Upper limit of Miller indices of BCC and FCC crystals?

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SUMMARY

The upper limit of Miller indices for Body-Centered Cubic (BCC) and Face-Centered Cubic (FCC) crystals, such as Iron (Fe), Copper (Cu), and Silver (Ag), is not definitively established. The discussion highlights that while higher (hkl) indices correspond to smaller interplanar spacings (d_hkl), there is a practical limit where these indices become meaningless. The smallest meaningful reciprocal distance is defined as 2π/(crystal size), which is particularly relevant in the context of nanomaterials.

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  • Understanding of Miller indices in crystallography
  • Knowledge of interplanar spacing (d_hkl) in crystal structures
  • Familiarity with reciprocal space concepts
  • Basic principles of nanomaterials and their properties
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  • Explore the relationship between interplanar spacing and crystal size
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Material scientists, crystallographers, and researchers in nanotechnology who are interested in the structural properties of BCC and FCC metals.

wangasu
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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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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.
 

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