# Why are certain reflections forbidden in body centered cubic and face centered cubic structures?

I know that for body centered cubic structures the allowed reflections only happen if h+k+l is even and reflections are forbidden is h+k+l is odd, and for basic face centered cubic structures (excluding diamond cubic) for a reflection to happen the h,k,l terms must be all add or even and if they're a mix of odd and even then the reflection is forbidden.

I've tried looking in textbooks/lecture notes as to how/why these selection rules come about but I can't find an answer which explains, it's just kind of stated that this happens. Why is it that you get these allowed and forbidden reflections?

I know it'll probably be something to do with the group space/symmetry/destructive interference within the structures but I can't come up with a definitive explanation other than just stating that it's to do with 'symmetry' or 'destructive interference within the cube'. Is there a more detailed and specific answer that explains what actually goes on within the structure?

• k-space (momentum space) is the Fourier transform of real space. Because of the high symmetry of fcc and bcc, it turns out when you crank through the math that lots of destructive interference occurs. In particular, following Ashcroft and Mermin's Solid State Physics, in chapter 6 they go through getting the Bragg structure factor of a bcc lattice, treating it as simple cubic with a basis. Problem 2 at the end of that chapter is to do it for fcc in a similar fashion. Apr 6, 2016 at 14:20
• I'm fairly sure all solid state chem texts will talk about it, imo Smart & Moore is a good option. Apr 17, 2016 at 21:25
• I will try find a copy of those somewhere, problem is the recommended textbooks for general inorganic courses don't really explain this sort of thing, it's just stated as a rule. Apr 18, 2016 at 13:20