# Hexagonal crystal structure

1. Feb 1, 2008

### stunner5000pt

1. The problem statement, all variables and given/known data
How many atoms are there in the unit cell of graphite?

2. The attempt at a solution
I know graphite is hexagonal crystal structure. hcp

also know that hcp has basis of hexagonal lattice which as 2 basis atoms.

is there some other info i need because the answer is supposed to be 4...

2. Feb 2, 2008

### flying fish

I'm not an expert so don't blindly trust my answer, but I believe that the unit cell for graphite may be twice as high, due to oppositely sloped ends of the structure. There are also no atoms in the center of the lattice (as in, the lattice would be a "hollow hexagonal pipe" of atoms). Therefore, you have (1/6)12 on the top and bottom, + (1/3)6 at the middle. This adds up to four.
http://www.chem.ox.ac.uk/icl/heyes/structure_of_solids/Lecture1/Lec1.html [Broken] (the picture of the 3D graphite structure is almost halfway down the page).

I don't think your graphite structure is HCP. HCP (Hexagonal close packed) actually adds up to 6, since it has 3 atoms fully contained, then 12(1/6) + 2(1/2). Of course, there are other variants of hexagonal which have less. For instance, I think there was one called Simple Hexagonal somewhere here: http://www.chem.lsu.edu/htdocs/people/sfwatkins/ch4570/lattices/lattice.html [Broken]

(SH should be 3 atoms...and that is also not the same as the graphite lattice ether because it has the half atoms at the end center in addition to not having the sloped top and bottom)

Last edited by a moderator: May 3, 2017