Chapter 5 – Detection and Imaging Tools that Use Nonoptical Waves 171
Measuring the diffraction intensity with the CCD and calculating the respective phases in
principle would allow 3D reconstruction of the sample. However, thus far, samples have been
limited to being relatively thin. But even so, this method, in eradicating spherical aberration
limits, has improved spatial resolution at 30 kV by a factor of ~5 compared to equivalent
energies in a conventional TEM.
Worked Case Example 5.1: Applying Electron Microscopy
A thin section of skin tissue was prepared to purify planar cell membrane components
normal to an electron beam in a diffraction experiment in a 200 kV electron microscope.
Some of the transmitted electrons were diffracted with a first-order deflection of 0.5°,
while a minority were scattered back with a first-order maxima deflections of 0.015° from
the axis normal to the membrane surface. Comment of the angular deflections and inten
sity of the scattered/diffracted electrons.
Answers
Using the nonrelativistic approximation for electron wavelength and the de Broglie
relation indicates
λ =
×
√
×
×
×
×
×
×
(
) =
×
−
−
−
−
(6.62
10
/
m
34
31
19
3
12
2
9 1 10
1 6
10
200
10
2 7
10
)
.
.
.
Using the Bragg reflection formula and rearranging indicate a periodic spacing
perpendicular to the membrane of db = (1 × 2.7 × 10−12)/(2 × sin(0.015°)) = 5.1 ×
10−9 m.
Using the Bragg transmitted diffracted beam formula and rearranging indicate a
periodic spacing parallel to the membrane of dt = (1 × 2.7 × 10−12)/(sin(0.5°)) = 2.4 ×
10−10 m.
The estimated value of db is consistent with the width of a cell membrane and might
thus be due to interference from the polar head groups that are separated by ~5 nm
at either side of the membrane (see Chapter 2). The estimated value of dt is consistent
with the lateral spacing of polar head groups if the phospholipid monomers are
tightly packed. Constructive interference can occur between several adjacent head
groups to generate a first-order diffraction peak of the transmitted beam, whereas
interference can only occur between two layers for the backscattered interference (as
the cell membrane is a bilayer), and thus the intensity of the first-order maxima will
be much less.
5.3 X-RAY TOOLS
X-rays (originally known as “Röntgen rays” in Germany where they were first discovered) are
composed of high-energy electromagnetic waves, which have a typical range of wavelength of
~0.02–10 nm. This is very similar to the length scale for the separation of individual atoms in
a biological molecule and also for the size of certain larger scale periodic features at the level
of molecular complexes and higher length-scale molecular structures, which makes x-rays
ideal probes of biomolecular structure. X-ray diffraction, in particular, is an invaluable bio
physical tool for determining molecular structures—in excess of 90% of all known molecular
structures that have been determined using x-ray diffraction techniques, compared to ~10%
by NMR and <1% by EM methods, at the time of writing.
KEY BIOLOGICAL
APPLICATIONS:
EM
Determining molecular
structures; Imaging tissue,
cellular, and subcellular
architectures; Imaging surface
topologies.