 Solution

The four FCC translations give a lattice structure factor that is nonzero only when $h,k,l$ are all even or all odd. The identical two-atom motif then multiplies it byFor $(200)$ the FCC part is allowed, but the motif factor is $1+e^{i\pi }=0$. HenceIn the projection, equal numbers of atoms occur at $x/a=0,1/4,1/2,3/4$. Their $(200)$ phases are respectively $+1,-1,+1,-1$. The paired layers cancel exactly for equal silicon scattering amplitudes. This diamond-basis diffraction extinction is additional to the FCC centring rule; it is not evidence that no atoms lie on the nominal reflecting planes.