Atom Embedded

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How many silicon atoms are there in each unit cell?

Silicon crystallizes in the face-center diamond structure (just like diamond). Look at this link to get a clearer picture:

http://en.wikipedia.org/wiki/File:Silicon-unit-cell-3D-balls.png

Keeping in mind that this is a face-centered structure, you have the following amount of atoms:

1 in each corner of the unit cell (8 total)
1 on each face of the cell (6 total)
4 atoms completely inside the cell

The atoms located in the corner are shared by 8 units cells; therefore they only contribute 1/8 of an atom to each unit cell.
The atoms located on the faces of the cube are shared by 2 unit cells; therefore they only contribute 1/2 of an atom to each unit cell.
The atoms embedded in the unit cell contribute completely to the unit cell.

Adding up this values gives a total number of atoms of:

atoms = 8(1/8) + 6(1/2) + 4(1) = 1 + 3 + 4 = 8

So, each unit cell has 8 atoms of silicon.

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