How do HCP and CCP compare in terms of volume?

[berry2]

Hi! I have two questions. "How do the two more efficient forms of packing (hexagonal closest packing and cubic closest packing) compare regarding volume?" and "What is the relationship between coordination number, packing, and density (as mass/volume)?" I am taking this Grade 12 Chem course by correspondence, and I do not have a teacher that I can have explain this to me. These two question have to do with each other, they refer to hexagonal closest packing, cubic closest packing, and body-centred space lattice.

My first question is, are the two volumes the same for HCP and CCP? Here is what I came up with off the Internet but I'm not sure if it is right. The volume of a hexagonal closest packing is V = 8(2)1/2 r3. The volume of a face centered or cubic closest packing is V=16(2)½r3. If these are correct (are they?), then they do not seem to be the same volumes, but then how do I get the same denstiy percentages of 74.05%?

My second question, "What is the relationship between coordination number, packing, and density (as mass/volume)?" Is the following a reasonable answer?

The relationship between coordination number, packing and density is - coordination number is the number of atoms touching a specific atom; the packing is the different ways the spheres are structured; the density brings the two coordination number and packing together. Even reading what I just wrote confuses me, so any help or advice would be greatly appreciated.

Thanks!

 

[big man]

The reason you get the same atomic packing factor for those two different strucutres is because of the difference in the number of atoms per unit cell. The FCC (which is a CCP structure) unit cell has 4 atoms per unit cell. The HCP unit cell only has 2 atoms.