Past exam of the materials science course of the University of Cambridge / 2018 / Paper 1 / 3 / a / Solution

For a cubic phase, $d_{hkl}=a/\sqrt{h^2+k^2+l^2}$ and Bragg's law givesThe first six FCC-allowed squared-index sums are $3,4,8,11,12,16$, from indices all odd or all even. The labels1–6 are thereforeRemember that the plot reports $2\theta$, not $\theta$. The first peak givesThe last peak provides an independent estimate,Thus $a\simeq 0.3638\mathrm{nm}$ is appropriate to the supplied precision. The two estimates differ by about $0.08\%$; high-angle data are less sensitive to a fixed angular error, so the $400$ estimate is useful for the composition calculation. The printed angles do not justify many more significant figures or an exact fit of all six positions.