Past exam of the materials science course of the University of Cambridge / 2017 / Paper 1 / 3 / b / iv

The all-even $(220)$ reflection is allowed. Here $d_{220}=0.1980\mathrm{nm}$ and $2{\theta }_B=45.77^{\circ }$. Its normal is $45^{\circ }$ from $[100]$ and can lie in the horizontal scattering plane in an edge-aligned mounting. Nevertheless it is not parallel to the large $(100)$ face, so the ordinary coupled symmetric scan misses it.

Independent sample rotation can bring the $(220)$ normal onto the Bragg bisector, but there is an important specimen constraint: ${\theta }_B=22.89^{\circ }$ is less than the $45^{\circ }$ surface inclination. One ray then traverses the slab rather than emerging from the incident face. Thus a thin transmission specimen or access through another face can permit detection after suitable remounting, whereas a thick absorbing slab in front-face reflection is unfavourable. A $(110)$-cut crystal allows a straightforward symmetric $(220)$ measurement, and a powder specimen supplies the needed orientations. Unlike $(300)$, no extinction prohibits it; whether the original portable mounting can reach it depends on independent rotation, holder clearance and the transmitting path.