Graphene is a one-atom-thick planar sheet of sp2-bonded carbon atoms that are densely packed in a honeycomb crystal lattice. Graphene sheets are weakly bonded to other graphene layers above and below to form Graphite. The difference between two layers is approximately 0.335 nm .
Graphite can conduct electricity due to the vast electron delocalization within the carbon layers (a phenomenon called aromaticity). These valence electrons are free to move; as a result, they are able to conduct electricity. However, this only occurs within the plane of the layers.
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