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

International Tables for Crystallography (2006). Vol. C, ch. 4.1, p. 189

Section 4.1.4. Special applications of X-rays, electrons, and neutrons

V. Valvodaa

aDepartment of Physics of Semiconductors, Faculty of Mathematics and Physics, Charles University, Ke Karlovu 5, 121 16 Praha 2, Czech Republic

4.1.4. Special applications of X-rays, electrons, and neutrons

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Special sources and/or special properties of these radiations are used in general crystallography.

4.1.4.1. X-rays, synchrotron radiation, and γ-rays

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X-ray beams from rotating-anode tubes are approximately one hundred times more intensive than those from normal X-ray tubes. Laser plasma X-ray sources yield intensive nanosecond pulses of the line spectrum of nearly electron-free ions in the X-ray region with a spectral breadth of [\Delta\lambda/\lambda\approx10^{-3}.] Several such pulses may be repeated per hour (Frankel & Forsyth, 1979[link]). Synchrotron radiation is characterized by a continuous spectrum of wavelengths, high spectral flux, high intensity, high brightness, extreme collimation, sharp time structure (pulses with 30–200 ps length emitted in ns intervals), and nearly 100% polarization in the orbital plane (Kunz, 1979[link]; Bonse, 1980[link]). Some of these properties are utilized in ordinary structure analysis: for example, fine tuning of the wavelength of synchrotron radiation for the solution of the phase problem by resonant scattering on chosen atomic species constituting the material under study. But these radiations also offer new advantages in other fields of crystallography, as, for example, in X-ray topography (Tanner & Bowen, 1980[link]), in time-resolving studies (Bordas, 1980[link]), in X-ray microscopy (Parsons, 1980[link]), in studies of local atomic arrangements by extended X-ray absorption fine structure (XAFS) investigations (Lee, Citrin, Eisenberger & Kincaid, 1981[link]) or studies of surface structures by X-ray photoemission spectroscopy (XPS) (Plummer & Eberhardt, 1982[link]), etc. γ-rays emitted by radioactive sources such as 198Au (t1/2 = 2.7 d), 153Sm (t1/2 = 46.8 h), 192Ir (t1/2 = 74.2 d) or 137Cs (t1/2 = 29.9 a) are characterized by short wavelengths (typically hundreds of Å), by narrow spectral breadth [(\Delta E\approx10^{-8}\ {\rm eV},\Delta\lambda/\lambda\approx10^{-6})] and by relatively low beam intensity (∼108–109 m−2 s−1). They are mainly used for studies of the mosaic structure of single crystals (Schneider, 1983[link]) or for the determination of charge density distribution (Hansen & Schneider, 1984[link]). The typical absorption length of ∼1–4 cm and the increase of the extinction length by a factor of about 50 compared with ordinary X-rays are advantages utilized in these experiments. γ-rays also find applications in magnetic structure studies and in the determination of gradients of electric fields by Mössbauer diffraction and spectroscopy (Kuz'min, Kolpakov & Zhdanov, 1966[link]).

For Compton scattering, see Sections 6.1.1[link] and 7.4.3[link] .

4.1.4.2. Electrons

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Low-energy electrons (10–200 eV) have wavelengths near 1 Å and a penetration of a few Å below the surface of a crystal. Low-energy electron diffraction (LEED) is thus used for the study of surface-layer structures (Ertl & Küppers, 1974[link]). High-energy electrons are also currently used in electron microscopy in materials science. Under certain conditions, images of lattice planes with a resolution of 2 Å or better can be obtained. Transmission electron microscopy is also used for reconstruction of the three-dimensional structure of biological objects (such as viruses), alternatively in combination with X-ray diffraction (de Rosier & Klug, 1968[link]).

4.1.4.3. Neutrons

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The most important application of neutron diffraction is found in studies of magnetic structures (Marshall & Lovesey, 1971[link]). The magnetic moment of neutrons is equal to 1.913 μN, where μN is the nuclear magneton, and neutrons have spin I = 1/2. They can thus interact with the magnetic moments of nuclei or with the magnetic moments of the electron shells with uncompensated spins. Changes in wavelength from 1 to 30 Å enable one to study non-uniformities of different sizes and structures of polymers and biological objects by the small-angle method. Inelastic scattering of neutrons is used for determining phonon-dispersion curves. Neutron topography and neutron texture diffraction can be utilized for the relatively large samples used in technological applications. The pulsed spallation neutron sources are used for high-resolution time-of-flight powder diffraction (Windsor, 1981[link]) or for time-resolved Laue diffraction.

References

Bonse, U. (1980). X-ray sources. Characterization of crystal growth defects by X-ray methods, edited by B. K. Tanner & D. K. Bowen, Chap. 11, pp. 298–319. New York: Plenum. [NATO Advanced Study Institute Series B63.]
Bordas, J. (1980). A synchrotron radiation camera and data acquisition system for time resolved X-ray scattering studies. J. Phys. E, 13, 938–944.
Ertl, G. & Küppers, J. (1974). Monographs in modern chemistry, Vol. 4. Energy electrons and surface chemistry, edited by H. F. Ebel, Chap. 9, pp. 129–192. Weinheim: Verlag Chemie.
Frankel, R. D. & Forsyth, J. M. (1979). Nanosecond X-ray diffraction from biological samples with a laser-produced plasma source. Science, 204, 622–624.
Hansen, N. K. & Schneider, J. R. (1984). Charge-density distribution of Be metal studied by γ-ray diffractometry. Phys. Rev. B, 29, 917–926.
Kunz, C. (1979). Editor. Topics in current physics, Vol. 10. Synchrotron radiation, techniques and applications. Berlin: Springer Verlag.
Kuz'min, R. N., Kolpakov, A. V. & Zhdanov, G. S. (1966). Rassejanie messbauerovskovo izlutschenija kristallami. Kristallografiya, 11, 511–519. [English translation: Sov. Phys. Crystallogr. (1967), 11, 457–465.]
Lee, P. A., Citrin, P. H., Eisenberger, P. & Kincaid, B. M. (1981). Extended X-ray absorption fine structure – its strengths and limitations as a structural tool. Rev. Mod. Phys. 53, 769–806.
Marshall, W. & Lovesey, S. W. (1971). Theory of thermal neutron scattering. Oxford: Clarendon Press.
Parsons, D. F. (1980). Editor. Ultrasoft X-ray microscopy: its application to biological and physical sciences. New York: New York Academy of Sciences.
Plummer, E. W. & Eberhardt, W. (1982). Advances in chemical physics, Vol. XLIX. Angle-resolved photoemission as a tool for the study of surfaces, edited by I. Prigogine & S. I. Rice. New York: John Wiley.
Rosier, D. J. de & Klug, A. (1968). Reconstruction of three dimensional structures from electron micrographs. Nature (London), 217, 130–134.
Schneider, J. R. (1983). Characterization of crystals by γ-ray and neutron diffraction methods. J. Cryst. Growth, 65, 660–671.
Tanner, B. K. & Bowen, D. K. (1980). Editors. Characterization of crystal growth defects by X-ray methods. NATO Advanced Study Institute Series B63. New York: Plenum.
Windsor, C. G. (1981). Pulsed neutron scattering. London: Taylor and Francis.








































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