Analysis of randomly oriented structures by grazing-incidence small-angle neutron scattering

Denis Korolkov; Peter Busch; Lutz Willner; Emmanuel Kentzinger; Ulrich Rücker; Amitesh Paul; Henrich Frielinghaus; Thomas Brückel

doi:10.1107/S0021889812002324

Analysis of randomly oriented structures by grazing-incidence small-angle neutron scattering

Denis Korolkov^*, Peter Busch, Lutz Willner, Emmanuel Kentzinger, Ulrich Rücker, Amitesh Paul, Henrich Frielinghaus, Thomas Brückel

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

A formalism is presented which allows the quantitative evaluation of data from grazing-incidence small-angle neutron and X-ray scattering-GISANS and GISAXS-in the framework of the distorted wave Born approximation. While several aspects have been reported previously, this formalism combines solutions for scattering intensities in both reflection and transmission hemispheres, taking into account instrumental resolution effects. This formalism is applied to the case of GISANS from self-organized diblock copolymers, ordered in perpendicular lamellar structures on an Si wafer in randomly oriented short-range-ordered regions. The periodicity of D = 85 (9) nm found for deuterated polystyrene-polybutadiene of molecular weight M _w = 165 kg mol ^-1 and a molecular weight fraction of the deuterated polystyrene block of 52% is consistent with atomic force microscopy and specular neutron reflectivity results.

Original language	English
Pages (from-to)	245-254
Number of pages	10
Journal	Journal of Applied Crystallography
Volume	45
Issue number	2
DOIs	https://doi.org/10.1107/S0021889812002324
State	Published - 9 Feb 2012
Externally published	Yes

Keywords

distorted wave Born approximation
grazing-incidence small-angle neutron scattering
grazing-incidence small-angle X-ray scattering
random orientation

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title = "Analysis of randomly oriented structures by grazing-incidence small-angle neutron scattering",

abstract = "A formalism is presented which allows the quantitative evaluation of data from grazing-incidence small-angle neutron and X-ray scattering-GISANS and GISAXS-in the framework of the distorted wave Born approximation. While several aspects have been reported previously, this formalism combines solutions for scattering intensities in both reflection and transmission hemispheres, taking into account instrumental resolution effects. This formalism is applied to the case of GISANS from self-organized diblock copolymers, ordered in perpendicular lamellar structures on an Si wafer in randomly oriented short-range-ordered regions. The periodicity of D = 85 (9) nm found for deuterated polystyrene-polybutadiene of molecular weight M w = 165 kg mol -1 and a molecular weight fraction of the deuterated polystyrene block of 52% is consistent with atomic force microscopy and specular neutron reflectivity results.",

keywords = "distorted wave Born approximation, grazing-incidence small-angle neutron scattering, grazing-incidence small-angle X-ray scattering, random orientation",

author = "Denis Korolkov and Peter Busch and Lutz Willner and Emmanuel Kentzinger and Ulrich R{\"u}cker and Amitesh Paul and Henrich Frielinghaus and Thomas Br{\"u}ckel",

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Analysis of randomly oriented structures by grazing-incidence small-angle neutron scattering. / Korolkov, Denis; Busch, Peter; Willner, Lutz; Kentzinger, Emmanuel; Rücker, Ulrich; Paul, Amitesh; Frielinghaus, Henrich; Brückel, Thomas.

In: Journal of Applied Crystallography, Vol. 45, No. 2, 09.02.2012, p. 245-254.

Research output: Contribution to journal › Article › peer-review

TY - JOUR

T1 - Analysis of randomly oriented structures by grazing-incidence small-angle neutron scattering

AU - Korolkov, Denis

AU - Busch, Peter

AU - Willner, Lutz

AU - Kentzinger, Emmanuel

AU - Rücker, Ulrich

AU - Paul, Amitesh

AU - Frielinghaus, Henrich

AU - Brückel, Thomas

PY - 2012/2/9

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N2 - A formalism is presented which allows the quantitative evaluation of data from grazing-incidence small-angle neutron and X-ray scattering-GISANS and GISAXS-in the framework of the distorted wave Born approximation. While several aspects have been reported previously, this formalism combines solutions for scattering intensities in both reflection and transmission hemispheres, taking into account instrumental resolution effects. This formalism is applied to the case of GISANS from self-organized diblock copolymers, ordered in perpendicular lamellar structures on an Si wafer in randomly oriented short-range-ordered regions. The periodicity of D = 85 (9) nm found for deuterated polystyrene-polybutadiene of molecular weight M w = 165 kg mol -1 and a molecular weight fraction of the deuterated polystyrene block of 52% is consistent with atomic force microscopy and specular neutron reflectivity results.

AB - A formalism is presented which allows the quantitative evaluation of data from grazing-incidence small-angle neutron and X-ray scattering-GISANS and GISAXS-in the framework of the distorted wave Born approximation. While several aspects have been reported previously, this formalism combines solutions for scattering intensities in both reflection and transmission hemispheres, taking into account instrumental resolution effects. This formalism is applied to the case of GISANS from self-organized diblock copolymers, ordered in perpendicular lamellar structures on an Si wafer in randomly oriented short-range-ordered regions. The periodicity of D = 85 (9) nm found for deuterated polystyrene-polybutadiene of molecular weight M w = 165 kg mol -1 and a molecular weight fraction of the deuterated polystyrene block of 52% is consistent with atomic force microscopy and specular neutron reflectivity results.

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KW - grazing-incidence small-angle neutron scattering

KW - grazing-incidence small-angle X-ray scattering

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