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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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Spherical-wave dynamical theory: Ii. Takagi’s theory

Spherical-wave dynamical theory: Ii. Takagi’s theory

Chapter:
(p.277) 11 Spherical-wave dynamical theory: Ii. Takagi’s theory
Source:
Dynamical Theory of X-Ray Diffraction
Author(s):

ANDRÉ AUTHIER

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198528920.003.0011

This chapter describes Takagi's dynamical theory of the diffraction of incident spherical waves. It considers the crystal wave to be developed as a sum of modulated waves. The fundamental equations are generalized as a set of partial differential equations (Takagi's equations). Their solutions for an incident spherical wave are first obtained by the method of integral equations for both the transmission and reflection geometries. The hyperbolic nature of Takagi's equations is shown and their solution derived using the method of Riemann functions for a point source located on the entrance surface or away from the incident surface. An appendix describes the properties of hyperbolic partial differential equations.

Keywords:   spherical wave, point sources, modulated waves, Takagi equations, hyperbolic equations, Riemann equations

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