# Propagation of X-rays in highly deformed crystals

# Propagation of X-rays in highly deformed crystals

This chapter concerns highly deformed crystals where the Eikonal approximation is no longer valid. An expression is given for the limit of validity of this approximation. Takagi's equations are extended so as to apply to highly deformed crystals. Their resolution is the discussed and the principle of their numerical integration in an inverted Borrmann triangle given. The ray concept is generalized to the case of strong deformations by noting that new wavefields are generated in the highly strained regions; this is known as the interbranch scattering effect. The last part of the chapter is devoted to an account of the statistical dynamical theories for highly imperfect crystals, with emphasis on Kato's statistical theories. Examples of experimental test of the dynamical theory are also given.

*Keywords:*
Eikonal approximation, strong deformations, deformed crystals, Takagi equations, Borrmann triangle, numerical integration, interbranch scattering, statistical dynamical theory

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