Monochromatisation
of Synchrotron Radiation

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• Introduction / General
• Two steps of monochromatisation
  • High-heat-load (HHL) monochromator
  • High-resolution monochromator (HRM)
    • Four-bounced Nested channel-cut
    • Two-bounced individual crystals
• Remarks (assymetry parameter)

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Due to the sharp nuclear levels (in the order of 10^-11…10^-8 eV) involved in the scattering process the x-rays interact only in a narrow energy band with the nuclei.

This means that the x-rays with an energy other than the resonance energy (table) penetrate the sample without resonant interaction (only Thomson scattering) and cause an enormous instantaneous background. This creates problems for the detector system and the electronics. Reducing this background while reducing the signal of interest only to a small amount is possible by manipulating the SR beam by x-ray optics, e.g. changing parameters like the energy bandwidth, angle, divergence or the size of the beam.

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Bragg diffraction

Using perfect single crystals, the energy at a specific angle of the reflected beam follows Bragg's law

2 d ·  sin(QB) =  n · l

(1)

where d is the lattice spacing of crystallographic planes relevant for the reflection, Q_B is the Bragg angle, which is defined as the angle between the incident beam and the lattice planes, l is the wavelength and n denotes the order of the reflection.

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With the derivative of Bragg's law the monochromatization of the radiation can be expressed as a function of

-    DE E   =    Dl l   =    Dd d   +  DQB  ctg(QB)

(2)

With an energy band of DE = 1.5 meV at the transition energy E = 14.413 keV of the allowed variation of the lattice constant [(Dd)/(d)] is determined by [(DE)/(E)]   »  10^-7.

Therefore,

• only perfect silicon crystals are applicable and
• externally induced perturbation such as vibrations, stresses, temperature gradients over the crystal or temperature instabilities have to be avoided.
  • Stress and vibrations can be avoided by fixing the crystals with an appropriate mechanical setup and crystal design.
  • The high power density of the radiation delivered by the undulator or wiggler leads to a high heat load
    on the first optical element in the beam.

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Two steps of monochromatization

are therefore necessary for NRS experiments:

• a high heat load monochromator (HHL) and
• a high resolution monochromator (HRM)
  that provides the meV energy resolution.

The figure above indicates the beam trace through the crystal monochromator systems: The high heat load monochromator (left side) selects an energy band of approximately 3 eV from the incident 300 eV broad energy band. The beam is further monochromatized to 6 meV or less by a high resolution monochromator.

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High heat-load (HHL) monochromator

The design of the high heat-load monochromator
is governed by the following demands:

• fixed exit
• short and long term stability
• high accuracy and resolution
• reliable energy defining element
• matching of the divergence of the source and
  the angular acceptance of the monochromator crystal

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The fixed exit monochromator of KOHZU consists of

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The KOHZU mechanics provides perfect

The rotation stage for the first crystal is mounted to a horizontal translation, whereas the rotation stage of the second crystal (which is more stable because of less heat load) is rigidly attached to a base plate. This improved the

of the monochromatized beam. Once the energy is adjusted with the second crystal, which is the more stable one, the first crystal is optimized for maximum intensity coming through the setup.

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A cryogenic liquid N₂ cooling system keeps both Si(111) crystals at a temperature of about 80 K, where silicon has a zero temperature expansion. Because of the cryogenic cooling, the monochromator operates at UHV conditions (10^-7 mbar). Due to the efficient cooling, the monochromator has no "transition time" after refill: it provides a proper flux at proper energy next minute after the beam is back to user mode.

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The high resolution
monochromators (HRM)

If perfect crystals are used, the energy resolution in the case of Bragg diffraction can be approximated by DE / E » Dq cot q_B, where Dq is the divergence of the incident beam (typically ~15 mrad at third generation synchrotron radiation sources).

One therefore attempts to achieve high energy resolution using reflections with large Bragg angles (i.e. large values of the Miller indices), for in this case cotq_B becomes small.

Bragg angle and width of the reflection for 14.4 keV radiation for often used crystal reflection

reflection	QB	DQB
[in Si]	[o]	[arcsec]
(1 1 1)	7.88	3.72
(4 2 2)	22.83	1.17
(12 2 2)	77.53	0.40
(9 7 5)	80.40	0.35

This choice has nevertheless a drawback:

For a symmetrically cut crystal, the angular acceptance of a reflection corresponds to its Darwin width, which becomes smaller as the Bragg angle increases (only when q_B goes above ~ 80^° it starts to increase again), so that the beam divergence that is accepted by the reflection is very small (typically < 1 mrad). The problem can be overcome if the beam divergence is previously reduced. This can be achieved by using an asymmetrically cut crystal (for details see below).

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Up to now four different energy resolutions at 14.413 keV with different fluxes were achieved at ESRF:

Parameters for different high resolution monochromators for 14.4 keV. DE denotes the energy resolution (FWHM) and DQ_B the calculated angular acceptance of the monochromator in arcsec. The flux was measured at a storage ring current of 90 mA [22].

	DE	crystal reflections			DQB	flux	reference
	[meV]				[arcsec]	[phot./s]
a	6.4	Si(4 2 2)	Si(12 2 2)		4.13	1.8 x 109
b	4.4	Si(4 2 2)	Si(9 7 5)		3.71	0.6 x 109
c	1.7	Si(9 7 5)	Si(9 7 5)		0.91	1.2 x 108
d	0.65	Ge(3 3 1)	Si(9 7 5)	Si(9 7 5)	1.84	1.1 x 108

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Scheme of different kinds of high resolution monochromators. b denotes the asymmetry factor for the different crystals. For setup a and b channel cuts are used, for setup c and d individual crystals. c provides a beam of about 38° exit angle and d close to horizontal.

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Four bounce nested
channel-cut HR Monochromators

So far nested monochromators have been used for NFS experiments with four successive reflections on two nested channel-cut crystals. This geometry provides

• high energy resolution (5 to 10 meV),
• large angular acceptance,
• high temperature and mechanical stability
• horizontal outgoing beam and
• easy handling compared to individual crystal setups.

• The asymmetric cut of the outer crystal (4 2 2) is tailored in a way that the angular acceptance DQ₁ of the crystal matches the angular divergence of the SR beam and the angular emittance DQ₂ of the crystal matches the angular acceptance of the inner channel cut. The illuminated area on the asymmetrically cut crystals is very large and consequently the crystals have to be large and their surfaces have to be perfect.
• The inner, high indexed [(12 2 2) or (9 7 5)] channel-cut crystal is mounted in a dispersive geometry relative to the outer one. This results in high energy resolution.

Both channel-cut crystals are mounted on a goniometer with two co-axial axes one sitting on the other. By this means one assured a compact design and reached high temperature and mechanical stability over the crystals. Furthermore, we benefit from the fact that only one relative angular measurement with high resolution and accuracy is necessary.

In order to ensure a good energy calibration of the system a linear encoder with a resolution of 10 nm which corresponds to 0.015 arcsec is used. The corresponding encoder resolutions are tabulated below:

energy res.	[meV]	6.4	4.4	1.7
encoder res.	[meV / step]	0.2108	0.1646	0.08814

For nuclear forward scattering (NFS) the desired energy band is in the range of 10^-6 eV... 10^-9 eV, depending on the magnitude of the hyperfine splitting. Since the monochromatization 'only' serves as background reduction, the nested monochromators are appropriate for this kind of experiment.

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Two bounced HR monochromators

The high energy resolution on the other hand was found to be necessary also for recording the energy dependence of inelastic excitations (NIS) in the sample. Those experiments demand even higher energy resolutions which have been achieved by cuts of larger asymmetry:

The whole setup is shrunk to a two-bounce monochromator adopting two asymmetric Si (9 7 5) reflections. Compared to channel-cuts it is much easier to polish individual crystals perfectly to obtain a higher throughput. On the other hand this makes the alignment of the following experimental setup difficult, because the beam exits the monochromator at an angle of about 38° to the horizontal plane. In order to compensate this deflection and to get a nearly horizontal exit a Ge (3 3 1) is added as a third reflector.

Furthermore the two Si (9 7 5) crystals are cut with higher asymmetry in order to achieve a better energy resolution (down to 0.65 meV at 14.4 keV with a flux of 1.1 x 10⁸ photons/s (at 90mA)). However, the flux of resonant quanta is substantially reduced compared to the four-bounce monochromators.

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About 15 different HRMs for various nuclear transitions and applications were built up.

The most frequently used cases are summarized in the following table.

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Remarks:

The asymmetry parameter

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Last modified 6/18/02 04:47 PM by Ernst Schreier