Monochromatization of the Hard X-ray Radiation
Patrik Vagovič
Foschungszentrum Karlsruhe GmbH, Institute fuer Synchrotron Strahlung, Karlsruhe, Germany
On the leave from
Institute for
Electrical Engineering of Slovak Academy of Sciences, Piešťany, Slovakia
Keywords: X-ray monochromators, DuMond diagrams, Backscatering,
Abstract
Nowadays experiments with high energy X-rays often requires probe beams with narrow energy bandwidth. The selection of the finite range of the wavelengths (energies) around given value of wavelength is called monochromatization. Because available synchrotron sources (bending magnets, undulators, wigglers …) of the hard X-ray radiation provides polychromatic beam (white beam) for many application there is a need to select only a small energy band. In the region of hard x-rays mainly absorption filters, X-ray mirrors crystal monochromators and multilayer monochromators are used. Filters and mirrors remove from the incoming spectrum only long or short wavelengths, and therefore are used as premonochromators. Highest energy resolution is achieved by the crystal monochromators. If there is no need for the very narrow wavelength band, multilayer monochromators are often employed. Aim of this lecture is to provide overview about basic principles of the monochromatization of the hard X-ray synchrotron radiation and optics which is utilized for this purpose.
Crystal Monochromators
Crystal monochromators play important role in the monochromatization of
the hard X-ray radiation. They usually consist of one or more successively
arranged diffractors mainly in Bragg geometry. Crystal monochromators are prepared from
perfect crystals such as Si, Ge and for description of their diffractive
properties the dynamical theory of the X-ray radiation is used [1]. Spectral
and angular properties of the one or more successfully arranged monochromators can
be visualized with very useful graphic tool called DuMond diagrams [2]. Using these
diagrams one can estimate width of the spectral range passed by the monochromator
as well as the input angular acceptance and the output angular divergence.
Figure 1 is showing the DuMond diagram for a single crystal monochromator.
|
Fig. 1
DuMond diagram. Point 1) represents the
planar electromagnetic wave, vertical line 2) represents the polychromatic
parallel radiation and vertical line represents the divergent monochromatic
radiation. The crystal function in this space is represented as a stripe 4). |
Fig.
2 Single crystal
monochromator in Bragg configuration. |
For monochromatization of hard X-rays multiple crystal arrangements are
utilized rather than single crystal monochromators. The basic multiple crystal
arrangements (figure 3) consists of the non-dispersive (+, -) and the dispersive
(+, +) configuration which properties are analyzed into details. The attention is
paid to the double crystal monochromator (DCM) in non-dispersive (+, -) arrangement,
which becomes a standard for hard X-ray monochromatization at synchrotrons. Possibilities
how to reject harmonics, to increase the resolution by detuning and more others
are explained. By utilizing asymmetry angles one can increase the acceptance or
increase the angular resolution or achieve the compression or the expansion [3,
4, 5] of the beam.
Fig. 3 Basic
coplanar double crystal monochromators arrangements, a) non-dispersive (+n, -n)
arrangement,
b)
dispersive (+n, +n) arrangement.
Successive diffractions, dispersive and non-dispersive, are possible to
achieve also in the one single crystal. This monochromators are monolithic [6, 7,
8] and have several advantages and also some disadvantages in comparison with
polylithic devices. For example the dispersive monolithic configuration is well
known as a channel-cut monochromator.
This monochromator has naturally adjusted diffractors and the output beam is
parallel with the input beam. But by using the channel-cut monochromator we are
losing some benefits of the polylithic non-dispersive arrangement. By combining
two channel-cut monochromators in the dispersive configuration one can obtain the
Bartels monochromator [9]. This monochromator combines properties of dispersive
and non-dispersive crystal configurations. Bartels monochromator becomes a
standard for laboratory X-ray sources.
For applications where very narrow energy band of the incoming radiation is required in the range of meV and sub meV, it is necessary to accommodate monochromators with higher reflection. There are several possibilities how to achieve sub meV resolution. One of them is to use crystal in so-called backscattering geometry where Bragg angles are close to π/2 [10]. Another way is to use dispersive or nested [11] configurations, with higher reflection, where Bragg angles do not need to be necessarily close to π/2.
References
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