SAXS Predictor
In small-angle X-ray scattering (SAXS) the maximum scattering angle is determined by
the size of the detector, which is best thought of as a camera with many pixels, and how
far the detector is from the sample. This schematic below shows the arrangement.
One pixel at the maximum radius
ymax

X-ray source
Circular
detector
xsd
The SAXS instrument at LSU’s CAMD synchrotron has a detector with a diameter of 8
inches. The distance from sample to detector can only take certain values: 20 inches, 72
inches and 108 inches and these lengths define the range of angles available. It is
incumbent on the user to figure out which value of xsd to choose, and it’s an important
calculation because detector setup requires an hour or more and places the detector at risk
(the detectors don’t like to be moved). For example, if you are trying to get the radius of
some small, spherical particle while the detector is at 108 inches, there may not be
enough decrease in intensity, even at the highest angle corresponding to the outer edge of
the detector, to measure (i.e., all angles may be too small). So, you need some idea of the
particle size before you try for an accurate measurement.
Make an Excel spreadsheet that plots the scattering response (Intensity vs. q) for a
spherical particle of size R at all three sample-to-detector distances (better yet, make it
easy to switch the detector radius using buttons). In making your plot, just select 100
points between angle zero and the maximum angle obtainable. The equation describing
the response is expressed as a quotient of intensity at q to that you could obtain at q=0, if
you could safely make that measurement:
I (q)  3

  3 (sin u  u cos u )
I (0)  u

2
where u = qR.
Which value of xsd would you choose if you thought your sample had an approximate
radius of 15 nm?