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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 slightly deformed crystals

Ray tracing in slightly deformed crystals

(p.355) 13 Ray tracing in slightly deformed crystals
Dynamical Theory of X-Ray Diffraction


Oxford University Press

This chapter is devoted to the propagation of X-ray wavefields in slightly deformed crystals where the deformation is small enough for the notions of dispersion surface and wavefields to be locally valid. A local reciprocal-lattice vector and local effective misorientation are defined. The trajectories of the wavefields (ray tracing) are determined using the Eikonal approximation. The case of a constant strain gradient is considered in detail and it is shown that the ray trajectories are bent, giving rise to the mirage effect; both the transmission and reflection geometries are considered. The diffracted intensities are calculated for an incident plane wave and an incident spherical wave. Shape of the Pendellösung fringes in a deformed crystal is discussed.

Keywords:   deformed crystals, constant strain gradient, ray tracing, effective misorientation, Eikonal approximation, plane waves, spherical waves, mirage effect

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