Tables for
Volume H
Powder diffraction
Edited by C. J. Gilmore, J. A. Kaduk and H. Schenk

International Tables for Crystallography (2018). Vol. H, ch. 2.1, pp. 43-44

Section Reflective X-ray optics

A. Kerna*

aBruker AXS, Östliche Rheinbrückenstrasse 49, Karlsruhe 76187, Germany
Correspondence e-mail: Reflective X-ray optics

| top | pdf | Multilayer mirrors

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Multilayer mirrors used in laboratory X-ray diffractometers are efficient beam conditioners, using total reflection as well as Bragg reflection on inner interfaces of a multilayer structure to modify beam divergence, cross-section size, shape and – to some extent – spectral bandwidth. A comprehensive description of current mirror designs and important mirror properties is found in the VDI/VDE Guideline 5575 Part 4 (2011[link]).

Multilayer mirrors consist of a multilayer coating deposited on a flat or curved substrate. The imaging characteristics are mostly determined by the contour of the mirror surface as defined by the substrate surface. The most common contours include planes, ellipsoids, paraboloids, elliptic cylinders or parabolic cylinders. The spectral reflection properties are determined by the coating, which may consist of some 10 up to 1000 alternating layers of amorphous low-density (`spacer') and high-density (`reflector') materials, with a period of a few nanometres. The first curved mirrors were produced by depositing the multilayers on a flat substrate that was subsequently bent to the desired contour, yielding typical r.m.s. slope errors of about 15 arcsec. By using prefigured substrates with r.m.s. slope errors below 1.7 arcsec, significantly improved reflectivity and lower beam divergence are obtained. Laterally graded multilayer mirrors (so-called `Göbel mirrors') have a layer thickness gradient parallel to the surface (Schuster & Göbel, 1996[link]), which, when combined with a planar, parabolic or elliptic substrate contour, produce a divergent, parallel or focusing beam. Fig. 2.1.19[link] illustrates graded multilayer mirrors for parallelization and focusing in the plane of diffraction.

[Figure 2.1.19]

Figure 2.1.19 | top | pdf |

Schematic of graded multilayer mirrors. (a) Parabolic mirror for parallelization of a divergent beam, or, if reversed, focusing of a parallel beam. In the latter case the mirror will also filter some specimen fluorescence. (b) Elliptical mirror for focusing of a divergent beam.

For beam conditioning in two perpendicular directions, two perpendicularly oriented curved mirrors may be used, as illustrated in Fig. 2.1.20[link]. In the Kirkpatrick–Baez scheme (Kirk­patrick & Baez, 1948[link]), two mirrors are cross-coupled as shown in Fig. 2.1.20[link](a). This setup has some issues related to the inherently different capture angles and magnification of both mirrors, resulting in less flux from smaller sources and in different divergences in both directions for elliptical mirrors. The Montel optics (Montel, 1957[link]) shown in Fig. 2.1.20[link](b) overcome these issues by arranging both mirrors in a `side-by-side' configuration.

[Figure 2.1.20]

Figure 2.1.20 | top | pdf |

Examples for orthogonally positioned curved mirrors for beam conditioning. (a) Kirkpatrick–Baez scheme employing two parabolic mirrors to create a parallel beam, (b) Montel optics employing two elliptical mirrors side-by-side to create a focusing beam.

Mirrors are available for all characteristic wavelengths used in laboratory X-ray powder diffractometers. A wealth of different materials are being used as double layers (reflector/spacer), including but not limited to W/Si, W/B4C, Ni/C, Ru/B4C, Ti/B4C, V/B4C, Cr/B4C and Mo/B4C. The double-layer materials may be selected according to the energies of their absorption edges to make the mirror act as a filter as well. While none of these mirrors is strictly speaking a monochromator, appropriate selection of the double-layer materials, depending on the wavelength used, will allow monochromatization of the radiation to Kα while Kβ and Bremsstrahlung are suppressed.

Within the past two decades mirror systems have become invaluable for all applications requiring a small and/or highly parallel beam. In particular, coupling of a parallel-beam mirror with multiple-reflection channel-cut monochromators allows the use of a wider solid-angle range of the X-ray source and a gain of nearly two orders of magnitude in intensity (Schuster & Göbel, 1995[link]). For applications requiring ideal powders, however, too-small as well as too-parallel beams may result in too small a number of diffracting crystallites, which will generally reduce the diffracted intensity, and may additionally lead to particle statistics errors (see also Section[link]).

Today, advanced sputtering techniques allow the fabrication of a wealth of different multilayer optics with virtually arbitrary beam divergences to generate focusing, parallel and divergent beams, for both point- and line-focus applications. The most comprehensive overview of currently available mirrors and up-to-date specifications will be found in manufacturers' brochures. Capillaries

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X-ray capillary optics are finding increasing use in applications where a small focused beam with high intensity is required. Their design, important properties and applications are discussed by e.g. Bilderback (2003[link]), He (2009[link]), and the VDI/VDE Guideline 5575 Part 3 (2011[link]).

X-ray capillary optics employ total external reflection by the inner surface of hollow glass tubes to guide and shape X-ray radiation. For incidence angles lower than the critical angle of total reflection the X-ray radiation is guided through the optics at very low losses. The transmission efficiency depends upon the X-ray energy, the capillary materials, reflection surface smoothness, the number of reflections, the capillary inner diameter and the incident beam divergence, and is thus determined by the particular design of the given optics. Generally, the transmission efficiency decreases with increasing X-ray energy owing to the decreasing critical angle of total reflection. The role of X-ray capillary optics as energy filters is insignificant, therefore capillaries are usually used in combination with monochromatization devices such as metal filters, incident-beam graphite monochromators or graded multilayers. Gains in flux density of more than two orders of magnitude compared to pinhole systems have been reported. The most common X-ray capillary optics currently used in laboratory X-ray powder diffractometers can be categorized as either monocapillaries or polycapillaries.

Monocapillaries consist of ellipsoidal or paraboloidal capillaries for focusing or parallelizing X-rays by means of single or multiple total reflections, as illustrated in Fig. 2.1.21[link]. The exit-beam divergence is controlled by the capillary diameter and length as well as the critical angle of total reflection; typical spot sizes range from some 20 mm down to less than 1 µm. Single-reflection monocapillaries are achromatic and almost 100% efficient. Their most important limitations are figure slope errors limiting the spot size. Multi-reflection monocapillaries can have the smallest spot sizes, which do not depend on the source size. An important drawback is that the beam is smallest at the capillary tip. In order to obtain the smallest possible spot size the sample has to be positioned to within 10–100 times the diameter of the tip exit size, e.g. 10–100 µm for a capillary with a 1 µm tip exit size.

[Figure 2.1.21]

Figure 2.1.21 | top | pdf |

Schematic of monocapillary optics. (a) Elliptical and (b) parabolic monocapillary. S = source; F = focal point.

Polycapillaries (e.g. Kumakhov & Komarov, 1990[link]) are monolithic systems of micro-structured glass consisting of thousands up to several millions of channels, which are tapered at one or both ends to form desired beam profiles as illustrated in Fig. 2.1.22[link]. A single channel can efficiently turn an 8 keV beam by up to 30° by multiple total reflections. Polycapillaries can collect a very large solid angle up to 20°, resulting in very high intensity gains. Typical spot sizes range from some 20 mm down to about 10 µm and are energy dependent, getting larger at lower energies.

[Figure 2.1.22]

Figure 2.1.22 | top | pdf |

Schematic of polycapillary optics. (a) Focusing and (b) parallel-beam polycapillary. S = source; F = focal point.


Bilderback, D. H. (2003). Review of capillary X-ray optics from the 2nd International Capillary Optics Meeting. X-ray Spectrom. 32, 195–207.Google Scholar
He, B. B. (2009). Two-Dimensional X-ray Diffraction. New York: Wiley.Google Scholar
Kirkpatrick, P. & Baez, A. V. (1948). Formation of optical images by X-rays. J. Opt. Soc. Am. 38, 766–774.Google Scholar
Kumakhov, M. A. & Komarov, F. F. (1990). Multiple reflection from surface X-ray optics. Phys. Rep. 191, 289–350.Google Scholar
Montel, M. (1957). X-ray microscopy with catamegonic roof-shaped objective. In X-ray Microscopy and Microradiography, pp. 177–185. New York: Academic Press.Google Scholar
Schuster, M. & Göbel, H. (1995). Parallel-beam coupling into channel-cut monochromators using curved graded multilayers. J. Phys. D Appl. Phys. 28, A270–A275.Google Scholar
Schuster, M. & Göbel, H. (1996). Application of graded multilayer optics in X-ray diffraction. Adv. X-ray Anal. 39, 57–72.Google Scholar
VDI/VDE Guideline 5575 Part 3 (2011). X-ray Optical Systems: Capillary X-ray Lenses. Berlin: Beuth.Google Scholar
VDI/VDE Guideline 5575 Part 4 (2011). X-ray Optical Systems: X-ray Mirrors. Total Reflection Mirrors and Multilayer Mirrors. Berlin: Beuth.Google Scholar

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