The number of lattice point in FCC?

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SUMMARY

The face-centered cubic (FCC) structure contains 4 lattice points per unit cell, while the body-centered cubic (BCC) structure contains 2 lattice points. In FCC, atoms are located at each corner of the cube and at the center of each face. Each corner atom contributes 1/8 of an atom to the unit cell, and each face atom contributes 1/2, leading to a total of 4 lattice points. In contrast, BCC has 1 atom at the center and 8 corner atoms, contributing a total of 2 lattice points.

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hermtm2
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The number of lattice point in FCC?

Hi, I am having a trouble to figure the number of lattie point in FCC structure out. My textbook said simple cubic has 1 lattice point, BCC has 2 points, and FCC has 4 points. However there is no further explanation or figures. I am a kind of understand about the simple cubic structure since the atom on every corner is the lattice point.

Can you guys explain that how the lattice points in FCC and BCC are 4 and 2?

Thanks.
 
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hermtm2 said:
Hi, I am having a trouble to figure the number of lattie point in FCC structure out. My textbook said simple cubic has 1 lattice point, BCC has 2 points, and FCC has 4 points. However there is no further explanation or figures. I am a kind of understand about the simple cubic structure since the atom on every corner is the lattice point.

Can you guys explain that how the lattice points in FCC and BCC are 4 and 2?

Thanks.

Atoms on the sides are shared between two unit cells, so you can only count each one as 1/2 atom. Atoms on the edges are shared four unit cells, so they count as 1/4 atoms. Atoms on the corners are shared between eight unit cells, so they count as 1/8 atoms. Do the numbers add up now?
 


So, one whole atom represents for one lattice point, right?
 


hermtm2 said:
So, one whole atom represents for one lattice point, right?

Yes. If you like, just replace "atom" by "lattice point" everywhere in my previous post.
 

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