# Elementary dynamical theory

# Elementary dynamical theory

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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