X-ray dynamical diffraction from single crystals with arbitrary shape and strain field: A universal approach to modeling

Abstract

The effects of dynamical diffraction in single crystals engender many unique diffraction phenomena that cannot be interpreted by the kinematical-diffraction theory, yet knowledge of them is vital to resolving a vast variety of scientific problems ranging from crystal optics to strain measurements in crystalline specimens. Although the fundamental dynamical-diffraction theory was established decades ago, modeling it remains a challenge in a general case wherein the crystal has complex boundaries and mixed diffraction geometries (Bragg or Laue). Here, we propose a universal approach for modeling x-ray dynamical diffraction from a single crystal with arbitrary shape and strain field that is based on the integral representation of the Takagi-Taupin equations. Using it, we can construct the solution iteratively via a converging series, independent of the diffraction geometry. Moreover, the integral equations offer additional insights into the diffraction physics that are not readily apparent in its differential counterparts. To demonstrate this approach, we studied the dynamical diffraction from a slab of single crystal with both Bragg and Laue diffraction excited on the entrance boundaries, a problem that is difficult to model by other methods. We also explored the mirage effect caused by the presence of a linear strain field and compared it to the Eikonal theory. Lastly, we derived a dynamical-diffraction equation correlating the structural properties of a particle to its far-field Bragg-diffraction pattern, shedding light on how dynamical diffraction affects these kinematical-diffraction-based inverse techniques for reconstructing the shape and the strain field.