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Topic: Coordination numbers of unit cells  (Read 11794 times)

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Offline djstorman

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Coordination numbers of unit cells
« on: May 30, 2011, 05:48:59 PM »
I am getting pretty confused by the coordination of face centered cubic unit cells. 
I can understand why simple cubic unit cells have a cn of 6, I understand why body centered unit cells have a cn of 8.
 I dont understand why a face centered cubic until cell has 12, it would seem to me that with each corner and the faces interacting with other unit cells around it, the cn would be 14

Offline cth

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Re: Coordination numbers of unit cells
« Reply #1 on: May 31, 2011, 07:39:35 AM »
it would seem to me that with each corner and the faces interacting with other unit cells around it, the cn would be 14

What you describe (coordination with each corners and each faces) would be for an atom at the center of the cube. But there isn't any atom sitting in the center. Remark, in the case you describe, the cube corners are too far away -> the coordination of an atom that would be sitting at the center of the cube would be 6.

To answer your question, consider the atom at the center of a cube face. How many other atoms are close to it?
- First, you have 4 atoms located at the corners of the considered face;
- Then you also have the 8 atoms located at the centers of each of the eight faces perpendicular to the considered face.

It may not be easy to see, lets take an example.

Lets consider the atom at the center of the face closest to us:
- You have the four atoms at the corners of the face which are at the distance a(√2)/2.
- You have the atom at the center of the face at the top of the cube. It is also at a distance a(√2)/2. You see it? In total there are 8 atoms equivalent to that one.

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