Phase of the transmitted wave in the dynamical theory and quasi-kinematical approximation

TL;DR

This paper introduces a quasi-kinematical approximation to describe the phase of transmitted x-ray beams in crystals, bridging the gap between dynamical and kinematical theories for thin crystals in ptychography.

Contribution

It develops a new quasi-kinematical theory that accurately models transmitted wave phase in crystals thinner than the extinction length, simplifying analysis beyond traditional kinematical limits.

Findings

The quasi-kinematical theory matches dynamical theory results for thin crystals.

It provides analytical expressions for phase variations in transmitted x-ray beams.

Applicable for crystal thicknesses below the extinction length.

Abstract

Variation of the phase of the beam transmitted through a crystalline material as a function of the rocking angle is a well known dynamical effect in x-ray scattering. Unfortunately, it is not so easy to measure directly these phase variations in a conventional scattering experiment. It was recently suggested that the transmitted phase can be directly measured in ptychography experiments performed on nanocrystal samples. Results of such experiment for different crystal thickness, reflections and incoming photon energies, in principle, can be fully described in the frame of dynamical theory. However, dynamical theory does not provide a simple analytical expression for the further analysis. We develop here quasi-kinematical theory approach that allows to describe correctly the phase of the transmitted beam for the crystal thickness less than extinction length that is beyond applicability of the conventional kinematical theory.