Upper limit of Miller indices of BCC and FCC crystals?

In summary, the smallest meaningful reciprocal distance for metals such as Fe, Cu, and Ag would be 2pi/(crystal size). This is due to the fact that planes with high (hkl) indices have small interplanar spacing, which corresponds to smaller real space distances. However, there is no specific upper limit for these metals.
  • #1
wangasu
33
0
does anybody know the upper limit of the bcc and fcc metals like Fe, Cu, Ag? According to the fact that the planes with high (hkl) indices have small interplanar spacing d_hkl, the smallest spacing would be present. what is that? atomic diameter of a specifc metal?
 
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  • #2
I don't think that there really is an upper limit, but you are right that larger and larger reciprocal space vectors correspond to smaller and smaller real space distances, and at some point that becomes meaningless. As far as I can tell, in practice nobody is ever bothered by this.

The smallest meaningful reciprocal distance would be 2pi/(crystal size). That is something experimentally relevant, for example in nanomaterials.
 

1. What is the upper limit of Miller indices for BCC crystals?

The upper limit of Miller indices for BCC crystals is 4. This means that the highest possible Miller indices for a BCC crystal would be (4 4 4).

2. What about the upper limit for FCC crystals?

The upper limit of Miller indices for FCC crystals is also 4. This is because FCC crystals have a cubic structure similar to BCC crystals, and therefore have the same maximum Miller indices.

3. Why is the upper limit for both BCC and FCC crystals 4?

The upper limit of Miller indices is determined by the number of lattice points in the unit cell of a crystal structure. BCC and FCC crystals have a unit cell with 4 lattice points, hence the upper limit of 4 for their Miller indices.

4. Can the upper limit of Miller indices be different for other crystal structures?

Yes, the upper limit of Miller indices can vary for different crystal structures. For example, HCP crystals have a maximum Miller indices of (10 10 12), while diamond crystals have a maximum of (8 8 8).

5. How is the upper limit of Miller indices useful in crystallography?

The upper limit of Miller indices is important in crystallography as it helps in determining the symmetry and orientation of a crystal. It also plays a role in understanding the physical and chemical properties of a crystal and in determining the atomic arrangement within the crystal structure.

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