Chapter 6
X-ray Absorption and EXAFS
6.1 Introduction
When X-rays impinge on a sample, they can be transmitted, scattered elastically
(Rayleigh scattering and diffraction), scattered inelastically (Raman and Compton
scattering), or absorbed. At high X-ray energies, the higher the atomic number of an
element, the stronger the absorption, and this contrast mechanism is employed for
X-ray imaging of broken bones, at the dentist’s office, in mammography, and a
myriad of other applications. In this chapter, we will consider the energy dependence
of X-ray absorption in more detail.
An X-ray absorption measurement in transmission mode is really quite simple,
and the principles are the same as for UV-visible or infrared absorption spectroscopy. For a fixed X-ray energy E, measure the fraction of X-rays absorbed in a
sample with pathlength t (Fig. 6.1). The ratio of transmitted flux (I ) to incident flux
(I 0 ) is called the transmittance (T ), while the absorbance (A) is defined by
A ¼ Àlog 10 T ¼ log 10 I 0 /I. By repeating this measurement over a range of energies,
one obtains an absorption spectrum A(E) vs. E. For every element, there is a typical
energy where there is just sufficient energy to ionize a particular core electron. At
this point in the spectrum, there is a rapid rise in the absorption coefficient—the
so-called absorption edge. The edge energy (E 0 ) is approximately halfway up the
edge. The various edges available for Mo and other elements are illustrated in
Fig. 6.2, and Appendix G lists the more commonly used absorption edge energies.
“I already have FT-IR and UV-visible spectrometers in my lab,” you object.
“Why should I bother going to a synchrotron for yet another absorption measurement?” It turns out that X-ray absorption spectroscopy (“XAS”) has many special
attributes that will make the trip worthwhile. It is:
• Element specific. One beauty of X-ray absorption is that every element has
absorption edge features in specific energy ranges. At a given energy, you
© Springer Nature Switzerland AG 2020
S. P. Cramer, X-Ray Spectroscopy with Synchrotron Radiation, Biological and Medical
Physics, Biomedical Engineering, https://doi.org/10.1007/978-3-030-28551-7_6
131
X-ray Absorption and EXAFS
6.1 Introduction
When X-rays impinge on a sample, they can be transmitted, scattered elastically
(Rayleigh scattering and diffraction), scattered inelastically (Raman and Compton
scattering), or absorbed. At high X-ray energies, the higher the atomic number of an
element, the stronger the absorption, and this contrast mechanism is employed for
X-ray imaging of broken bones, at the dentist’s office, in mammography, and a
myriad of other applications. In this chapter, we will consider the energy dependence
of X-ray absorption in more detail.
An X-ray absorption measurement in transmission mode is really quite simple,
and the principles are the same as for UV-visible or infrared absorption spectroscopy. For a fixed X-ray energy E, measure the fraction of X-rays absorbed in a
sample with pathlength t (Fig. 6.1). The ratio of transmitted flux (I ) to incident flux
(I 0 ) is called the transmittance (T ), while the absorbance (A) is defined by
A ¼ Àlog 10 T ¼ log 10 I 0 /I. By repeating this measurement over a range of energies,
one obtains an absorption spectrum A(E) vs. E. For every element, there is a typical
energy where there is just sufficient energy to ionize a particular core electron. At
this point in the spectrum, there is a rapid rise in the absorption coefficient—the
so-called absorption edge. The edge energy (E 0 ) is approximately halfway up the
edge. The various edges available for Mo and other elements are illustrated in
Fig. 6.2, and Appendix G lists the more commonly used absorption edge energies.
“I already have FT-IR and UV-visible spectrometers in my lab,” you object.
“Why should I bother going to a synchrotron for yet another absorption measurement?” It turns out that X-ray absorption spectroscopy (“XAS”) has many special
attributes that will make the trip worthwhile. It is:
• Element specific. One beauty of X-ray absorption is that every element has
absorption edge features in specific energy ranges. At a given energy, you
© Springer Nature Switzerland AG 2020
S. P. Cramer, X-Ray Spectroscopy with Synchrotron Radiation, Biological and Medical
Physics, Biomedical Engineering, https://doi.org/10.1007/978-3-030-28551-7_6
131