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

TL;DR

This paper develops and verifies a generalized dynamical diffraction theory for multiple-beam X-ray diffraction in crystals, including numerical methods and experimental validation using synchrotron X-rays, with implications for protein crystallography.

Contribution

The paper introduces a Takagi-Taupin based n-beam dynamical diffraction theory, provides computational solutions, and experimentally verifies the theory for the first time.

Findings

Explicit verification of Ewald-Laue and Takagi-Taupin theories for n-beam cases

Development of numerical methods for solving n-beam diffraction equations

Experimental confirmation using synchrotron X-ray data

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.