Quasi-Forbidden Bragg peaks from soft matter

This week’s item is a rather technical Nature Materials paper by Forster et al., “Order causes secondary Bragg peaks in soft materials”[Nature Materials 6, 888 – 893 (2007)].

Atomic crystals can often be well-ordered, meaning that the correlation length on which “perfect” atomic order exist can extend over many thousands (or even millions) unit cells. Grain boundaries, dislocations and other defects are a common cause of breaking the perfectly ordered chain of atoms.

Soft materials – liquid crystals, colloids, mesoporous materials etc. – typically consist of fairly large unit cells and it is more difficult to get these materials as well-ordered as atomic crystals. All atoms are identical, but colloidal solutions, for example, are often fairly polydisperse, and therefore crystallize with some difficulty – if at all. It is no surprise that the correlation lengths – especially when expressed in unit cells – is far shorter in soft matter, compared to atomic crystals, such as Si or Pb.

Correlation lengthscales can be determined via Debye-Scherrer formalism that relates width of the x-ray or neutron scattering peak to the typical coherent domain size within the sample.

Forster et al. address the issue of finite correlation lengths by analysis of secondary “forbidden” (or quasi-forbidden) Bragg reflections. For example, for a perfect body-centered cubic lattice 001 reflection does not exist – only (002), (011) and other indices that add up to an even number. But once you introduce some disorder, these forbidden peaks become “alive”, since destructive interference responsible for precisely canceling out contributions to these forbidden reflections becomes somewhat faulty.

Surprisingly enough, people haven’t dealt much with ordered, but only over short-range distances materials, at least not to the extent of coming up with sophisticated treatment of intensities of these secondary Bragg peaks that can answer questions like: is the material truly homogeneous but has a lot of disorder, or is it “patchy”? Forster’s paper represents a key step in dealing with these important issues.

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