Past exam of the materials science course of the University of Cambridge / 2016 / Paper 1 / 3 / a

Measure ring centers and radii against the printed scale, rather than comparing raw squared radii. A representative reading of the four rings is $R\simeq 6.0,7.0,10.6,13.2\mathrm{mm}$, with broad photographic lines. For a flat plate at distance $L$,With $L=16\mathrm{mm}$ the ${\sin }^2\theta$ ratios are approximately $1:1.33:2.67:3.67$, givingFor identical atoms at the four conventional FCC positions,The structure factor is $4f$ for indices all even or all odd, and zero for mixed parity. Thus, for example, 100, 110 and 210 are systematic absences. The allowed squared-index sums begin $3,4,8,11,12,16,\dots$. Only the first four rings fit within the displayed field; 222 and later allowed reflections are not forbidden merely because they are outside the image. The central shadow and its holder are not extra diffraction peaks.