The number of lattice point in FCC?

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Discussion Overview

The discussion revolves around understanding the number of lattice points in face-centered cubic (FCC) and body-centered cubic (BCC) crystal structures. Participants seek clarification on how these numbers are derived, particularly in relation to the simple cubic structure.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant expresses confusion about the number of lattice points in FCC and BCC structures, noting that their textbook states FCC has 4 points and BCC has 2 points.
  • Another participant explains that atoms on the sides of the unit cell are shared between two unit cells, contributing 1/2 atom each, while atoms on the edges are shared among four unit cells, contributing 1/4 atom each. Atoms on the corners are shared among eight unit cells, contributing 1/8 atom each.
  • A participant questions whether one whole atom corresponds to one lattice point.
  • A later reply confirms that one whole atom does represent one lattice point, suggesting a substitution of terms for clarity.

Areas of Agreement / Disagreement

Participants generally agree on the concept that atoms contribute fractions to the lattice points based on their positions, but there is no consensus on the overall understanding of how these contributions lead to the total counts for FCC and BCC.

Contextual Notes

The discussion does not resolve the initial confusion regarding the derivation of the lattice point counts, and assumptions about the definitions of lattice points and their contributions remain implicit.

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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