Graphene is graphite - which is actually composed of single-atom-thick planes of carbon atoms in a planar lattice arrangement. An individual plane of graphite, called graphene, can be separated from a piece of graphite by simply putting Scotch tape on graphite and then pulling the tape off. The gray that can be seen sticking to the transparent tape will be one, or a few, layers of graphene. Graphene has interesting properties and is thought to be a candidate for microelectronic application. You should definitely do a search on the term and learn more.
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