# Hexagional Bravais Latice Question

1. Nov 6, 2009

### TFM

1. The problem statement, all variables and given/known data

The hexagonal close-packed structure (hcp) is the hexagonal Bravais lattice with a basis of two identical atoms associated with each lattice point, one at (0,0,0) and the second at

$$r = \frac{2}{3}a_1 + \frac{1}{3}a_2 + \frac{1}{2} a_3$$

where $$\left|a_1\right|$$ = $$\left|a_2 \right|$$ and $$a_1$$ and $$a_2$$ are at 120 degrees in the basal plane and $$a_3$$ is parallel to the c-axis. By considering the atoms to be hard spheres with nearest neighbour contact, show that the “c/a” ratio $$\frac{a_3}{a_1}$$ is 1.633.

2. Relevant equations

3. The attempt at a solution

I am not quite sure what to do with this question. I am not quite sure how to get a3 and a1.

Any ideas?

many thanks,

TFM

Last edited: Nov 6, 2009