X-ray multiple-beam (n-baem) dynamical diffraction theories, numerical methods to solve them and experimental verification by using the synchrotron X-rays

Abstract

Behavior of X-rays diffracted in a perfect or quasi-perfect crystal can be described by the dynamical theory of X-ray diffraction. Study on the two-beam cases in which only transmitted and one reflected X-ray beams are strong has a history of one hundred years. However, the population of researchers who study on the multiple-beam cases (n-beam cases) in which more than two beams are simultaneously strong is small. The present author has derived the Takagi-Taupin (T-T) dynamical theory that can be applied to the n-beam cases, coded the computer programs to solve it and experimentally verified them by using the synchrotron X-rays. The equivalence between the Ewald-Laue (E-L) and the T-T dynamical theories described by the Fourier transform also for the n-beam cases is explicitly verified in the present paper. Further, the methods of the computer simulations and the experiments are also described. Furthermore, a hypothesis concerning the too large values of R-factor in protein crystallography is also described. This might be extremely important in protein crystallography in the future.

35 pages, 20 figures. The present manuscript has been translated by the author for submission to arXiv from a review article published in Journal of the Japanese Society for Synchrotron Radiation Research (2020) 33 61-80 [in Japanese]