Graphene

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Graphene
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Graphene

• Carbon is perhaps the most fascinating element in
  nature
• The principal forms of carbon are? Graphite?
  Diamond? Fullerene, nanotubes and related
  structures

• A single sheet of graphite is called graphene
• It is sp2 hybridized ? covalently bonded
• The bonding between the graphene sheets in
  graphite is of van der Walls type

• In this set of slides we consider
  crystallographic concepts related to graphene
• It is a hexagonal array of Carbon atoms, which is
  NOT a lattice

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Part of the hexagonal array of C atoms which
forms the Graphene structure
Not all carbon positions form a lattice
As atoms A B do not have identical surrounding
both cannot be lattice points
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Structure of single graphene sheet
Crystal Lattice Motif
Grey atoms sit on the lattice sites.
Motif 1 grey (0,0) 1 green (½, ½) (in
positions as shown)

• Either the green or the grey carbon atoms can be
  considered to be located at lattice points (but
  not both).
• In motif (in-plane) consists of two C atoms.
• The unit cell is as marked.

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Q A
Overlay symmetry operators on the structure.

• The symmetry of the structure is 6mm.
• Note that the origin of the unit cell has been
  placed at the 3-fold (Fig.a) (unlike the
  conventional representation of the 6mm symmetry,
  wherein the origin is placed at the 6-fold
  (Fig.b)).
• All atomic sites are seats of 3-fold axes and
  centres of all hexagons are that of 6-fold.

(a)
6mm
(b)