Systematic absence

A systematic absence is a class of diffraction reflections forced to vanish by symmetry or a repeated structural motif, rather than merely being weak by accident. It follows from exact cancellation in a crystal lattice structure factor or crystal basis structure factor within the stated scattering model.

For identical body-centering-related scatterers, $1+(-1{)}^{h+k+l}$ vanishes whenever $h+k+l$ is odd. Changing the motif can lift the cancellation, as in chemical ordering and body-centering extinction. Additional effects such as unequal species amplitudes, disorder or multiple scattering can also produce intensity where a simplified model predicts zero. Reflection conditions therefore help infer structure, but an observed weak or missing spot needs a measurement and model qualification before it is treated as an exact symmetry statement.

The identical two-atom motif adds a factor $1+\exp [i\pi (h+k+l)/2]$ to the FCC lattice structure factor. Among even-index FCC diffraction reflections, only those with $h+k+l$ divisible by4 survive. The allowed FCC reflection200 therefore vanishes for equal motif scattering amplitudes.