Anomalous X-ray scattering

Anomalous X-ray scattering AXRS or XRAS is a non-destructive determination technique within X-ray diffraction that makes use of the anomalous dispersion that occurs when a wavelength is selected that is in the vicinity of an absorption edge of one of the constituent elements of the sample. It is used in materials research to study nano-meter sized differences in structure.

Atomic scattering factors

In X-ray diffraction the scattering factor f for an atom is roughly proportional to the number of electrons that it possesses. However, for wavelengths that approximate those for which the atom strongly absorbs radiation the scattering factor undergoes a change due to anomalous dispersion. The dispersion not only affects the magnitude of the factor but also imparts a phase shift in the elastic collision of the photon. The scattering factor can therefore best be described as a complex number^[1]

f= f_o + Δf' + i.Δf"

Contrast variation

The anomalous aspects of X-ray scattering have become the focus of considerable interest in the scientific community because of the availability of synchrotron radiation. In contrast to desktop X-ray sources that work at a limited set of fixed wavelength, synchrotron radiation has a continuous spectrum from which one can select a single wavelength by means of a monochromator. This allows scientists to vary the wavelength, which in turn makes it possible to vary the scattering factor for one particular element in the sample under investigation. Thus a particular element can be 'high-lighted'. This is known as contrast variation. In addition to this effect the anomalous scatter is more sensitive to any deviation from sphericity of the electron cloud around the atom. This can lead to resonant effects involving transitions in the outer shell of the atom: Resonant anomalous X-ray scattering.

References

1. ↑ X-ray diffraction in crystals, imperfect crystals and amorphous bodies. A. Guinier. Dover 1994 ISBN 0-486-68011-8 original publication 1963