Texture tomography with high angular resolution utilizing sparsity.

Area of Science:

• Materials Science
• Crystallography
• Data Science

Background:

• Scanning probe X-ray diffraction tomography is crucial for analyzing material microstructures.
• Reconstructing data from anisotropic polycrystalline samples with sparse textures presents significant challenges.
• Existing methods often struggle with samples containing small, highly mosaic crystalline domains.

Purpose of the Study:

• To develop a novel reconstruction approach for scanning probe X-ray diffraction tomography data.
• To enable stable, high-resolution mapping of orientation distribution functions in 3D bulk samples.
• To overcome limitations of existing methods, particularly for samples with sparse textures and mosaic microstructures.

Main Methods:

• Reconstruction of a voxel map containing orientation distribution functions for each voxel.
• Utilizing non-negativity in orientation space with specific basis functions for sparse textures.
• Avoiding traditional peak-finding steps, making the method applicable to challenging crystalline structures.

Main Results:

• Stable solutions achieved at high angular resolutions, even in underdetermined scenarios.
• Successful mapping of twinning microstructure in the interior of a shot-peened martensite sample.
• Demonstrated applicability to gastropod shell with a mosaic microstructure, requiring only a single rotation axis.

Conclusions:

• The developed method offers a robust approach for X-ray diffraction tomography data reconstruction.
• It effectively handles anisotropic polycrystalline samples and utilizes texture sparsity for efficient data acquisition.
• This technique expands the capability to analyze complex microstructures in bulk materials without resolving individual lattice domains.