THE discovery of fullerenes1,2 and carbon nanotubes3,4 has led to the
realization that it should be possible to tailor the properties of gra
phitic sheets if their geometry can be controlled5-7. In exploring the
se possibilities, we have found that the folding and tearing of graphi
tic sheets follow well defined patterns which seem to be governed by t
he formation of sp3-like line defects in the sp2 graphitic network. Ou
r studies with the atomic force microscope and scanning tunnelling mic
roscope reveal that these folds and tears occur preferentially along t
he symmetry axes of graphite, and that 'ripples' are observed in the c
urved portions of the folds. We also see ripples in deformed carbon na
notubes. They lie along the directions for which sp3-like line defects
can form most easily to relieve strain. Our ab initio molecular orbit
al calculations indicate that the ripples stabilize the pi-electronic
energy in the bent structures with the total energy balance being dete
rmined by the amount of nuclear repulsion. These results provide insig
ht into the geometries that graphitic structures will preferentially a
ccommodate, and the properties that might ensue.