= Solution
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 $(\pm2,0,0),(0,\pm2,0),(\pm2,\pm2,0)$, with the transmitted beam at the centre. The nearest-neighbour separation is \b[$2/a_{\rm Al}$] in the crystallographic reciprocal-distance convention, or $4\pi/a_{\rm Al}$ in the angular-wavevector convention. No matrix lattice parameter is supplied, so a numerical matrix spacing would require extra data.
\Image[/past-exam-of-the-materials-science-course-of-the-university-of-cambridge/2022/paper-1-diffraction.png]
{title=Calculated zero-order diffraction spots before and after chemical ordering}
{description=Original kinematic spot diagrams with reciprocal coordinates normalized by the relevant cubic cell edge. The right panel shows additional superlattice positions; actual intensity also depends on thickness, excitation and scattering factors.}
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