Deterministic Bragg Coherent Diffraction Imaging

On the use of the scattering amplitude in coherent X-ray Bragg diffraction imaging

Lens-less imaging of crystals with coherent X-ray diffraction offers some unique possibilities for strain-field characterization. It relies on numerically retrieving the phase of the scattering amplitude from a crystal illuminated with coherent X-rays. In practice, the algorithms encode this amplitude as a discrete Fourier transform of an effective or Bragg electron density. This short article suggests a detailed route from the classical expression of the (continuous) scattering amplitude to this discrete function. The case of a heterogeneous incident field is specifically detailed. Six assumptions are listed and quantitatively discussed when no such analysis was found in the literature. Details are provided for two of them: the fact that the structure factor varies in the vicinity of the probed reciprocal lattice vector, and the polarization factor, which is heterogeneous along the measured diffraction patterns. With progress in X-ray sources, data acquisition and analysis, it is believed that some approximations will prove inappropriate in the near future.

Simulation of X-ray diffraction in a cylindrical crystal

Using the two-dimensional recurrence relations of X-ray dynamical diffraction, a numerical simulation of reflection and transmission intensity in a cylindrical crystal has been performed. It is shown that for crystals with a small radius Bragg diffraction is realized. For crystals of large radius, Bragg–Laue diffraction occurs, which is characterized by Bragg diffraction on the upper part of the crystal, as well as the presence of Pendellösung oscillations inside the cylindrical crystal. The reciprocal space maps of dynamical and kinematical diffraction have been calculated.

Three-Dimensional Imaging of Phase Ordering in an Fe-Al Alloy by Bragg Ptychography

We show three-dimensional images of phase ordering in a Fe_{55}Al_{45} alloy obtained by coherent x-ray diffraction Bragg ptychography. Fe-Al alloys display ordered phases where the atoms organize on sublattices resulting in the emergence of otherwise forbidden superlattice reflections. The degeneracy of the ordering results in antiphase domain boundaries that, in addition to the general lattice strain, provide phase shifts of the diffracted beam depending on the reflection. The reconstructed phase images can be separated into components originating from B2 phase domains and lattice strain by performing Bragg ptychography on both the (002) fundamental and the (001) superlattice reflections.

Applications of dynamical theory of X-ray diffraction by perfect crystals to reciprocal space mapping

The classical dynamical theory of X-ray diffraction is expanded to the special case of transversely restricted wavefronts of the incident and reflected waves. This approach allows one to simulate the two-dimensional coherently scattered intensity distribution centred around a particular reciprocal lattice vector in the so-called triple-crystal diffraction scheme. The effect of the diffractometer's instrumental function on X-ray diffraction data was studied.