I Questions About Reciprocal Lattice Edge Length

AI Thread Summary
Reciprocal lattice edge lengths can be confusing, particularly when comparing BCC and FCC structures. The expected edge length of the reciprocal lattice for BCC is indeed 4π/a, not 2π/a, due to the nature of Fourier transforms which account for both positive and negative values. This results in a total length that effectively doubles the expected value. The discussion references a diagram from a Wiki page that supports this explanation. Understanding the relationship between spatial frequency and reciprocal lattice dimensions is crucial for accurate calculations.
lemonxx
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TL;DR Summary
Reciprocal Lattice Edge Length
Hi. So, i am currently studying reciprocal lattices, and am not quite sure how to find the edge length of a reciprocal lattice. for example I had expected the RL of BCC, which is FCC, to have edge lengths 2pi/a but it turns out it is 4pi/a, how come?
 
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lemonxx said:
TL;DR Summary: Reciprocal Lattice Edge Length

Hi. So, i am currently studying reciprocal lattices, and am not quite sure how to find the edge length of a reciprocal lattice. for example I had expected the RL of BCC, which is FCC, to have edge lengths 2pi/a but it turns out it is 4pi/a, how come?
I'm going back a long time here but iirc, the reciprocal lattice will have a side length corresponding to the highest spatial frequency. So that would suggest 2π/a but the Fourier transform will give positive and negative values so you get both signs of the reciprocal length, which is a total length of +2π/a to -2π/a, which gives twice the length =4π/a
The first row of this diagram (from the Wiki page) seems to confirm my idea.
1734889435789.png

As no one has answered you yet, this may be enough for you but I could be corrected by a ton of knowledge from elsewhere.
 
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