Crystal truncation rod X-ray scattering: exact dynamical calculation

Abstract

A new method is presented for a calculation of the reciprocal-space distribution of X-ray diffracted intensity along a crystal truncation rod. In contrast to usual kinematical or dynamical approaches, the method is correct both in the reciprocal-lattice points and between them. In the method, the crystal is divided into a sequence of very thin slabs parallel to the surface; in contrast to the well known Darwin dynamical theory, the electron density in the slabs is constant along the surface normal. The diffracted intensity is calculated by a matrix formalism based on the Fresnel reflection and transmission coefficients. The method is applicable for any polarization of the primary beam and also in a noncoplanar scattering geometry.

Nanoscale characterization of bismuth telluride epitaxial layers by advanced X-ray analysis

“…The simple kinematic approach, which neglects refraction and rescattering events of diffracted photons, can be good enough for weak reflections and regions in between peaks, but strong peaks at lower angles and diffraction peaks from single-crystal substrates may require an approach accounting for the effects of refraction and rescattering. A similar situation is found in the investigation of surface structures by scanning crystal truncation rods (Caticha, 1994;Feidenhans'l, 1989;Kaganer, 2007;Holý & Fewster, 2008;Coelho et al, 2013). At the moment, these effects are accounted for in dynamical diffraction theories suitable for very crystalline materials.…”

“…There are a few fundamental differences between the approach summarized by equations (2) and the most similar approaches aimed at simulating the entire reflectivity curve from grazing to normal angles of incidence (Caticha, 1994;Holý & Fewster, 2008). Basically, here dynamical diffraction corrections due to photon rescattering have been solved in between any two atomic layers, independently of the stacking sequence, i.e.…”

A new theory for X-ray diffraction

“…Therefore the intensity contributions from within the critical angle are set to zero in the 'sinc' function and dynamical models, since this is the closest approximation without modelling the crystal shape. A more fundamental approach to the dynamical model based on the atomic positions and scattering factors, not requiring structure factors or Bragg angles, can yield the amplitudes by slicing the crystallite into very thin parallel lamellae ($0.001 nm) (Holý & Fewster, 2008). However, the calculation time is increased substantially and the results are essentially unchanged from those calculated here, unless the crystallites are very small, in which case the scattering is well represented by kinematical theory or the Debye formula (Debye, 1915).…”

Interfacial roughness of Fe3Si/GaAs(001) films studied by X‐ray crystal truncation rods

“…Several recent theoretical studies were devoted to X‐ray diffraction from surfaces and thin films at any point in reciprocal space and along an arbitrarily long scan 1–3. We have shown 1 that the multibeam dynamical and kinematical (extended by the distorted wave Born approximation, DWBA, when needed) calculations give coinciding results, except in the vicinity of Bragg reflections where the reflectivity is close to 1 and the kinematical theory fails.…”