Chemistry Reference
In-Depth Information
where
λ
cut
is the longest wavelength of an X-ray beam that can be refracted at
the given incident angle. A beam with a wavelength that is still longer than
λ
cut
will not be refracted but totally reflected. For X-rays,
α
2
is somewhat smaller
than
α
1
and consequently the radicand is always positive.
Equation 1.82 can be transformed for photon energies of the refracted
beam:
E
cut
α
crit
E
2
q
α
1
(1.83)
α
2
where
E
cut
is the cutoff energy, which is the smallest possible photon energy of
a beam that can be refracted; a beam with an even smaller photon energy is
totally reflected. The product of
E
cut
and
α
crit
is constant for a specific material.
It is equal to
hc
0
p
2
C
m
and amounts to 1.778 for a silicon wafer if the energy is
given in keV and the angle is entered in degrees. The photon energy of the exit
beam is demonstrated in Figure 1.38 in dependence of the exit angle and four
fixed incident angles. The range of possible exit angles is between 0
°
and
α
1
and
the respective range of photon energies is between
E
crit
and
∞
. In all cases, the
photon energy of the incident beam
E
1
is only a little bit higher than that of the
exit beam
E
2
.
Hayashi
etal
. investigated the refraction of X-rays in silicon at grazing
incidence [78]. The authors turned a polychromatic beam of a Mo tube on a Si
Figure1.38.
Energy of photons
in
the refracted beam dependent on the respective exit angle. It is
provided that the incident beam strikes a silicon wafer at a fixed glancing angle of 0.125
°
, 0.150
°
,
0.175
°
, and 0.200
°
.
Search WWH ::
Custom Search