International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

International Tables for Crystallography (2006). Vol. C, ch. 2.7, pp. 120-121

Section 2.7.4.2. Incident-beam monochromatization

A. R. Langa

aH. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, England

2.7.4.2. Incident-beam monochromatization

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In order to achieve extremely small beam divergences and wavelength pass bands (dλ/λ), and, in particular, to suppress transmission of harmonic wavelengths, arrangements much more complicated than the double-crystal systems shown in Figs. 2.7.3.1[link] and 2.7.3.3[link] have been applied in synchrotron-radiation topography. The properties of monochromator crystals are discussed in Section 4.2.5[link] . In synchrotron-radiation topographic applications, the majority of monochromators are constructed from perfect silicon, with occasional use of germanium. Damage-free surfaces of optical quality can be prepared in any orientation on silicon, and smooth-walled channels can be milled into silicon monoliths to produce multireflection devices. First, for simpler monochromatization systems, one possibility is to set up a monochromator crystal oriented for Bragg reflection with asymmetry [b\gg1] (i.e. giving [W_{\rm out}/W_{\rm in}\ll1)] to produce a narrow monochromatic beam with which section topographs can be taken (Mai, Mardix & Lang, 1980[link]). The standard [+\;-] double-crystal topography arrangement is frequently used with synchrotron sources, the experimental procedure being as described in Section 2.7.3[link] and benefiting from the small divergence of the incident beam due to remoteness of the source. An example of a more refined angular probe is that obtainable by employing a pair of silicon crystals in [+\,+] setting to prepare the beam incident on the specimen crystal, the three crystals together forming a [+\,+\,-] arrangement (Ishikawa, Kitano & Matsui, 1985[link]). The first mono­chromator is oriented for asymmetric 111 Bragg reflection, the second for highly asymmetric [55\bar3] reflection ([W_{\rm out}/W_{\rm in}=64] at λ = 0.12 nm), resulting in a divergence of only [0.5\times10^{-6}] in the beam impinging on the specimen.

Multireflection systems, some of which were proposed by Du Mond (1937[link]) but not at that time realizable, have become a practicality through the advent of perfect silicon and germanium. When multiple reflection occurs between the walls of a channel cut in a perfect crystal, the tails of the curve of angular dependence of reflection intensity can be greatly attenuated without much loss of reflectivity at the peak of the curve (Bonse & Hart, 1965a[link]). Beaumont & Hart (1974[link]) described combinations of such `channel-cut' monochromators that were suitable for use with synchrotron sources. One combination, consisting of a pair of contra-rotating channel-cut crystals, with each channel acting as a pair of reflecting surfaces in symmetrical [+\;-] setting, has found much favour as a monochromatizing device producing neither angular deviation nor spatial displacement of the final beam, whatever the wavelength it is set to pass. The properties of monoliths with one or more channels and employing two or more asymmetric reflections in succession have been analysed by Kikuta & Kohra (1970[link]), Kikuta (1971[link]), and Matsushita, Kikuta & Kohra (1971[link]).

Symmetric channel-cut monochromators in perfect undistorted crystals transmit harmonic reflections. Several approaches to the problem of harmonic elimination may be taken, such as one of the following procedures (or possibly more than one in combination).

  • (1) Using crystals of slightly different interplanar spacing (e.g. silicon and germanium) in the + − setting, which then becomes slightly dispersive (Bonse, Materlik & Schröder, 1976[link]; Bauspiess, Bonse, Graeff & Rauch, 1977[link]).

  • (2) Laue case (transmission) followed by Bragg case (reflection), with deliberate slight misorientation between the diffracting elements (Materlik & Kostroun, 1980[link]).

  • (3) Asymmetric reflection in non-parallel channel walls in a monolith (Hashizume, 1983a[link], b[link]).

  • (4) Misorientating a multiply reflecting channel, either one wall with respect to the opposite wall, or one length segment with respect to a following length segment (Hart & Rodrigues, 1978[link]; Bonse, Olthoff-Münter & Rumpf, 1983[link]; Hart, Rodrigues & Siddons, 1984[link]).

For X-ray topographic applications, it is very desirable to have a spatially wide beam issuing from the multiply reflecting device. This is achieved, together with small angular divergence and spectral window, and without need of mechanical bending, in a monolith design by Hashizume, though it lacks wavelength tunability (Petroff, Sauvage, Riglet & Hashizume, 1980[link]). The configuration of reflecting surfaces of this monolith is shown in Fig. 2.7.4.1[link]. Reflection occurs in succession at surfaces 1, 2, and 3. The monochromator characteristics are listed in Table 2.7.4.1[link]. The wavelength is very suitable in many topographic applications, and this design has proved to be an effective beam conditioner for use in synchrotron-radiation `plane-wave' topography.

Table 2.7.4.1| top | pdf |
Monolithic monochromator for plane-wave synchrotron-radiation topography

Reflection 1 333
Reflection 2 [\bar131]
Reflection 3 [1\bar3\bar1]
Output wavelength 0.12378 nm
Spectral pass band, dλ/λ [\sim7\times10^{-6}]
Angular divergence of exit beam [\sim1.4\times10^{-6}]
Size of exit beam [15\times15] mm
[Figure 2.7.4.1]

Figure 2.7.4.1 | top | pdf |

Monolithic multiply reflecting monochromator for plane-wave topography.

References

Bauspiess, W., Bonse, U., Graeff, W. & Rauch, H. (1977). A bicrystal monochromator of moderate wavelength resolution for use with X-rays or thermal neutrons. J. Appl. Cryst. 10, 338–343.
Beaumont, J. H. & Hart, M. (1974). Multiple Bragg reflection monochromators for synchrotron X radiation. J. Phys. E, 7, 823–829.
Bonse, U. & Hart, M. (1965a). Tailless X-ray single-crystal reflection curves obtained by multiple reflection. Appl. Phys. Lett. 7, 238–240.
Bonse, U., Materlik, G. & Schröder, W. (1976). Perfect-crystal monochromators for synchrotron X-radiation. J. Appl. Cryst. 9, 233–230.
Bonse, U., Olthoff-Münter, K. & Rumpf, A. (1983). Monolithic double-grooved-crystal monochromators with tunable harmonic suppression for neutrons and X-rays. J. Appl. Cryst. 16, 524–531.
Du Mond, J. W. M. (1937). Theory of the use of more than two successive X-ray crystal reflections to obtain increased resolving power. Phys. Rev. 52, 872–883.
Hart, M. & Rodrigues, A. R. D. (1978). Harmonic-free single-crystal monochromators for neutrons and X-rays. J. Appl. Cryst. 11, 248–253.
Hart, M., Rodrigues, A. R. D. & Siddons, D. P. (1984). Adjustable resolution Bragg reflection systems. Acta Cryst. A40, 502–507.
Hashizume, H. (1983a). Asymmetrically grooved monolithic crystal monochromators for suppression of harmonics in synchrotron X-radiation. J. Appl. Cryst. 16, 420–427.
Hashizume, H. (1983b). Asymmetrically grooved monolithic crystal monochromators for suppression of harmonics in synchrotron X-radiation: erratum. J. Appl. Cryst. 16, 648.
Ishikawa, T., Kitano, T. & Matsui, J. (1985). Synchrotron plane wave X-ray topography of GaAs with a separate (+, +) monochro-collimator. Jpn. J. Appl. Phys. Part 2, 24, L968–L971.
Kikuta, S. (1971). X-ray crystal collimators using successive asymmetric diffractions and their applications to measurements of diffraction curves. II. Type I collimator. J. Phys. Soc. Jpn, 30, 222–227.
Kikuta, S. & Kohra, K. (1970). X-ray crystal collimators using successive asymmetric diffractions and their applications to measurements of diffraction curves. I. General considerations on collimators. J. Phys. Soc. Jpn, 29, 1322–1328.
Mai, Z.-H., Mardix, S. & Lang, A. R. (1980). A high-resolution section topograph technique applicable to synchrotron radiation sources. J. Appl. Cryst. 13, 180–187.
Materlik, G. & Kostroun, V. O. (1980). Monolithic crystal monochromators for synchrotron radiation with order sorting and polarising properties. Rev. Sci. Instrum. 51, 86–94.
Matsushita, T., Kikuta, S. & Kohra, K. (1971). X-ray crystal collimators using successive asymmetric diffractions and their applications to measurements of diffraction curves. III. Type II collimator. J. Phys. Soc. Jpn, 30, 1136–1144.
Petroff, J. F., Sauvage, M., Riglet, P. & Hashizume, H. (1980). Synchrotron-radiation plane-wave topography. I. Application to misfit dislocation imaging in III–V heterojunctions. Philos. Mag. A42, 319–338.








































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