Distance between two layers in FCC unit cell

In summary, a/√3 is the distance between two planes in a FCC unit cell, which is equal to the edge length a.
  • #1
zorro
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How is the distance between any two layers in a FCC unit cell equal to a/√3, where a is the edge length? I think it should be a/2 because the distance of a face centered atom from any 4 edges surrounding it is a/2. Can someone explain it geometrically?
 
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  • #2
Abdul Quadeer said:
How is the distance between any two layers in a FCC unit cell equal to a/√3, where a is the edge length? I think it should be a/2 because the distance of a face centered atom from any 4 edges surrounding it is a/2. Can someone explain it geometrically?

Divide the area density of atoms within a plane by the volume density of atoms in the crystal. This gives the distance between the chosen plane and the nearest parallel plane.

Of course, this still means you need to decide which planes you're measuring the distance between.
 
  • #3
PhaseShifter said:
Divide the area density of atoms within a plane by the volume density of atoms in the crystal. This gives the distance between the chosen plane and the nearest parallel plane.

Going that way I got a/2.

PhaseShifter said:
Of course, this still means you need to decide which planes you're measuring the distance between.

a/√3 is the distance between which two planes in a fcc unit cell? Not the nearest ones?
 
  • #4
Abdul Quadeer said:
a/√3 is the distance between which two planes in a fcc unit cell? Not the nearest ones?

Generally you'll be interested in the planes of greatest density rather than the closest planes. In fact, you can find planes arbitrarily close together, if you pick planes with a very low density.
 
  • #5
That does not answer my question. a/√3 is the distance between which two planes in a fcc unit cell?
(btw I found this distance in the derivation of the height of a hexagonal unit cell)
 
  • #6
It's the distance between planes parallel to the (111) plane.
 
  • #7
(111) = ? :confused:
 
  • #9
I learned something new there :smile:
Thanks!
 

Related to Distance between two layers in FCC unit cell

1. What is the distance between two layers in an FCC unit cell?

The distance between two adjacent layers in an FCC unit cell is equal to the length of the unit cell's edge divided by the square root of 2. This can be calculated using the formula d = a/√2, where d is the distance between layers and a is the length of the unit cell's edge.

2. How is the distance between two layers in an FCC unit cell related to the lattice constant?

The distance between two layers in an FCC unit cell is directly related to the lattice constant, which is the length of the unit cell's edge. This relationship can be expressed as d = a/√2, where d is the distance between layers and a is the lattice constant.

3. Why is the distance between two layers in an FCC unit cell important?

The distance between two layers in an FCC unit cell is important because it affects the overall structure and properties of the material. It determines the spacing between atoms in a crystal lattice and can impact the material's mechanical, electrical, and thermal properties.

4. How does the distance between two layers in an FCC unit cell compare to that in other unit cells?

The distance between two layers in an FCC unit cell is larger than that in other unit cells such as the simple cubic, body-centered cubic, and hexagonal close-packed unit cells. This is because the FCC unit cell has a more open and loosely packed structure, resulting in a larger distance between layers.

5. Can the distance between two layers in an FCC unit cell be changed?

Yes, the distance between two layers in an FCC unit cell can be changed by altering the lattice constant or by applying external forces such as pressure or temperature. This can affect the material's properties and can be utilized in various applications such as in controlling the expansion and contraction of materials or in creating new materials with desired properties.

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