Texture tomography with high angular resolution utilizing sparsity

TL;DR

This paper introduces a new high-angular-resolution texture tomography method that reconstructs orientation distributions in 3D samples without peak-finding, effectively handling sparse textures in anisotropic polycrystalline materials.

Contribution

It presents a novel reconstruction approach that leverages sparsity and non-negativity in orientation space, enabling stable high-resolution mapping of complex microstructures without traditional peak detection.

Findings

Successfully mapped twinning microstructure in martensite sample

Demonstrated effective reconstruction of mosaic microstructure in gastropod shell

Achieved stable solutions at high angular resolutions using sparsity constraints

Abstract

We demonstrate a novel approach to the reconstruction of scanning probe x-ray diffraction tomography data with anisotropic poly crystalline samples. The method involves reconstructing a voxel map containing an orientation distribution function in each voxel of an extended 3D sample. This method differs from existing approaches by not relying on a peak-finding and is therefore applicable to sample systems consisting of small and highly mosaic crystalline domains that are not handled well by existing methods. Samples of interest include bio-minerals and a range of small-graines microstructures common in engineering metals. By choosing a particular kind of basis functions, we can effectively utilize non-negativity in orientation-space for samples with sparse texture. This enables us to achieve stable solutions at high angular resolutions where the problem would otherwise be under determined. We demonstrate the new approach using data from a shot peened martensite sample where we are able to map the twinning micro structure in the interior of a bulk sample without resolving the individual lattice domains. We also demonstrate the approach on a piece of gastropods shell with a mosaic micro structure.