# Homework Help: Lattice Parameter c of HCP

1. Feb 10, 2010

### Hashmeer

1. The problem statement, all variables and given/known data
I'm trying to figure out the lattice parameter, c, of the HCP crystal structure.

2. Relevant equations
I know that a=2r, where r is the atomic radius of whatever atoms make up the structure. I'm not really sure what else is relevant, it seems to be a problem of geometry and I'm having trouble working it out.

3. The attempt at a solution
I can't really type out my math that I've attempted to do since I am having trouble conceptually. I think that the way to go about doing it is with a triangular pyramid, since with the way that the atoms sit on top of each other you will get an equilateral triangle as your base (sides=a) and then the height is c/2. However I can't seem to get this to work out mathematically. I got c to be 2*sqrt(3)*r, which is incorrect.

Thanks for the help.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

Last edited by a moderator: Apr 24, 2017
2. Feb 12, 2010

### Lok

If the height of a triangular piramid is what you seek then a simple method is pytagora with a being the distance between 2 corners.

that is the height of a equilateral triangle is (3^0.5)/2 which means that the pyramid triangle will have a base of 2/3 of the height. That is (3^0.5)/3 so:

Pytagora : a^2(1-3/9)=a^2*c^2 where c=(6/9)^0.5=0.8164

Last edited: Feb 12, 2010
3. Feb 12, 2010

### Astronuc

Staff Emeritus
c/a must > 1, and a ~ 2r.

Last edited: Feb 12, 2010