Past exam of the materials science course of the University of Cambridge / 2022 / Paper 1 / 3 / b / i

For the L12 structure, the crystal basis structure factor isEqual parity of $h,k,l$ makes all three phase factors $+1$, henceThe electron scattering factors are evaluated at the reflection's scattering vector.

For mixed parity, one of the three pair sums is even and two are odd. Thus their phase factors sum to $-1$, givingThese superlattice reflections reveal chemical ordering. Their kinematic intensity is proportional to $|f_{\mathrm{Sc}}-f_{\mathrm{Al}}{|}^2$, and vanishes in the hypothetical limit of equal species scattering factors.