X-ray Takagi-Taupin dynamical theory generalized to n-beam diffraction cases.
A new X-ray dynamical diffraction theory that can deal with n-beam cases comprehensively (n in [3, 4, 6, 8, 12]) has been derived based on the Takagi-Taupin dynamical theory. The new theory takes into account correctly the effects of arbitrarily polarized incident X-rays and the polarization states of X-ray wavefields in a crystal. Furthermore, an arbitrary lattice displacement in the crystal can be dealt with. The new theory has a high symmetry and therefore can be written with one equation supposing that suffixes are taken in 2n ways, where the suffixes indicate ordinal numbers of waves and polarization states. This simplicity of the theory enables a computer program to solve the equations to be coded easily. A method to solve the theory numerically is also described. 'Six-beam X-ray section topographs' computer simulated based on the new theory are also presented.
Dynamical diffraction effect in a curved multi-plate crystal cavity.
A modified algorithm for X-ray dynamical diffraction theory is presented for curved boundary crystals and a detailed description of the numerical procedure is given. The simulated and experimental results both show an anomalous focusing behavior in a curved multi-plate crystal cavity of silicon under the (12,4,0) back-diffraction condition at a photon energy of 14.4388 keV. The focusing effects are analyzed, within the framework of the dynamical theory of X-ray diffraction, from the excitation of the dispersion surface and modification of the index of refraction with respect to the non-plane-parallel boundaries of a curved crystal cavity.
Elliptically Polarized X-Rays Produced by the σ and π Components of Linearly Polarized X-Rays in the Laue Case Dynamical Diffraction
Interference phenomena between the σ and π components of linearly polarized X-rays are studied in the Laue case dynamical diffraction. It is shown experimentally that the polarization characteristics of the diffracted X-rays from Si change clearly with thicknesses of the specimen and elliptically polarized X-rays are produced by phase differences between the σ and π components. Theoretical calculations also confirm the experimental results.