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 journalArticlepeer-review

8 Scopus citations


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 languageEnglish
Pages (from-to)245-254
Number of pages10
JournalJournal of Applied Crystallography
Issue number2
StatePublished - 9 Feb 2012
Externally publishedYes


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


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