Eur. Phys. J. E 27, 275-296 (2008)
DOI: 10.1140/epje/i2008-10380-9

Elastic theory of defects in toroidal crystals

L. Giomi and M. J. Bowick

Department of Physics, Syracuse University, 13244-1130, Syracuse, New York, USA

lgiomi@physics.syr.edu
bowick@physics.syr.edu

Received 1 August 2008 / Published online 4 November 2008

Abstract

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.

Supplementary material in the form of a pdf file available from the journal web page at 10.1140/epje/i2008-10380-9 and are accessible for authorised users.

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.

Correspondence: lgiomi@physics.syr.edu


© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2008