The edge length of a reciprocal lattice for a body-centered cubic (BCC) structure, which corresponds to a face-centered cubic (FCC) lattice, is calculated as 4π/a, contrary to the expected 2π/a. This discrepancy arises from the Fourier transform of the lattice, which accounts for both positive and negative values, effectively doubling the length. The highest spatial frequency in the reciprocal lattice dictates this calculation, confirming that the total length is indeed 4π/a.
PREREQUISITESStudents and researchers in solid-state physics, crystallographers, and materials scientists who are studying the properties of reciprocal lattices and their applications in material characterization.
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/alemonxx said: