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where
a
1
and
a
2
are horizontal distances. For small angles
α
1
and
α
2
, it can be
approximated by
w
2
a
1
Δ
α
a
2
α
2
(3.10)
This quantity is independent of
α
1
and only dependent on
α
2
and the total
distance in the denominator. Finally, the irradiated area of the first reflector
can be determined by the width
w
2
sin
α
2
sin
α
1
w
1
(3.11)
For an actual example, a Mo-tube may be chosen as the X-ray tube and quartz
glass as reflector material;
α
2
shall be set to 0.07
°
in order to ensure total reflection
at the sample carrier (recommended in Section 4.5.1),
α
1
may be set to 0.09
°
in
order to cut off the spectrum above 20 keV by means of the first reflector. The
signal intensity is optimized by close distances between the X-ray tube, the first
reflector, and the sample carrier. If the distances
a
1
and
a
2
are kept to a minimum
of 100 mm and 40 mm, respectively, the first reflector has to be raised by
h
1
=
49
μ
m and the X-ray focus lowered by about
h
0
=
143
μ
m. The X-ray beam has to be
limited to
t
=
24
μ
m in height, determining an aperture of
Δ
α
=
0.01
°
. In this case,
the first reflector is irradiated within a width of
w
1
=
16 mm while the second
reflector, that is, the sample carrier, is irradiated within a width
w
2
=
20 mm.
3.4.2SimpleMonochromators
For surface- and thin-layer analyses, intensity profiles have to be recorded that
are uniquely dependent on the glancing angle and not on the photon energy.
Consequently, considerable demands on the spectral purity have to be made.
The primary beam needs to be fairly monochromatic, which can be realized
neither by a low-pass filter nor a foil filter but only by a monochromator.
However, even trace analyses may profit from monochromatic excitation, as
already mentioned earlier. For such cases, the first reflector of Figure 3.9 must
be a natural crystal or a synthetic multilayer. Both types of crystals are used as
Bragg reflectors with a definite energy band selected at a particular angle of
reflection, as discussed in Section 2.1.2.
This angle should be set in accord with Equation 2.8. For a chosen photon
energy
E
in keV, the angle can be calculated by
0
:
620
Ed
α
arcsin
(3.12)
where
d
is the interplanar spacing (in nm) of the reflector in use. A lithium-
fluoride, LiF(200), or a graphite crystal, C(002), can be used; the latter should
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