Physical Principles of Electron Microscopy: An Introduction to TEM ...

TEM Specimens and Images 101
4.4 Scattering Contrast from Amorphous Specimens
Most TEM images are viewed and recorded with an objective aperture
(diameter D) inserted and centered about the optic axis of the TEM objective
lens (focal length f ). As represented by Eq. (3.9), this aperture absorbs
electrons that are scattered through an angle greater than � � 0.5D/f.
However, any part of the field of view that contains no specimen (such as a
hole or a region beyond the specimen edge) is formed from electrons that
remain unscattered, so that part appears bright relative to the specimen. As a
result,
this central-aperture image is referred to as a bright-field image.
Biological tissue, at least in its dry state, is mainly carbon and so, for this
common type of specimen, we can take Z = 6, A = 12, and �� 2 g/cm 2 =
2000 kg/m 3 . For a biological TEM, typical parameters are E0 = 100 keV =
1.6 � 10 -14 J and �� 0.5D/f = 10 mrad = 0.01 rad, taking an objective-lens
focal length f = 2 mm and objective-aperture diameter D = 40 �m. With
these values, Eq. (4.15) gives Pe(�) � 0.47 for a specimen thickness of t = 20
nm. The same parameters inserted into Eq.(4.16) give Pi(>�) � 0.08, and the
total fraction of electrons that are absorbed by the objective diaphragm is
P(>10
mrad) � 0.47 + 0.08 = 0.54 .
We therefore predict that more than half of the transmitted electrons are
intercepted by a typical-size objective aperture, even for a very thin (20 nm)
specimen. This fraction might be even larger for a thicker specimen, but our
single-scattering approximation would not be valid. In practice, the specimen
thickness must be less than about 200 nm, assuming an accelerating potential
of 100 kV and a specimen consisting mainly of low-Z elements. If the
specimen is appreciably thicker, only a small fraction of the transmitted
electrons pass through the objective aperture, and the bright-field image is
very dim on the TEM screen.
Because (A/Z) is approximately the same (�2) for all elements, Eq.(4.16)
indicates that Pi(>�) increases only slowly with increasing atomic number,
due to the density term �, which tends to increase with increasing Z. But
using the same argument, Eq. (4.15) implies that Pe(>�) is approximately
proportional to �Z. Therefore specimens that contain mainly heavy elements
scatter electrons more strongly and would have to be even thinner, placing
unrealistic demands on the specimen preparation. Such specimens are
usually examined in a “materials science” TEM that employs an accelerating
voltage of 200 kV or higher, taking advantage of the reduction in �e and Pe
with increasing E0; see Eqs. (4.13) and (4.15).
For imaging non-crystalline specimens, the main purpose of the objective
aperture is to provide scattering contrast in the TEM image of a specimen