# A unit cell for graphene

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:

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

• well considering graphene is a single layer of carbon atoms it's not really appropriate to try and define a unit cell.
– A.K.
Commented Feb 26, 2017 at 21:28
• 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. Commented Feb 26, 2017 at 22:38
• The upper-right picture is graphite: en.wikipedia.org/wiki/Graphite Commented Feb 26, 2017 at 23:06
• As graphene isn't crystalline, what sense would it have to apply rules of crystalline structure to it? Commented Feb 26, 2017 at 23:59
• Commented Dec 6, 2023 at 13:53

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.
$$^1$$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