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I have spent hours on finding the primitive cells of honeycomb lattice of graphene. Based on the definition of graphene from most of solid state physics books, as I quoted from Wikipedia, and in which P.K. Misra, Physics of Condensed Matter book agreed,

a primitive cell is a minimum volume cell (a unit cell) corresponding to a single lattice point of a structure with discrete translational symmetry.

What I understand is that in the primitive cell we define, must contain single lattice point. But, what I found from all articles explaining graphene, the cell they defined is a unit cell which contain two lattice point, as I attached below (taken from here), Primitive

Isn't that a non-primitive unit cell? Some articles just mentioned it as unit cell, but some others claiming that it is the primitive cell of graphene. And me myself, try to find the primitive cells of graphene for hours, and still no result.

So, is my understanding of primitive cells wrong? Or, I just hadn't found the primitive cell yet?

Thanks for the help.

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  • $\begingroup$ The base has two atoms. It is the smallest lattice, there are no shorter translation vectors. $\endgroup$ – Pieter Jan 23 '18 at 16:30
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The unit cell in articles is a primitive cell, and the two points are not two lattices - instead, they are two sublattices of a primitive cell, since they cannot get to each other from translation over a unit vector.

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  • $\begingroup$ Thanks for your explanation. But I still couldn't get the grasp on, when we should consider a case where a lattice should be described by a primitive cell containing multiple sublattice points, or just treat all points as single lattice point and continue the search of primitive cell. Could you elaborate on that? $\endgroup$ – luckreez Jan 23 '18 at 17:23
  • $\begingroup$ @luckreez you might first find the translation symmetry of your system, then I think things are pretty obvious. Points that cannot be connected by translation belong to new sublattice point. $\endgroup$ – RoderickLee Jan 23 '18 at 17:32

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