metals (see Table 7.5); suitable sources for these examples are
204
Tl and
63
Ni
respectively.
7.3.3 Special applications: electron microscopy
Knowledge of the relationships between the properties, structure and com-
patibility of materials under a wide range of conditions underpins many of
the processing, manufacturing and heavy engineering sectors of industry.
Electron microscopy, which involves the application of many of the scienti®c
principles discussed in this book, has been used to advance knowledge in
these areas. In simple terms, an electron microscope comprises a source of
electrons and a series of electro-magnets, which perform functions similar to
that of lenses in optical microscopes.
The fundamental difference between optical and electron microscopes is
the mechanism of formation of the contrasts resulting in the image. In light
optics, images result from differences in absorption of the light illuminating
the object; in electron microscopy they arise from the complex processes of
electron scattering and diffraction.
In both types of instruments, the Rayleigh criterion requires that the limit
of resolution, d, is a function of the incident wavelength given by d =kl/a
where k is a constant, l is the wavelength of the incident radiations and a is
the aperture of the microscope, all in consistent units. For optical micro-
scopes, the resolution lies in the range 0.2 and 0.5 mm (2000 to 5000 A
Ê
),
leading to a maximum magni®cation of around 10006.
The wavelengths of electrons decrease as their energies increase i.e. with
increasing accelerating voltage. Electron wavelengths are very short, only
0.09 A
Ê
at 20 keV and 0.025 A
Ê
at 200 keV, and so substantially less than the
average interatomic spacings which are about 2 A
Ê
. With modern high-
resolution techniques, well maintained and properly aligned transmission
electron microscopes can resolve at the atomic scale. However, due to a
number of instrumental effects, the resolution for scanning electron micro-
scopes is limited to between 50 and 200 A
Ê
, which corresponds to magni®ca-
tions of about 100 0006.
The interaction of higher energy electrons (> 5 keV) with the atoms of the
specimen leads to the generation of X rays. These comprise both bremsstrah-
lung (Section 3.8.1) and ¯uorescent X rays (Section 3.9.1). The latter are used
to map the distribution of elements in the sample. In addition, structural
information may be obtained through the analysis of electron diffraction
patterns. Readers seeking further information are referred to works by
Hunter et al. (1993), Williams and Carter (1996) and Watt (1997).
7.3 Applications of beta particles and electrons 209