Micron Sizing

Can conventional SAXS probe micron sizes?

In principle yes…..in practice no….and here’s why:

In short,  the sizes that can be probed with SAXS are limited by the resolution of the instrument being used.

And, the resolution in Small Angle X-ray Scattering (SAXS) is determined by

  1. the minimum q value that can be measured and
  2. a convolution of the incident beam angular divergence and that of the scattered radiation collected in a defined solid angle, giving a composite angular resolution dq

This angular resolution dq, is used to calculate the resolution in q, and this in turn, gives the resolution in real space dD = 2π/dq.

Extending the conventional instrument

Now, a typical laboratory SAXS system is on the order of 3 meters in length with 1.5 meter lengths for both the incident beam collimation and the scattered radiation flight path.  Typical qmin in this configuration is 0.003 1/A and this corresponds to a real space probe of 0.2micron.

The dq is typically smaller than qmin, which curiously means that it could be possible to resolve feature below the qmin,  One may see this in samples with large spherical particles where the first oscillation may be hidden behind the beam stop, but where the higher order oscillations are clearly resolved.

Now of course, one can extend the length of the system in order to reduce qmin and probe larger length scales.  If we double or even triple the length of the system, we could start to “touch” length scales on the order of 6000A. But we will quickly run into  space constraints in the laboratory.

And actually “touching” these length scales doesn’t give you enough data-points to do anything useful with the scant few point you get in this region.  In addition, qmin doesn’t actually tell us about structure we can measure.  For example, what if there were a primary peak at the qmin?  One would not know it’s a peak because we can’t see the other side at lower q.  So in fact, to be able to resolve structures of size D, we need to go at least as low as qmin/2, and so now we are at systems of a total length of 20 meters!

So the simple idea of extending the length of the system becomes considerably less desirable, especially if detail is really required at low q.

A solution

Luckily there is a solutiion:

Instead of using apertures and system length to achieve high resolution, the Bonse-Hart (BH) geometry, first demonstrated almost 50 years ago, uses the high angular selectiveness of perfect crystals to achieve high resolution and uses multiple bounces to suppress the inherent tails.

As such, the BH geometry continues to be the only solution for achieving micron scattering probe lengths, since no other approach is capable of delivering “a significant number of points at q vectors smaller than 0.001 1/A ; not just 1 or 2 points.”, ( the community’s accepted definition of USAXS).

Schematic of USAXS