= Solution
The all-even $(220)$ reflection is allowed. Here $d_{220}=0.1980\,\mathrm{nm}$ and \b[$2\theta_B=45.77^\circ$]. 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 \b[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.
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