Modification of specularly reflected X-ray intensity by grazing incidence coplanar Bragg-case diffraction

Abstract

The intensity of the specularly reflected X-ray beam is investigated in the case of grazing incidence simultaneously satisfying a coplanar Bragg-case diffraction. Fresnel's formula and the extended dynamical theory of X-ray diffraction give identical results if the specular reflection is not influenced by diffraction. The modification of the specular intensity by simultaneous diffraction can be described by using an extended dynamical theory. This intensity modulation of the specular beam is calculated and experimentally verified by measurements with synchrotron radiation in the cases of strong and weak absorption. The results can be interpreted as a variation of the refractive index by simultaneous diffraction. Die Intensitat des spiegelnd reflektierten Rontgenstrahls wird fur den Fall streifender Inzidenz bei gleichzeitiger Erfullung einer koplanaren Bragg-Beugung untersucht. Die Fresnelschen Formeln und die erweiterte dynamische Theorie der Rontgenbeugung ergeben identische Ergebnisse, wenn die spiegelnde Reflexion durch Beugung nicht beeinfluBt wird. Die Modifizierung der gespiegelten Intensitat durch gleichzeitige Beugung la5t sich mit Hilfe einer erweiterten dynamischen Theorie beschreiben. Diese Intensitatsmodulation des gespiegelten Strahls wird berechnet und experimentell durch Messungen mit Synchrotronstrahlung fur die Falle starker und schwacher Absorption verifiziert. Die Ergebnisse konnen als h d e r u n g des Brechungsindex durch gleichzeitige Beugung interpretiert werden.

Transformation of the angular-dependent form of X-ray diffraction into the photon-energy-dependent form for grazing incidence

“…Neglecting second-and higher-order terms of Ak and A* in the serious expansion of the functions in (4) to (7), (8) leads to where I n the next approximation also the dynamical deviation from Bragg's law can be neglected, then (9) can be written in the well-known form…”

“…The transformation of an energy scale belonging to a diffraction pattern measured with tunable synchrotron radiation into an angular scale will be demonstrated for the example given in [9]: the (55i) Bragg reflection of germanium ( a = 0.56574 nm) with A [nm] 12.393/3 [keV]. 6, = 43.468" is equivalent to E = 11.370 keV.…”

Asymmetric skew X-ray diffraction at fixed incidence angle: application to semiconductor nano-objects

“…Therefore, the weak scattering signal from the nano-objects often becomes indistinguishable, especially in the close vicinity of the Bragg peaks from the substrate or the buffer layer (Krause et al, 2014). Certainly, for selected reflections and X-ray energies, coplanar diffraction could also be realized under grazing-incidence conditions (Hö che et al, 1988;Rhan et al, 1993;Kimura et al, 1994;Holý et al, 1995), resulting in enhanced diffraction signals from the surface structures. However, the coplanar scattering geometry has the intrinsic drawback that the angle of incidence changes during collection of the reciprocal-space map.…”