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While amorphous substances such as glass are encountered
both in natural and artificial materials, most inorganic mate-
rials are found to be crystalline on some scale, ranging from
sub-nanometer to centimeter or larger. A crystal consists of a
regular arrangement of atoms, the so-called “unit cell,” which
is repeated in a two- or three-dimensional pattern. In the pre-
vious discussion of electron beam–specimen interactions, the
crystal structure of the target was not considered as a variable
in the electron range equation or in the Monte Carlo electron
trajectory simulation. To a first order, the crystal structure
does not have a strong effect on the electron–specimen inter-
actions. However, through the phenomenon of channeling of
charged particles through the crystal lattice, crystal orienta-
tion can cause small perturbations in the total electron back-
scattering coefficient that can be utilized to image
crystallographic microstructure through the mechanism des-
ignated “electron channeling contrast,” also referred to as
“orientation contrast” (Newbury et al. 1986 ). The characteris-
tics of a crystal (e.g., interplanar angles and spacings) and its
relative orientation can be determined through diffraction of
the high-energy backscattered electrons (BSE) to form “elec-
tron backscatter diffraction patterns (EBSD).29.1 Imaging Crystalline Materials
with Electron Channeling Contrast
29.1.1 Single Crystals
The regular arrangement of atoms in crystalline solids can
influence the backscattering of electrons because of the regu-
lar three-dimensional variations in atomic density in the
crystal compared to those same atoms placed in the near
random three-dimensional distribution of an amorphous
solid. If a well-collimated (i.e., highly parallel) electron beam
is directed at a crystal array of atoms along a series of differ-
ent directions, the density of atoms that the beam encounters
will vary with the crystal orientation, as shown in the simple
schematic of. Fig. 29.1. A sense of this effect can be obtained
by manual manipulation of a macroscopic, three- dimensional
ball-and-stick model of a crystal. For certain orientations of
the model, the observer can see through the “atoms” along
the open gaps between the planes in the model. In a real solid,
the atoms are tightly packed, limited in their approach by the
repulsive interaction of their atomic shells. The “channels” in
reality are regions of the crystal where the atomic packing
creates lower charge density with which the beam electrons
will interact more weakly. When the beam is aligned with
the channels, a small fraction of the beam electrons penetrate
more deeply into the crystal before beginning to scatter. For
beam electrons that start scattering deeper in the crystal, the
probability that they will return to the surface as backscat-
tered electrons is reduced compared to the amorphous target
case, and so the measured backscatter coefficient is lowered
compared to the average value from the amorphous target.For other crystal orientations where denser atom packing is
found, the beam electrons begin to scatter immediately at the
surface, increasing the backscatter coefficient relative to the
amorphous target case. As seen in the Monte Carlo simula-
tion of an amorphous target, the elastic scattering of beam
electrons rapidly randomizes their trajectories out of their
initially well-collimated condition, reducing and eventually
eliminating sensitivity to channeling in the crystal. For a bulk
target, the modulation of the backscatter coefficient between
the maximum and minimum channeling case is small, typi-
cally only about a 2–5 % difference. Nevertheless, this crys-
tallographic or electron channeling contrast can be used to
form SEM images that contain information about the impor-
tant class of crystalline materials.
To determine the likelihood of electron channeling, the
properties of the electron beam (i.e., its energy, E, or equiva-
lently, wavelength, λ) are related to the critical crystal prop-
erty, namely the spacing of the atomic planes, d, through the
Bragg diffraction relation:n=λθ2sdin B (29.1)where n is the integer order of diffraction (n = 1, 2, 3, etc.).
Equation 29.1 defines a special beam incidence angle relative
to a particular set of the crystal planes with spacing d
(referred to as the “Bragg angle,” θB) at which the channeling
condition changes sharply from weak to strong as the beam
incidence angle increases relative to that particular set of
crystal planes. Since a real crystal contains many different
possible sets of atom planes, the degree of channeling. Fig. 29.1 Schematic illustration of the channeling effect: the atomic
area density that the beam encounters depends on its orientation rela-
tive to the crystal
Chapter 29 · Characterizing Crystalline Materials in the SEM