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Phys128

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- Homework Statement
- Graphene is a 2D crystal made entirely of carbon atoms. The crystal lattice can defined by the lattice vectors a and b, where the magnitudes |a|=|b|= 2.46 Å and the angle between the lattice vectors is 60°. The crystal has a basis of two carbon atoms, where the basis vectors are r1 = 0 and r2 = a/3 + b/3.

Sketch the unit cell of the crystal structure of graphene and calculate the carbon- carbon bond length (in Å).

- Relevant Equations
- Bond length = |r2|

Somewhat embarrassingly as a third year undergrad, this question has been completely stumping me for far too long now (2 hours). The solution is 1.42 Å and the working is given as

|r2| = 2cos(30)*1/3(2.46)

or alternatively

|r2| = (1/2|a|)/cos(30)

But I cannot grasp where this comes from. Please someone put me out of my misery