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X-ray powder diffraction in education. Part I. Bragg peak profiles
Robert Dinnebier1, Paolo Scardi2
1Max Planck Institute for Solid State Research, Heisenbergstrasse 1, Stuttgart, 70569, Germany.
Journal of Applied Crystallography
|December 29, 2021
Summary
This study introduces interactive Wolfram language scripts for understanding X-ray powder diffraction peak profiles. It details mathematical concepts like convolution and aberrations for educational purposes.
Area of Science:
- Crystallography
- Materials Science
- Computational Physics
Background:
- X-ray powder diffraction (XPD) is crucial for materials characterization.
- Understanding peak profiles requires detailed mathematical and physical insights.
- Existing educational tools may lack interactive visualization of complex concepts.
Purpose of the Study:
- To develop interactive educational tools for XPD peak profile analysis.
- To provide a clear mathematical description of diffraction patterns.
- To serve as a foundational resource for teaching XPD.
Main Methods:
- Utilized the Wolfram Language for script development in Mathematica.
- Implemented interactive visualizations for distribution functions and convolution.
- Detailed explanations of instrumental aberrations and microstructural effects.
Main Results:
- Created a suite of scholarly scripts for XPD peak profile analysis.
- Interactive visualizations enhance understanding of mathematical concepts.
- Comprehensive explanations cover real and Fourier space convolution.
Conclusions:
- The developed scripts offer a valuable resource for teaching XPD.
- Interactive tools facilitate a deeper comprehension of diffraction physics.
- This work forms the first part of a series on mathematical descriptions in XPD.