Physics and Engineering of Radiation Detection

12.1. Spectroscopy of Photons 679

now dedicated synchrotron radiation facilities exist in different parts of the world
where experimental time is made available to researchers.

hνm

ν>νm

ν<νm

L

M

K

Continuum

X−rays

Electron

Hole

Figure 12.1.5: Graphical depic-

tion of the process of photoelec-

tric absorption of x-ray photons

by an atom. An atom in the

ground state is transparent to

the photons having energy less

than the binding energy of the

core electron. X-rays having en-

ergy greater than the binding

energy are absorbed by an in-

ner core electron. The electron

then gets elevated to the contin-

uum and becomes free to move

around. The vacancy left by the

electron is called aholesince it

acts as an attractor for electrons

from outer shells.

The principle aim of x-ray absorption spectroscopy is to determine the XAFS of
the material. To understand how it is done we should first revisit the mechanisms
of photon interaction with matter. Fortunately for x-rays we should not be con-
cerned with all the interaction mechanisms since x-ray photons interact with atoms
predominantly through the process of photoelectric absorption. This interaction is
graphically depicted in Fig.12.1.5. Whenever a photon having energy equal to or
greater than the binding energy of the core electron interacts with the atom, it sets
the electron free. The vacancy created in the K-shell acts as an effective positive
charge and is sometimes referred to as ahole. We will shortly discuss its role in
absorption spectroscopy. First let us see how the elevation of the electron can lead
to the determination of XAFS. The process of photoelectric absorption completely
eliminates the photon, resulting in the reduction in beam intensity. Measurement
of the beam intensity after the material can therefore lead to the estimation of ab-
sorption by the material. And since the absorption is related to the binding energy
of the material, it can lead to determination of electronic states of the material and
possibly identification of the elements composing the material. This is the basic
principle oftransmissionXAFS. The reason why transmission XAFS works so well
can be understood by recalling that the absorption of photons in a material follows
an exponential of the form

Ix=I 0 e−μ(E)d, (12.1.1)

whereI 0 andIxare the incident and transmitted intensities. dis the thickness of
the material andμis the absorption coefficient of the material at that energy. This
relation can also be written as

μ(E)=

1

d

ln

(

I 0

Ix

)

. (12.1.2)