diffraction: structure factor

each type of lattice has a condition associated with it that describes positive interference during scattering. this is encapsulated within the so-called structure factor and explains the systematic absenses we see in x-ray and neutron images of crystals. the structure factor depends on how the atoms are arranged in the lattice. lets see how the structure factor effects the (simulated) diffraction patterns on the (100) plane

simple cubic:

face-centered cubic:

body centred cubic:

diamond:

we could explain with an argument about phase and odd/even values of (hkl), but check out the unit cell compositions of these structures to get an intuitive understanding of why we see this. it is to do with interference.