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# Unit Cell: Atoms Calculation watch

1. This question is annoying me. I know it's going to be quite easy.
I understand that each one at the face will count as 1/2 because atoms are placed at their center. What about the ones at the corners?

http://imgur.com/FBoDzjh
2. (Original post by Daniel Atieh)
This question is annoying me. I know it's going to be quite easy.
I understand that each one at the face will count as 1/2 because atoms are placed at their center. What about the ones at the corners?

http://imgur.com/FBoDzjh
Think about a stack of cubes. How many cubes can you fit around one corner?
3. (Original post by Chlorophile)
Think about a stack of cubes. How many cubes can you fit around one corner?
Thanks a bunch for your response.

I really can't imagine how it will be 1/8 atoms at each corner. When I was trying it, I thought it's 1/4. How do you look at it when answering this?

Attached Images

4. (Original post by Daniel Atieh)
Thanks a bunch for your response.

I really can't imagine how it will be 1/8 atoms at each corner. When I was trying it, I thought it's 1/4. How do you look at it when answering this?

It's a question where it helps to be good at visualising 3D objects which is either something you're good at or you're not. I'll try to explain it though. If you're working in two dimensions, then every vertex of a square in the grid will be 'connected' to 4 other squares, so if we were working in 2D then it would be 1/4 of an atom. However, lattices are 3D, not 2D. If you have a 3D 'grid', then every vertex is 'connected' to 8 cubes. This diagram shows this reasonably well:

On the diagram in the far right, you can see that the yellow sphere (which is at the corner of the cubes) is surrounded by 8 other cubes. Since an equal part of the atom is in each cube, the proportion of the atom in each cube is an eighth. Does that help?
Attached Images

5. (Original post by Chlorophile)
It's a question where it helps to be good at visualising 3D objects which is either something you're good at or you're not. I'll try to explain it though. If you're working in two dimensions, then every vertex of a square in the grid will be 'connected' to 4 other squares, so if we were working in 2D then it would be 1/4 of an atom. However, lattices are 3D, not 2D. If you have a 3D 'grid', then every vertex is 'connected' to 8 cubes. This diagram shows this reasonably well:

On the diagram in the far right, you can see that the yellow sphere (which is at the corner of the cubes) is surrounded by 8 other cubes. Since an equal part of the atom is in each cube, the proportion of the atom in each cube is an eighth. Does that help?
Brilliantly explained! Many thanks

I've no idea how I could have imagined such thing in an exam :/ That's sad

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Updated: January 18, 2015
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