphitelike systems – / 61.72.Lk Linear defects: dislocations, disclinations –
© Springer, 2008