Small-angle x-ray scattering under grazing incidence: The cross section in the distorted-wave Born approximation

1995 ◽  
Vol 52 (23) ◽  
pp. 16855-16863 ◽  
Author(s):  
M. Rauscher ◽  
T. Salditt ◽  
H. Spohn
Keyword(s):  
Cross Section ◽  
Small Angle ◽  
Born Approximation ◽  
Grazing Incidence ◽  
Distorted Wave ◽  
Distorted Wave Born Approximation ◽  
X Ray ◽  
X Ray Scattering ◽  
The Cross ◽  
Ray Scattering

Debye–Scherrer rings from block copolymer films with powder-like order

2011 ◽  
Vol 44 (2) ◽  
pp. 370-379 ◽  
Author(s):  
Peter Busch ◽  
Markus Rauscher ◽  
Jean-François Moulin ◽  
Peter Müller-Buschbaum
Keyword(s):  
Small Angle ◽  
Critical Angle ◽  
Grazing Incidence ◽  
Distorted Wave ◽  
Distorted Wave Born Approximation ◽  
X Ray ◽  
Copolymer Films ◽  
X Ray Scattering ◽  
Ring Shape ◽  
Neutron Time

The powder-like orientation of lamellar domains in thin films of the diblock copolymer polystyrene-block-poly(methyl methacrylate) is investigated using grazing-incidence small-angle X-ray scattering (GISAXS) and grazing-incidence small-angle neutron scattering (GISANS). Conventional monochromatic GISANS and GISAXS measurements are compared with neutron time-of-flight GISANS. For angles of incidence and exit larger than the critical angle of total external reflection of the polymer, Debye–Scherrer rings are observed. The position of the Debye–Scherrer rings is described quantitatively based on a reduced version of the distorted-wave Born approximation. A strong distortion of the ring shape is caused by refraction and reflections from the film interfaces. Close to the critical angle, the ring shape collapses into a banana shape.

Grazing-incidence small-angle X-ray scattering from thin polymer films with lamellar structures – the scattering cross section in the distorted-wave Born approximation

2006 ◽  
Vol 39 (3) ◽  
pp. 433-442 ◽  
Author(s):  
P. Busch ◽  
M. Rauscher ◽  
D.-M. Smilgies ◽  
D. Posselt ◽  
C. M. Papadakis
Keyword(s):  
Thin Films ◽  
Polymer Films ◽  
Small Angle ◽  
Born Approximation ◽  
Grazing Incidence ◽  
Thin Polymer Films ◽  
Distorted Wave ◽  
Distorted Wave Born Approximation ◽  
X Ray ◽  
Thin Polymer

Grazing-incidence small-angle X-ray or neutron scattering of thin polymer films reveals information about the ordering and preferential orientations of the phase-separated microdomains within the films. The grazing-incidence geometry enhances the surface sensitivity; however, the scattering has to be treated within the framework of the distorted-wave Born approximation. In this work, the case of thin films with lamellar mesostructure is studied, where the orientation of the lamellae is either perpendicular or parallel to the film interfaces. For perpendicular lamellae, Bragg rods are found, which are extended along the film normal, whereas for parallel lamellae, peaks along the film normal appear. The positions of the maxima present in the latter case are explained by accounting for refraction at the film surface and reflection at the film–substrate interface. The results are relevant for thin films of lamellar diblock copolymers.

scholarly journals Unwarping GISAXS data

IUCrJ ◽  
2018 ◽  
Vol 5 (6) ◽  
pp. 737-752 ◽  
Author(s):  
Jiliang Liu ◽  
Kevin G. Yager
Keyword(s):  
Born Approximation ◽  
Grazing Incidence ◽  
Initial Guess ◽  
Reciprocal Space ◽  
Scattering Data ◽  
Distorted Wave ◽  
Distorted Wave Born Approximation ◽  
X Ray ◽  
X Ray Scattering ◽  
Transmission And Reflection

Grazing-incidence small-angle X-ray scattering (GISAXS) is a powerful technique for measuring the nanostructure of coatings and thin films. However, GISAXS data are plagued by distortions that complicate data analysis. The detector image is a warped representation of reciprocal space because of refraction, and overlapping scattering patterns appear because of reflection. A method is presented to unwarp GISAXS data, recovering an estimate of the true undistorted scattering pattern. The method consists of first generating a guess for the structure of the reciprocal-space scattering by solving for a mutually consistent prediction from the transmission and reflection sub-components. This initial guess is then iteratively refined by fitting experimental GISAXS images at multiple incident angles, using the distorted-wave Born approximation (DWBA) to convert between reciprocal space and detector space. This method converges to a high-quality reconstruction for the undistorted scattering, as validated by comparing with grazing-transmission scattering data. This new method for unwarping GISAXS images will broaden the applicability of grazing-incidence techniques, allowing experimenters to inspect undistorted visualizations of their data and allowing a broader range of analysis methods to be applied to GI data.

A general model for estimating the ordering of mesoporous film by grazing incidence small angle X-ray scattering

2014 ◽  
Vol 115 (20) ◽  
pp. 204311 ◽  
Author(s):  
Nie Zhao ◽  
Chunming Yang ◽  
Qian Zhang ◽  
Xueming Lu ◽  
Yuzhu Wang ◽  
...  
Keyword(s):  
Small Angle ◽  
General Model ◽  
Grazing Incidence ◽  
X Ray ◽  
X Ray Scattering ◽  
Mesoporous Film ◽  
Ray Scattering

Grazing incidence small angle x-ray scattering from free-standing nanostructures

1999 ◽  
Vol 86 (12) ◽  
pp. 6763-6769 ◽  
Author(s):  
Markus Rauscher ◽  
Rogerio Paniago ◽  
Hartmut Metzger ◽  
Zoltan Kovats ◽  
Jan Domke ◽  
...  
Keyword(s):  
Small Angle ◽  
Grazing Incidence ◽  
Free Standing ◽  
X Ray ◽  
X Ray Scattering ◽  
Ray Scattering

Thermal quenching sample chamber for grazing incidence small angle x-ray scattering studies of polymer films

2007 ◽  
Vol 78 (11) ◽  
pp. 113910 ◽  
Author(s):  
M. A. Singh ◽  
M. N. Groves ◽  
M. S. Müller ◽  
I. J. Stahlbrand ◽  
D.-M. Smilgies
Keyword(s):  
Polymer Films ◽  
Small Angle ◽  
Thermal Quenching ◽  
Grazing Incidence ◽  
X Ray ◽  
X Ray Scattering ◽  
Sample Chamber ◽  
Ray Scattering

scholarly journals A grazing incidence small-angle x-ray scattering analysis on capped Ge nanodots in layer structures

2010 ◽  
Vol 22 (47) ◽  
pp. 474003 ◽  
Author(s):  
Hiroshi Okuda ◽  
Masayuki Kato ◽  
Keiji Kuno ◽  
Shojiro Ochiai ◽  
Noritaka Usami ◽  
...  
Keyword(s):  
Small Angle ◽  
Grazing Incidence ◽  
X Ray ◽  
X Ray Scattering ◽  
Layer Structures ◽  
Ray Scattering
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