Chemistry Reference
In-Depth Information
1) where 1 means the first order of reflection, which is the
strongest one and which is usually chosen. The minus sign means the counter
reflection of the second crystal. If a certain photon energy has to be selected
from the total spectrum, the glancing angle
Θ
has to be set in accord with
Bragg's law of Equation 1.62. This is usually done by simple motions of both
crystals with the aim of a fixed parallel exit beam [36].
The simplest way is to rotate the first crystal anticlockwise while shifting the
second crystal with a distance
y
and rotating it simultaneously with the first one
but clockwise. The distance
y
is given by the relationship
crystals is called (1,
z
tan 2
θ
y
(3.14)
where
z
is the vertical distance of both crystals (see Figure 3.12a). When
Θ
is
varied between 5
°
and 45
°
and
z
is chosen to be 3 cm the distance
y
has to be
reduced from 17 to 0 cm.
Another simple way to get a fixed emergent beam is to rotate crystals A and
B individually as mentioned beforehand by the Bragg angle
Θ
and to rotate
them additionally and jointly around the center of its connecting line AB with
constant distance
z
by an angle
χ
(see Figure 3.12b). The relation between
Θ
and
χ
is not quite easy:
cos
χ
1
tan
θ
(3.15)
sin
χ
1
=
tan 2
θ
However, it can be approximated by a linear function for
Θ
and
χ
in
°
:
χ
67
:
5
°
1
:
5
θ
(3.16)
It may be mentioned that the adjustment of the arrangements is somewhat
difficult; however, the setting of angles is no problem since all motions of
rotation and shifting are computer-controlled. Furthermore, it may be under-
lined that the illuminated spot is fixed in the first case, but shifted by some
millimeters along both crystals in the second case.
The spectral resolution of a DCM can be determined by rotating only the
second crystal and recording the X-ray intensity versus the glancing angle. This
so-called rocking curve (which looks like a Lorentzian profile) shows a width
δ
Θ
,
which is determined by the structure of a nonideal Bragg crystal. It is usually built
of small crystallites that are not all ideally parallel but somewhat tilted with
respect to each other (see Section 1.5.2). The spectral resolution or mono-
chromaticity expressed by the figure of merit
E
/
Δ
E
is determined by the ratio
E
Δ
E
tan
θ
2
δθ
(3.17)
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