Chemistry Reference
In-Depth Information
Figure1.37.
Dispersion of X-rays by refraction at a plane-parallel plate or a“rectangular prism,”
respectively. The incident polychromatic beam with several different photon energies strikes a
silicon wafer plate at a fixed glancing angle
α
1
. The beam is reflected at the same angle with a small
intensity of only about 1% in the range of 0.1
°
to 0.2
°
as is indicated by a dashed line. In addition, the
beam is refracted under exit angles
α
2
dependent on respective photon energies,
E
2,
with an
intensity of about 99% (after Ref. [78]). In a horizontal distance
x
dependent on
α
2
and
E
2
, all the
refracted beams leave the silicon plate at the original
α
1
. The exit beam in total is parallel to the
incident primary beam but is shifted to the right in dependency of the energy
E
2
. If the wafer has a
thickness of 0.5 mm the parallel shift is of the order of several 10 cm. A vertical shift of about some
10
μ
m can be observed if the wafer is cut in a distance of 10 mm.
demonstrated in Figure 1.32b.
6
For glancing angles below the critical angle of
total reflection
α
1
<
α
crit
, there is no refracted beam but only the reflected beam
with an intensity of nearly 100%.
The glancing angle of the refracted exit beam
α
2
for a given incident glancing
angle
α
1
can be calculated in accord with Snell's law. We find the approximation
for the refractive index of a substance [78,81,82]:
α
1
2
α
2
2
n
2
1
(1.81)
Comparison with Equation 1.67 leads to
q
α
1
α
2
λ
2
λ
cut
(1.82)
α
crit
6
The wavelength of the refracted beam is increased negligibly by 1/
n
2
; that is, by a factor smaller
than 1.0005 for silicon or quartz glass.
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