Phase Resolved Dark-Field X-ray Microscopy

Abstract

This thesis presents dark-field x-ray microscopy (DFXM) as a tool for characterizing ferroelectric domain structures and investigates new approaches to the data analysis of DFXM images based on methods from computational, coherent microscopy. The underlying theory of DFXM is described and applied to study characteristic diffraction peak splitting due to coherent twinning in perovskite ferroelectrics. This constitutes the first quantitative comparison of DFXM measurements with theoretical predictions based on coherent twinning of ferroelectrics and thereby provides new evidence for the quantitativeness of DFXM.It is shown that using Fourier Ptychography (FP), the phase-profile of the x-ray beam in transmission- and Bragg-scattering experiments can be recovered. This is promising for the study of crystals containing inversion domain boundaries, that are visible to x-ray scattering in the phase of the scattered beam. Furthermore, images of the complex aperture-function of the objective lens can be acquired. The reconstructions do not succeed in improving the resolution of the images compared to the conventional data-analysis which is shown to be identical to a kind of differential phase contrast (DPC).Several experimental challenges are investigated both theoretically and experimentally. This includes thick-lens behavior of the applied CRL objective lenses, multiple x-ray scattering effects in the sample crystal, and partial coherence of the incident x-ray light. The role of these experimental sources of error are discussed both in relation to conventional DFXM as well as FP. Finally, a complete simulation of a DFXM experiment based on the propagation of coherent wave fronts and the Takagi-Taupin approach to dynamical scattering is presented. The simulation is compared to experiment and good agreement is found