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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
Summary
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.
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.
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