The number of lattice point in FCC?

In summary, the number of lattice points in FCC (face-centered cubic) structure is 4, while BCC (body-centered cubic) has 2 lattice points. This is due to the fact that atoms at different locations within the unit cell are shared between multiple unit cells, resulting in a fractional count for each atom.
  • #1
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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  • #2


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?
 
  • #3


So, one whole atom represents for one lattice point, right?
 
  • #4


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.
 
  • #5


Hi there,

The number of lattice points in a crystal structure depends on the specific type of crystal lattice. In the case of face-centered cubic (FCC) structure, there are 4 lattice points per unit cell. This means that there are 4 points where the atoms are located, with each point representing a corner of a cube.

To visualize this, imagine a cube with atoms at each of the 8 corners. In an FCC structure, there is also an atom at the center of each face of the cube. This brings the total number of atoms to 4, and thus 4 lattice points.

For body-centered cubic (BCC) structure, there are 2 lattice points per unit cell. This is because there is an atom at each of the 8 corners, and one atom at the center of the cube.

I hope this helps clarify the difference between the number of lattice points in FCC and BCC structures. Keep in mind that different crystal structures have different numbers of lattice points per unit cell, depending on the arrangement of atoms within the structure.

Best of luck with your studies!
 

1. What is FCC and how does it relate to lattice points?

FCC stands for face-centered cubic, which is a type of crystal structure commonly seen in metals. Each lattice point in FCC represents the location of an atom or ion within the crystal lattice.

2. How many lattice points are there in an FCC unit cell?

There are a total of 4 lattice points in an FCC unit cell. This includes one lattice point at each of the 8 corners of the unit cell, and one lattice point at the center of each of the 6 faces.

3. Is the number of lattice points in FCC always the same?

Yes, the number of lattice points in an FCC unit cell is always 4. This is because the structure of an FCC crystal is defined by its unit cell, which is repeated in all directions to form the larger crystal lattice.

4. How does the number of lattice points in FCC compare to other crystal structures?

The number of lattice points in FCC is the same as in BCC (body-centered cubic) and HCP (hexagonal close-packed) structures. However, other crystal structures such as simple cubic and diamond have a different number of lattice points per unit cell.

5. Can the number of lattice points in FCC be calculated for different unit cell sizes?

Yes, the number of lattice points in FCC can be calculated for different unit cell sizes by using the formula n = 4 x (1 + 1/8), where n is the total number of lattice points and 1/8 represents the fractional contribution from the atoms at each of the 8 corners. This formula can be applied to any crystal structure with a known unit cell.

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