Thermal diffuse scattering removes intensity from the Bragg peaks and redistributes…

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Crystal structure, bonding and diffraction · Lattice dynamics and thermal properties of solids

Solid State Physics, Ch Diffraction as measurement: form factors, thermal motion and refinement

Problem

Thermal diffuse scattering removes intensity from the Bragg peaks and redistributes it through reciprocal space as a continuous background; because this background is weak and spread out rather than concentrated, measuring it usefully means collecting scattering from the full illuminated volume of a crystal, not just a thin surface layer. Cu K

\alpha

X-rays are attenuated to

1/e

of their intensity after passing through about

0.07\,\mathrm{mm}

of aluminium, while thermal neutrons of comparable wavelength are attenuated to

1/e

after about

10\,\mathrm{cm}

of aluminium. ((a)) Estimate, to the nearest power of ten, the factor by which the illuminated crystal depth (and hence, for the same beam cross-section, the scattering volume) differs between a neutron and an X-ray measurement of the diffuse halo around the aluminium

(220)

reflection. ((b)) Explain in one sentence why this favours neutrons for this particular measurement even though a neutron interacts far more weakly with each atom than an X-ray does.

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