# Packing density question (HCP/CCP/BC)

by berry2
Tags: density, hcp or ccp or bc, packing
 P: 255 Well you just need some good pictures to demonstrate this. Here are some notes I found a while back from a uni near me on the basics. They're pretty decent. This is just a start and I'm sure other people will chime in with a lot of useful information. http://www.physics.curtin.edu/teachi...s_Science_201/ Lectures 1 and 2 cover what you want to know I think. EDIT Lecture 2 from the above link gives you the formula for atomic packing factor (or packing density) $$APF = \frac {n V_s} {V_c_e_l_l}$$ Where Vs is the volume of a sphere and n is the number of atoms per unit cell for a particular structure. The volume of a cubic unit cell (Vcell) (simple-cubic, body-centred or Face-centred) is just $$a^3$$ (a is the lattice parameter). To solve for the APF you need to express a in terms of the atomic radius. Lecture 2 from my link I think clearly demonstrates how you do this. The volume of an HCP unit cell (Vcell) is obviously slightly different. The base of an HCP structure is a hexagon. The hexagon can be divided into 6 equal triangles. So you find the area of one of those triangles (using the fact that you know the lattice parameter) and multiply by 6 to get the area of the base of the HCP structure. Then multiply this area by the height (c, where c=1.633a) to obtain the volume of an HCP structure. The notes don't explain how to calculate the volume of the HCP structure, but if you use this explanation and look at the diagram in the notes maybe you can make some sense out of it??? The notes that I linked to (lecture 2) also give the formula for caculating the density of an element given the information of the crystal structure and the atomic mass. I'm probably not the best person to explain this though, because I'm not too good at clearly making a point, so if you don't understand what I've tried to say then just say so so that the others will help you. If you don't then they might think that your problem is sorted out.