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Title: Grating-based holographic diffraction methods for X-rays and neutrons: phase object approximation and dynamical theory

Abstract

A method dubbed grating-based holography was recently used to determine the structure of colloidal fluids in the rectangular grooves of a diffraction grating from X-ray scattering measurements. Similar grating-based measurements have also been recently made with neutrons using a technique called spin-echo small-angle neutron scattering. The analysis of the X-ray diffraction data was done using an approximation that treats the X-ray phase change caused by the colloidal structure as a small perturbation to the overall phase pattern generated by the grating. In this paper, the adequacy of this weak phase approximation is explored for both X-ray and neutron grating holography. Additionally, it is found that there are several approximations hidden within the weak phase approximation that can lead to incorrect conclusions from experiments. In particular, the phase contrast for the empty grating is a critical parameter. Finally, while the approximation is found to be perfectly adequate for X-ray grating holography experiments performed to date, it cannot be applied to similar neutron experiments because the latter technique requires much deeper grating channels.

Authors:
ORCiD logo [1]; ORCiD logo [2];  [3];  [3]; ORCiD logo [4]; ORCiD logo [4]; ORCiD logo [5]
  1. Indiana Univ., Bloomington, IN (United States). Center for Exploration of Energy and Matter and Physics Dept.
  2. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Biology and Soft Matter Division
  3. Rutherford Appleton Lab., Oxford (United Kingdom). ISIS Facility
  4. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Center for Nanophase Materials Science
  5. Indiana Univ., Bloomington, IN (United States). Center for Exploration of Energy and Matter and Physics Dept. ; Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Neutron Sciences Directorate
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division
OSTI Identifier:
1422549
Grant/Contract Number:  
AC05-00OR22725; FG02-09ER46279
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Applied Crystallography (Online)
Additional Journal Information:
Journal Name: Journal of Applied Crystallography (Online); Journal Volume: 51; Journal Issue: 1; Journal ID: ISSN 1600-5767
Publisher:
International Union of Crystallography
Country of Publication:
United States
Language:
English
Subject:
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND TECHNOLOGY; 36 MATERIALS SCIENCE; grating-based holography; phase object approximation; dynamical theory

Citation Formats

Feng, Hao, Ashkar, Rana, Steinke, Nina, Dalgliesh, Robert, Lavrik, Nickolay V., Kravchenko, Ivan I., and Pynn, Roger. Grating-based holographic diffraction methods for X-rays and neutrons: phase object approximation and dynamical theory. United States: N. p., 2018. Web. https://doi.org/10.1107/S1600576717016867.
Feng, Hao, Ashkar, Rana, Steinke, Nina, Dalgliesh, Robert, Lavrik, Nickolay V., Kravchenko, Ivan I., & Pynn, Roger. Grating-based holographic diffraction methods for X-rays and neutrons: phase object approximation and dynamical theory. United States. https://doi.org/10.1107/S1600576717016867
Feng, Hao, Ashkar, Rana, Steinke, Nina, Dalgliesh, Robert, Lavrik, Nickolay V., Kravchenko, Ivan I., and Pynn, Roger. Thu . "Grating-based holographic diffraction methods for X-rays and neutrons: phase object approximation and dynamical theory". United States. https://doi.org/10.1107/S1600576717016867. https://www.osti.gov/servlets/purl/1422549.
@article{osti_1422549,
title = {Grating-based holographic diffraction methods for X-rays and neutrons: phase object approximation and dynamical theory},
author = {Feng, Hao and Ashkar, Rana and Steinke, Nina and Dalgliesh, Robert and Lavrik, Nickolay V. and Kravchenko, Ivan I. and Pynn, Roger},
abstractNote = {A method dubbed grating-based holography was recently used to determine the structure of colloidal fluids in the rectangular grooves of a diffraction grating from X-ray scattering measurements. Similar grating-based measurements have also been recently made with neutrons using a technique called spin-echo small-angle neutron scattering. The analysis of the X-ray diffraction data was done using an approximation that treats the X-ray phase change caused by the colloidal structure as a small perturbation to the overall phase pattern generated by the grating. In this paper, the adequacy of this weak phase approximation is explored for both X-ray and neutron grating holography. Additionally, it is found that there are several approximations hidden within the weak phase approximation that can lead to incorrect conclusions from experiments. In particular, the phase contrast for the empty grating is a critical parameter. Finally, while the approximation is found to be perfectly adequate for X-ray grating holography experiments performed to date, it cannot be applied to similar neutron experiments because the latter technique requires much deeper grating channels.},
doi = {10.1107/S1600576717016867},
journal = {Journal of Applied Crystallography (Online)},
number = 1,
volume = 51,
place = {United States},
year = {2018},
month = {2}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Figures / Tables:

Figure 1 Figure 1: Schematic of the rectangular grating profile with grating period, p, groove width, w, and groove depth, h. The incident X-ray or neutron beam is in the xz plan and forms an angle θ with respect to the grating surface. Parameters for gratings used in neutron and X-ray experimentsmore » are given in Table 1.« less

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A new approach for probing matter in periodic nanoconfinements using neutron scattering
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Dynamical theory calculations of spin-echo resolved grazing-incidence scattering from a diffraction grating
journal, April 2010

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  • Journal of Applied Crystallography, Vol. 43, Issue 3
  • DOI: 10.1107/S0021889810010642

Confinement-induced liquid ordering investigated by x-ray phase retrieval
journal, February 2007


Space-time description of neutron spin echo spectrometry
journal, December 1996


Phase-object approximation in small-angle neutron scattering experiments on silicon gratings
journal, January 2007

  • de Haan, Victor-O.; Plomp, Jeroen; Bouwman, Wim G.
  • Journal of Applied Crystallography, Vol. 40, Issue 1
  • DOI: 10.1107/S0021889806047558

The scattering of high-energy electrons. I. Feynman path-integral formulation
journal, January 1978


Real-space interpretation of spin-echo small-angle neutron scattering
journal, January 2003

  • Krouglov, Timofei; de Schepper, Ignatz M.; Bouwman, Wim G.
  • Journal of Applied Crystallography, Vol. 36, Issue 1
  • DOI: 10.1107/S0021889802020368

Structure of confined fluids by x-ray interferometry using diffraction gratings
journal, January 2008

  • Nygard, K.; Satapathy, D. K.; Bunk, O.
  • Optics Express, Vol. 16, Issue 25
  • DOI: 10.1364/OE.16.020522

Grating-based holographic X-ray diffraction: theory and application to confined fluids
journal, October 2009

  • Nygård, K.; Satapathy, D. K.; Bunk, O.
  • Journal of Applied Crystallography, Vol. 42, Issue 6
  • DOI: 10.1107/S0021889809040990

Novel SANS instrument using Neutron Spin Echo
journal, July 1996

  • Rekveldt, M. Theo
  • Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, Vol. 114, Issue 3-4
  • DOI: 10.1016/0168-583X(96)00213-3

    Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.