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Dynamical Theory of X-Ray Diffraction$
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André Authier

Print publication date: 2003

Print ISBN-13: 9780198528920

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780198528920.001.0001

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Ray tracing in perfect crystals

Ray tracing in perfect crystals

(p.304) 12 Ray tracing in perfect crystals
Dynamical Theory of X-Ray Diffraction


Oxford University Press

This chapter describes the propagation of wavefields inside the crystal close to the Bragg angle. It shows that the direction of propagation of packets of wavefields as obtained by their group velocity is identical to that of the Poynting vector. The geometrical properties of wavefields trajectories (ray tracing) within the Borrmann triangle are determined and the intensity distribution along the base of the Borrmann triangle is calculated. A detailed account of the experimental observation of the double refraction of the X-ray wavefields at the Bragg angle is given. The propagation of wavefields in finite crystals giving rise to partial reflections and interference effects is then described. The Bragg–Laue, Bragg–Bragg, and Laue–Bragg geometries are successively considered, and the formation of the Borrmann–Lehmann fringes in the latter case analyzed. In the last section, the coherence properties of X-ray sources are discussed.

Keywords:   group velocity, wave packets, Poynting vector, ray tracing, Borrmann triangle, double refraction, Bragg–Laue geometry, Bragg–Bragg geometry, Laue–Bragg geometry, Borrmann–Lehmann fringes

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