Packing (HCP/CCP) comparing 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.

 

[Blueshift5]

Hello! I am happy to help you with your questions about packing (HCP/CCP) and their relationship to volume, coordination number, and density.

First, let's address your question about the volumes of HCP and CCP. You are correct in your calculations of the volumes for each type of packing. However, it is important to note that these volumes are for a single unit cell of each type of packing. In other words, they do not represent the total volume of a crystal made up of multiple unit cells. To get the same density percentage for both types of packing, we must consider the number of atoms in each unit cell. HCP has a coordination number of 12, meaning each atom is in contact with 12 other atoms. CCP has a coordination number of 8. This means that the number of atoms in each unit cell for HCP is greater than the number of atoms in a unit cell for CCP. Therefore, even though the individual unit cell volumes may be different, the overall density of a crystal made up of multiple unit cells will be the same for both types of packing.

Now, let's discuss the relationship between coordination number, packing, and density. You are correct in your understanding that coordination number refers to the number of atoms touching a specific atom. This is important in determining the overall structure and stability of a crystal. The packing refers to the arrangement of the atoms within a unit cell, whether it is HCP, CCP, or another type of packing. Density, as you mentioned, brings these two concepts together. Density is a measure of how tightly packed the atoms are within a crystal. As we discussed earlier, the coordination number and packing can affect the overall density of a crystal, but it is also influenced by the size of the atoms and their arrangement within the unit cell.

I hope this helps to clarify the relationship between coordination number, packing, and density. If you have any further questions, please don't hesitate to ask. Best of luck with your studies!