Structure Factor: BCC

We will now consider the structure factors for some important structures. Consider the reciprocal lattice of fcc and bcc crystals. The reciprocal lattices of cubic lattices are cubic, but some of the lattice points have a zero structure factor.

BCC structure

Consider the bcc lattice with single atoms at each lattice point, its unit cell can be reduced to two identical atoms. Atom 1 is at 000 with scattering factor f, and atom 2 is at ½ ½ ½ with a scattering factor f.

Click on the animation opposite to illustrate the bcc unit cell.

The structure factor for the bcc unit cell is therefore:

For diffraction from a plane where the sum of h+k+l is odd, the second term is -1, so

F_hkl_odd = f(1-1) = 0

If h+k+l is even, the second term is +1, so

F_hkl_even = f(1+1) = 2f

Thus, diffractions from bcc planes where h+k+l is odd are of zero intensity. They are forbidden reflections. These reflections are usually omitted from the reciprocal lattice.

Click on the animation opposite to illustrate the forbidden reflections from the bcc unit cell.

Structure Factor: Other structures