513.001 Molecular and Solid State Physics

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Graphene

Graphene is a two-dimensional lattice which is built by a continuous arrangement of regular hexagons of sp² hybridised carbon atoms (see below). The side length of the hexagons is 0.14 nm.

(a) What is the Bravais lattice of graphene?

(b) Draw the Wigner-Seitz primitive unit cell.

(c) How many atoms are there in a primitive unit cell?

(d) Determine the basis vectors that describe the postions of the atoms in the unit cell. Write these basis vectors first in terms of the absolute positions (with x- and y- componenets and distances in Angstroms) and then in fractional coordinates. For fractional coordiantes give the positions in terms of the conventional lattice vectors. The conventional lattice vectors are the same as the primitive lattice vectors in this case.