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In chromatography, a solute moves through a chromatographic column and tends to spread, forming a Gaussian-shaped band. The longer the solute spends in the column, the broader the band becomes. The broadening can lead to overlaps within the column, affecting separation effectiveness.
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Accounting for instrument resolution in the pair distribution functions obtained from total scattering data using

Shaojie Wang1, Min Gao2,3, Yinze Qin4

  • 1Institute of Atomic and Molecular Physics Sichuan University Chengdu Sichuan 610065 People's Republic of China.

Journal of Applied Crystallography
|August 6, 2025
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Hermite functions accurately model pair distribution functions (PDFs) from total scattering data. This method effectively accounts for experimental resolution, improving PDF analysis for neutron and X-ray scattering data.

Keywords:
Hermite functionspair distribution functionsresolutiontotal scattering

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Area of Science:

  • Materials Science
  • Condensed Matter Physics
  • Crystallography

Background:

  • Pair distribution functions (PDFs) are crucial for understanding atomic arrangements in materials.
  • Previous methods for PDF analysis from total scattering data have limitations in accounting for experimental resolution.
  • Hermite functions offer a mathematically advantageous form for analyzing scattering data due to their Fourier transform properties.

Purpose of the Study:

  • To demonstrate the utility of Hermite functions for deriving pair distribution functions (PDFs) from total scattering data.
  • To show how fitting Hermite functions to scattering data can incorporate experimental resolution effects.
  • To address technical challenges in PDF analysis, such as handling Bragg peaks and scaling.

Main Methods:

  • Fitting Hermite functions to total scattering data (synthetic and real X-ray/neutron data).
  • Utilizing the property that Hermite functions are eigenfunctions of the Fourier transform.
  • Modifying the Billinge & Farrow background removal method using Chebyshev functions.

Main Results:

  • Successful application of Hermite functions to describe both scattering data and PDFs.
  • Demonstrated ability to account for experimental resolution, particularly for neutron time-of-flight data.
  • Provided solutions for managing Bragg peaks and scaling issues in PDF analysis.

Conclusions:

  • Hermite functions provide a robust framework for accurate PDF determination from total scattering data.
  • The method effectively integrates experimental resolution, enhancing data interpretation.
  • The approach is validated with both synthetic and real-world synchrotron X-ray and spallation neutron scattering data.