A spherical harmonic transform approach to the indexing of electron back-scattered diffraction patterns.

Area of Science:

• Materials Science
• Crystallography
• Computational Methods

Background:

• Electron Back-Scattered Diffraction (EBSD) is crucial for microstructural analysis.
• Accurate and efficient indexing of EBSD patterns is essential for large-scale materials characterization.
• Existing dictionary indexing methods, while robust, can be computationally intensive.

Purpose of the Study:

• To develop a faster and robust algorithm for indexing Electron Back-Scattered Diffraction (EBSD) patterns.
• To leverage spherical harmonic transforms (SHT) for improved computational efficiency.
• To provide a versatile indexing approach applicable to various diffraction modalities.

Main Methods:

• Implementation of a spherical master EBSD pattern and cross-correlation using Spherical Harmonic Transform (SHT).
• Utilizing real-valued Fast Fourier Transforms (FFT) and incorporating crystallographic symmetry.
• Developing an orientation refinement procedure based on analytical derivatives of Wigner d functions.

Main Results:

• The proposed SHT-based algorithm demonstrates significantly faster indexing speeds compared to dictionary indexing.
• The algorithm maintains robustness against noise in EBSD patterns, validated on Nickel (Ni) datasets.
• Performance analysis explored the impact of SHT bandwidth on indexing speed and memory usage.
• Successful application demonstrated on a large shot-peened Aluminum (Al) dataset.

Conclusions:

• The new SHT-based approach offers a computationally efficient and robust solution for EBSD pattern indexing.
• The method's speed gains are attributed to optimized FFT, symmetry incorporation, and efficient memory management.
• The algorithm's applicability extends to other diffraction techniques involving spherical intensity distributions.