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The Asymmetric Bragg Reflection and its Application in Double Diffractometry

Published online by Cambridge University Press:  06 March 2019

M. Renninger
M. Renninger*
Affiliation:
Kristallographisches Institut der Universität Marburg, Germany
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Abstract

Guided by the dispersion, surface of dynamical theory, we easily obtain evidence of the fact that in asymmetrical surface reflections (Bragg case) of X-rays at a perfect crystal, the angular widths of the incident and reflected beams are different from the same widths in the symmetrical Bragg case. The beam with the smaller glancing angle to the surface is angularly expanded, the other one, contracted (though in cross section, the former is contracted and the latter, expanded). Consequently, if the incident glancing angle is the smaller one (striping incidence, Vreftection), the angular width of the reflected beam is smaller than in the symmetric case (S-reflection), and that of the reflected section out of the primary beam is greater, and vice versa (striping emergence, if-reflection). At striping incidence, a contraction occurs, whereas at striping emergence, expansion of the angular reflection range occurs. These facts offer a number of possibilities for applying asymmetrical reflections to the well-known technique of the two crystal diffractometer—the author proposes the term “diffractometer” instead of the widely used “spectrometer”—in the (nv, −n)-position. These possibilities extend the efficiency of the double diffractometer with multiple effects, and some of them are given below: (1) Realization of rocking curves of extremely small angular width in the (nv, −nR)-position, and consequently increased sensibility of that width to lattice distortions, (2) Use of the extremely small angular width (or more strictly, the sharp θ-λ-coordination) of the beam emerging from a first crystal. This is in V-reflection for scanning the intrinsic diffraction pattern of the second crystal used in S- or V-reflection [(nv, −ns) or (nv, −nv) -position], (3) Increased steepness of the sides of the rocking curves using (nv, −nR) or (nv, −ns)-positions which allows double diffractometric topography (Bond-Andrus, Bonse-Kappler) of increased angular resolving power. (4) Repeated ^-reflections (eventually within a single crystal provided with a suitable groove) leading to further angular contraction of the resulting reflected beam and therefore further increased angular resolving power [(nv, −nv, nR, −nR)- and (nv, −nv, +nS)-positions]. Here the tails of the rocking curve are also suppressed by multiple reflection (Bonse-Hart).

Type
Research Article
Information
Advances in X-Ray Analysis , Volume 10: Fifteenth Annual Conference on Applications of X-ray Analysis, August 10-12, 1966 , 1966 , pp. 32 - 41
Copyright
Copyright © International Centre for Diffraction Data 1966

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References

1. Renninger, M., “Uberlegungen zur Interferenztheorie,” Z. Krist. 97: 95–106, 1937.Google Scholar
2. Zachanasen, W. H., Theory of X-Ray Diffiaction in Crystals, John Wiley & Sons, Inc., New York, 1945.Google Scholar
3. Bubakova, R., “Diffraction Pattern of Germanium (111)-Asymmetdcal Bragg Case,” Czech. J. Phys. B12: 776–783, 1962.Google Scholar
4. Reiminger, M., “Asymmetrkhe Eragg-Reflexion am Idealkristall zur Erhöhung des Doppelspektrometer-Auflösungsverraogens,” Z. Naturforsch. 16a: 1110–1111, 1961.Google Scholar
5. Renninger, M., “ Messungen zur Rontgenstahl-Optik des Idealkristalls, (I) Bestatigung der Darwin-Ewald-Prins-Kohler-Kurve,” Acta Cryst, 8: 597–606, 1955.Google Scholar
6. Kohia, K., “An Application of Asymmetric Reflection for Obtaining X-Ray Beams of Extremely Narrow Angular Spread,” J. Phys. Soc. Japan 17: 589–590, 1962.Google Scholar
7. Bond, W. L. and Andrus, J., “Structural Imperfections in Quartz Crystals,” Am. Mineralogist 37: 622–632, 1952.Google Scholar
8. Bonse, U. and Kappler, E., “X-Ray Recording of Distortion Field Round Isolated Dislocations in Germanium Single Crystals,” Z. Naturforsch. 13a: 348–349, 1958.Google Scholar
9. Renninger, M., “Doppeldiffraktometrische Transmissions-Topographie,” Z. Naturforsch. 19a: 783–787, 1964.Google Scholar
10. Renninger, M., “Beitrâge zur doppeldiffraktometrischen Kristall-Topographie mit Rontgenstrahlen: I. Methodik und Ergebnisse typischer Art,” Z. Angew. Phys. 19: 20–33, 1965; “II. Ein Si-Kristallstab mit bemerkenswerten Verlauf von Versetztmgen und Punktdefekt- Konaetrationschwankungen,” Z. Angem. Phys. 19: 34—35, 1965.Google Scholar