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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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Elementary dynamical theory

Elementary dynamical theory

Chapter:
4 Elementary dynamical theory
Source:
Dynamical Theory of X-Ray Diffraction
Author(s):

ANDRÉ AUTHIER

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198528920.003.0004

This chapter presents the basic properties of dynamical diffraction in an elementary way. The relationship with the band theory of solids is explained. The fundamental equations of dynamical theory are given for scalar waves as a simplification; the solutions of the propagation equation are then derived for an incident plane wave in the 2-beam case; and the amplitude ratio between reflected and refracted waves deduced. The notions of wavefields, dispersion surface, and tie points are introduced. Two experimental set-ups are considered: transmission and reflection geometries. The boundary conditions at the entrance surface of the crystal are expressed in each case and the intensities of the refracted and reflected waves calculated as well as the anomalous absorption coefficient, due to the Borrmann effect, the Pendellösung interference fringe pattern and the integrated intensity. It is shown that the geometrical diffraction constitutes a limit of dynamical diffraction by small crystals. At the end of the chapter dynamic diffraction by quasicrystals is considered.

Keywords:   dynamical diffraction, wavefields, dispersion surface, anomalous absorption, transmission geometry, reflection geometry, integrated intensity, quasicrystals

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