56 2 Energy-Loss Instrumentation
the poleface angles (ε
1
and ε
2
). The pole faces are not curved; aberration correction
(including partial fourth and fifth orders) is achieved by means of three external
dodecupole (12-pole) lenses, one before the prism and two between the prism and
the energy-selecting slit. The poles of these lenses can be individually excited to
generate any combination of dipole, quadrupole, sextupole, and higher order ele-
ments, in order to control the prism focusing up to sixth order. Because these
different elements share the same optic axis, alignment is easier than with sepa-
rate elements. A further five dodecupoles (after the slit) project a spectrum or an
energy-filtered image onto the CCD detector.
2.2.4 Practical Considerations
The main aim when designing an electron spectrometer is to achieve good energy
resolution even in the presence of a large spread γ of entrance angles, enabling
the spectrometer system to have a high collection efficiency (see Section 2.3). For
γ = 10 mrad, correction of second-order aberrations allows a resolution ≈1eVfor
energy losses up to 1 keV (Krivanek and Swann, 1981; Colliex, 1982; Scheinfein
and Isaacson, 1984). The value of γ is limited by the internal diameter of the “drift”
tube (Fig. 2.9), which is necessarily less than the magnet gap g, so the historical
trend has been toward relatively large g/R ratios (see Table 2.1), even though this
makes accurate calculation of the fringing-field properties more difficult (Heighway,
1975). The use of multipole elements, giving partial correction up to fifth order, can
provide a resolution below 0.1 eV (Gubbens et al., 2010).
The energy range falling on the detector depends on the bend radius R and the
dispersion D, which increases with decreasing beam energy E
0
. In the standard (SR)
version of the GIF Quantum spectrometer, the bend radius R has been reduced from
100 to 75 mm, allowing 2 keV range for 200 keV electrons or 682 eV at 60 keV. An
even smaller value (50 mm) is scheduled for lower-voltage TEMs (15–60 keV) and
a larger one (200 mm) for high-voltage operation (400–1250 keV).
Spectrometer designs such as those in Table 2.1 assume that the magnetic induc-
tion B within the magnet is uniform or (in the gradient field case) varies linearly with
distance x from the optic axis. More generally, the induction might vary according to
B(x) = B(0)[1 − n(x/R) − m(x/R)
2
+···] (2.19)
where the coefficients n, m, ...introduce multipole components in the focusing. In
a gradient field spectrometer the value of n depends on the angle between the pole-
faces, which controls first-order focusing in the x- and y-directions, as an alternative
to tilting the entrance and exit faces. Likewise, a sextupole component (dependent
on m) could be deliberately added to control s econd-order aberrations (Crewe and
Scaduto, 1982). However, the focusing properties are quite sensitive to the values
of n and m; matrix calculations suggest that changing m by two parts in 10
−6
will
degrade the energy resolution by 1 eV, for γ = 10 mrad (Egerton, 1980b). Therefore