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

In the kinematic approximation, the face-centered cubic lattice contributes only reflections with $h,k,l$ all even or all odd. Viewing along $[001]$ selects the zero-order zone $l=0$, so the nonzero allowed spots within the cutoff are $(\pm 2,0,0),(0,\pm 2,0),(\pm 2,\pm 2,0)$, with the transmitted beam at the centre. The nearest-neighbour separation is $2/a_{\mathrm{Al}}$ in the crystallographic reciprocal-distance convention, or $4\pi /a_{\mathrm{Al}}$ in the angular-wavevector convention. No matrix lattice parameter is supplied, so a numerical matrix spacing would require extra data.