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In a study I have run into some questions asking for "How many atoms are contained in the unit cell" for graphene. I have some trouble understanding the unit cell of graphene which is always depicted as a mono-layer of atoms. What is a unit cell in a mono-layer?

The closest I could find is something like this picture:

enter image description here

The upper right image shows something soon-to-be a hexagonal structure. But when is such structure actually appearing?

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    $\begingroup$ well considering graphene is a single layer of carbon atoms it's not really appropriate to try and define a unit cell. $\endgroup$ – A.K. Feb 26 '17 at 21:28
  • $\begingroup$ I would go for one atom in special position (origin) and a planar hexagonal group p6mm, but as my International Tables for Crystallography are at university I can be mistaken. $\endgroup$ – Kris_R Feb 26 '17 at 22:38
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    $\begingroup$ The upper-right picture is graphite: en.wikipedia.org/wiki/Graphite $\endgroup$ – khaverim Feb 26 '17 at 23:06
  • $\begingroup$ As graphene isn't crystalline, what sense would it have to apply rules of crystalline structure to it? $\endgroup$ – Mithoron Feb 26 '17 at 23:59
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The unit cell for graphene is a two-dimensional rhombus according to the figure shown on page 31 of this paper.$^1$ (also here.) The result is that two atoms are contained per unit cell. The upper right structure actually appearing in graphite, stacked layers of graphene.

enter image description here

$^1$Zhou, J; Huang, R. Internal lattice relaxation of single-layer graphene under in-plane deformation. Journal of the Mechanics and Physics of Solids, 2008, 56(4), 1609-1623. https://doi.org/10.1016/j.jmps.2007.07.013

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Bit late, but a unit cell of graphene is just the 'surface' area of 2 carbon atoms.

enter image description here

This area is 0,052 nm2, which gives us a density of 0,77 mg/m2.

Same principle for all monolayer materials.

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