Principle of Small Angle X-ray Scattering

When X-rays pass through a sample they scatter off everything. X-rays are waves (typical wavelength λ=1.54 Angstroms) so they diffract and interfere just like ocean waves, light waves, sound waves or seismic waves. X-rays scatter in directions whree all the scattered waves are in phase.

Some samples are periodic such as atoms in a crystal or the tracks on a Compact Disk. This is shown in Figure One.

Other samples consist of a random arrangment of objects such as molecules in solution, fat globules in milk or water droplets in a cloud. This is shown in Figure Two.

The general relationship between scattering angle and size of the object is,

So,

1. A protein approximately 25 Angstroms size will scatter X-rays out to about 2 degrees. If eight protein molecules clump together to make a molecule of rough size 50 Angstroms, the X-ray scattering will now contract inside a disk of size 1 degree.

2. A soap film has a layer-to-layer spacing of 30 Angstroms so it scatters out in rings at 3 degrees, 6 degrees, 9 ... . When water is added the layer-to-layer spacing increases to 45 Angstroms. Now the rings are found at 2, 4, 6 ... degrees.

A bright ring means there is a periodic structure in that object with that repeat spacing.

Intense scattering over a range of angles means the structure is ordered on that length scale but is not be periodic.

Gruner Lab X-ray System

Synopsis - The X-ray system is designed for Small Angle (0.1 degrees to 20 degrees) X-ray scattering from biological, polymeric and other samples.

X-ray Source - X-rays are generated by a Rigaku Rotating Anode X-ray Generator. A beam of electrons is accelerated to high velocity and smashed into a copper target. The electrons emit X-rays when they hit the copper target. The copper target is water-cooled and rotates to prevent it from melting. Our X-ray sources operate around Voltage=50kV and Current=60mA producing a sharp spot of 1.54 Angstrom X-rays about 0.2mm by 0.2mm. The flux reaching the detector is around 10 to 40 million X-rays per second.

X-ray Optics - Although X-rays normally pass through matter they do bounce off metal mirrors at small angles just like the sun shining off a lake early or very late in the day. One or two X-ray mirrors are used to focus the beam to a sharp spot on the detector. Using slits the beam is cut to a size of about 1mm by 1mm at the detector. The beamline runs in a vacuum to prevent X-ray scattering from air.

Sample Stage - Sample position, temperature and pressure are computer controlled.

Samples : To obtain maximum signal most samples need to be about 1mm thick. X-ray capillaries (glass tubes with a wall thickness of 5 microns or so) to hold our samples.

X-ray Detectors : All the X-ray detectors in the lab are homebuilt. At the front of the detector, X-rays hit a phosphor screen (5cm*5cm approx). The phosphor converts X-rays to light. The light is then focussed through optics onto a low noise CCD detector. Typical exposures range from 1 second to 1 hour depending on the material being examined.