Diploma Thesis - Erich Schmid Institute

X-ray Diffraction – Measurements and Alignment
In the present case, the high resolution monochromator was manufactured out of a
piece of germanium single crystal, where the two channel cut crystals are joined by a
spring. This significantly simplifies the usually complicated alignment procedure.
The cut through the two blocks was done by taking into account two different
scattering planes. In the first block (1 1 1) and ( 1 1 1 ) and in the second block
( 2 2 0) and (2 2 0) planes are involved. The basic idea is that two couples of
reflection with non parallel scattering vectors are being obtained in the same crystal
for some specific geometry and by inducing a small bending δ of the crystal, as can
be seen in figure 9.4. The monolithic design makes it not necessary to tilt the
alignment like it is done with Bartels monochromator, since the crystal cut is designed
to guarantee that the scattering plane in the first and the second block coincide within
a good accuracy.
Figure 9.4: Monolithic monochromator under small bending
The final wavelength, dispersion and divergence are of interest for the measurement.
A way to qualitatively evaluate these parameters can be found by using DuMond
diagrams for multiple diffractions. According to the dynamical theory of X-ray
diffraction, the reflectivity of a perfect crystal for a fixed wavelength is close to 100%
in a finite ∆α range of several seconds of arc. Thus the DuMond diagram of a perfect
crystal is a band of width ∆α in the λ−α space. In the DuMond diagram, shown in
figure 9.5, two bands of wavelengths for several diffractions are plotted, one for the
first block with asymmetric (1 1 1) reflection and one for the second block with
symmetric (2 2 0) reflection. The cross section of the DuMond diagram for two
crystals gives the wavelength dispersion and the divergence of the final X-ray beam.
For the high resolution monochromator a wavelength dispersion ∆λ / λ = 2·10 -4 and a
divergence of ∆α = 15,4 arcsec is obtained, by using CuKα X-ray radiation.
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