Tutorial:Qualitative inspection

When analyzing data, the first thing one should do is get an overall sense of data. By applying a few simple rules-of-thumb, one can interpret a 2D x-ray scattering image, and infer quite a bit about the structure of the sample.

Amount of Order

TBD

Peak Position

Recall that reciprocal-space is inverted: i.e. peaks at large angle (large q) correspond to small-scale structures; whereas peaks at small angle (small q) correspond to larger (nanoscale) structures. Ultrasmall angle scattering (USAXS) probes yet larger (micron-scale) order. More specifically, when observing peaks at:

• Very large angle (0.5-4 Å⁻¹): Atomic packing distances (1-10 Å).
• Large angle (0.2-2 Å⁻¹): Molecular packing distances (0.3-3 nm). For instance, aromatic rings tend to pi-pi stack with a 0.3-0.4 nm repeat distance.
• Medium angle (0.03-0.3 Å⁻¹): Macromolecular distances (2-20 nm). For instance, polymers often crystallize into chain-folded lamellae with a period of 2-10 nm.
• Small angle (0.0002-0.04 Å⁻¹): Nanoscale distances (15-300 nm). For instance, block-copolymers and nanoparticle superlattices tend to organize in this size regime.
• Ultra-small angle (<0.0006 Å⁻¹): Micron sizes (>1 µm).

Peak Width

In scattering, sharp peaks correspond to large grain sizes, whereas broad peaks correspond to small grain sizes. This can be quantified through a Scherrer grain size analysis. Even qualitatively, however, it is usually easy to judge how well-ordered a material is based purely on peak widths. Consider a highly disordered system, such as an amorphous polymer. The polymer chains likely have some preferred chain-packing distance, but the 'lattice' only repeats once or twice before decorrelating; i.e. there isn't a well-defined crystal with well defined grain boundaries. In such a case one would see a very broad halo. In even more disordered systems, only diffuse scattering would be seen (this can be thought of as the ultimate limit of a broad peak).

On the other hand, extremely sharp peaks indicate that the lattice repeats in a well-correlated well over very large distances.

Scattering Intensity

The scattering intensity (counts on the x-ray detector) scales with the amount of scattering material. Thus, a bigger sample yields a stronger scattering signal. (Of course if you try to scatter through a sample that is too thick, absorption will at some point instead reduce the signal.) For a given scattering volume, the intensity of the scattering can be thought of as a probe of the fraction of the material in the given state/phase/configuration. I.e. if a given peak is stronger in one sample vs. another, then this means that the phase (crystal form, etc.) corresponding to that peak appears more frequently in that sample. One must be careful, however, as many other things are implicated in peak heights (orientation, disorder, etc.).

Note that in general, well-ordered systems will appear to scatter more strongly than weakly-ordered systems. A broad scattering peak (small grains) will have lower maximum intensity than a sharp scattering peak (big grains). More generally, periodically ordered structures give rise to scattering events, whereas homogeneous systems do not scattering the incident radiation.

Higher Orders

TBD