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

Take ${\lambda }_{\mathrm{Fe}}\simeq 0.1937\mathrm{nm}$ for the unresolved iron $K_{\alpha }$ doublet. The underlying tabulated $K_{\alpha 1}$ and $K_{\alpha 2}$ wavelengths are approximately $0.193604$ and $0.193998\mathrm{nm}$.^[ref]

Using the inferred $a\simeq 0.348\mathrm{nm}$, Bragg's law gives the following approximate cone angles:The exact angles inherit the lattice-parameter uncertainty. Five reflection families are kinematically possible with this longer wavelength: $h^2+k^2+l^2\le (2a/{\lambda }_{\mathrm{Fe}}{)}^2\simeq 12.9$. The next FCC family, 400, cannot satisfy Bragg's law.

A cylindrical Debye-Scherrer camera records paired curved lines where each diffraction cone intersects the film. Both forward and backward cones can be intercepted. The last three families are back reflections here, unlike the rings recorded on the original forward flat plate. Film position is proportional to camera angle along the equatorial circumference, rather than to $L\tan 2\theta$; the incident and transmitted beam holes must also be distinguished from reflections. A sufficiently resolved exposure may separate the characteristic doublet, but the schematic does not claim to predict line intensities.