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.
X-ray four-quadrant diamond phase-retarder system to compensate for off-axis and chromatic aberrations.
An X-ray transmission-type double phase-retarder system that can compensate for off-axis aberration (phase-shift inhomogeneity due to angular divergence of incident X-rays) has been developed and its advantage over a conventional single transmission-type X-ray phase retarder was demonstrated. However, it was noticed that the transmission-type X-ray phase retarder suffers from not only off-axis aberration but also chromatic aberration (phase-shift inhomogeneity due to energy spread of incident X-rays). In this paper, a transmission-type X-ray four-quadrant phase-retarder system is proposed that can compensate for both off-axis and chromatic aberrations. The X-ray four-quadrant phase-retarder system is composed of four transmission-type X-ray phase retarders. The scattering planes of four phase-retarder diamond crystals are set to be inclined by 45 degree, 135 degree (= 45 degree + 90 degree), 225 degree (= 45 degree + 180 degree) and 315 degree (= 45 degree + 270 degree), respectively, with respect to the plane of incident polarization. Under the conditions of 7709 eV photon energy, 1.5 eV energy spread and 45" angular divergence (FWHM) of incident X-rays, the X-ray four-quadrant phase-retarder system created 0.98 degree of vertical-linear polarization from horizontal-linear polarization. This value was favorably compared to 0.89 and 0.96, which were obtained by the single and double phase-retarder systems, respectively. The principle of the X-ray four-quadrant phase-retarder system will be described together with its advantage over the single and double phase-retarder systems.
Polarization states of dynamically diffracted X‐ray beams
A phase difference between the coherent σ and π components of dynamically diffracted X-rays was observed in the Laue case. The incident X-ray beam was linearly polarized Cu Kα radiation. A Si single crystal was used to produce the phase difference. The Ge 333 reflexion was used to polarize the incident beam and also to examine the polarization state of the diffracted beam in the 220 Laue-case reflexion from a Si crystal. For comparison, the polarization state in the Bragg case was also analysed.