What is the Lattice Parameter c of an HCP Crystal Structure?

[Hashmeer]

Homework Statement

I'm trying to figure out the lattice parameter, c, of the HCP crystal structure.

Here are a couple links showing the structure: http://images.google.com/imgres?img...agonal+close+packed&hl=en&safe=off&sa=N&um=1"

Homework 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.

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.

Homework Statement

Homework Equations

The Attempt at a Solution

 

[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

 

[Astronuc]

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