Undergrad Questions About Reciprocal Lattice Edge Length

[lemonxx]

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?

 

[sophiecentaur]

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.

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.