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Are Bragg Peaks Gaussian?

Boualem Hammouda1

  • 1National Institute of Standards and Technology, Gaithersburg, MD 20899.

Journal of Research of the National Institute of Standards and Technology
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PubMed
Summary
This summary is machine-generated.

Bragg peaks in neutron scattering are often assumed Gaussian. However, this study shows that sample structure spread makes them asymmetric, requiring an exponentially modified Gaussian function for accurate modeling.

Keywords:
Bragg peaksGaussian functionMcStas1ray tracing simulationresolution functionsmall-angle neutron scattering

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Area of Science:

  • Neutron Scattering Physics
  • Materials Science
  • Crystallography

Background:

  • Bragg scattering peaks are commonly modeled as Gaussian functions.
  • Gaussian functions are standard for instrumental smearing corrections in scattering experiments.

Purpose of the Study:

  • To investigate the actual shape of Bragg peaks in small-angle neutron scattering (SANS).
  • To determine if Gaussian functions accurately represent Bragg peaks under various conditions.
  • To identify appropriate functions for modeling Bragg peaks when sample structure influences their shape.

Main Methods:

  • Utilized Monte Carlo ray tracing simulations to model a realistic SANS instrument.
  • Generated Bragg peaks by including a single-crystal sample with large d-spacing.
  • Analyzed peak shapes considering contributions from both instrumental resolution and sample structure spread.

Main Results:

  • Bragg peaks exhibit Gaussian shapes only under resolution-limited conditions with negligible sample spread.
  • When sample structure spread is significant, Bragg peaks deviate from Gaussian.
  • The exponentially modified Gaussian function provides a more accurate representation of asymmetric Bragg peaks.

Conclusions:

  • The assumption of Gaussian Bragg peaks is only valid when sample structure effects are minimal.
  • Asymmetry (skewness) in Bragg peaks arises from sample structure spread and broad neutron wavelength distributions.
  • The exponentially modified Gaussian function is essential for accurately describing Bragg peaks influenced by sample structure.