Exact and fast calculation of the X-ray pair distribution function.

Area of Science:

• Crystallography
• Materials Science
• Data Analysis

Background:

• The powder pair distribution function (PDF) is crucial for analyzing atomic arrangements in crystalline and disordered materials.
• Conventional PDF calculation methods often involve approximations for atomic form factors, limiting exactness for certain radiation types.
• Efficient and accurate PDF calculation is essential for advancing materials characterization.

Purpose of the Study:

• To present a novel, fast, and exact algorithm for calculating the powder pair distribution function (PDF).
• To enable precise PDF analysis for periodic structures using X-ray and electron diffraction data.
• To overcome limitations of existing methods by avoiding simplifications in atomic form factors.

Main Methods:

• The algorithm calculates the PDF by transforming reciprocal space data through a sine Fourier transform.
• It processes the normalized total powder diffraction pattern directly.
• This approach bypasses the need for simplifying assumptions regarding X-ray and electron atomic form factors.

Main Results:

• The new algorithm achieves exact PDF calculation for X-ray and electron diffraction, comparable to conventional methods for neutron diffraction.
• Significant improvements in calculation speed were observed.
• Enhanced capabilities include better error detection in primary data, handling of preferred orientation, and simplified treatment of magnetic scattering.

Conclusions:

• The developed algorithm offers a faster and more exact method for PDF determination in periodic structures.
• It provides a robust framework for analyzing diffraction data, accommodating complex instrumental effects and various scattering types.
• This advancement facilitates more accurate materials characterization and structural analysis.