I Questions About Reciprocal Lattice Edge Length

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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
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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