RELATIVE STABILITY OF SINGLE GRAPHITE SHEETS OF POSITIVE, NEGATIVE AND ZERO CURVATURE

The relative stability of single graphite sheets of zero, positive and negative curvature is investigated through a simple model where both strain and dangling bond energy are taken into account. Although it is found that flat sheets are always more stable than negatively curved ones, calculations show that above a critical radius of curvature there is a crossover from positive to negative curvature as the more stable geometry for a single sheet. A maximum size for a negatively curved sheet is also predicted. Similarly positive curvature is found to be energetically favored over zero curvature below some value of the curvature radius and above a certain number of atoms of the sheet. These results are discussed in view of available transmission electron microscopy observations of sp(2) amorphous carbon.