A basic theory is provided for the creation of orientation representations using three-dimensional visualizations. An extensive set of visualizations in both standard and anaglyph movie format is made available as supplementary material.

This paper applies three-dimensional visualization techniques to synthetic and experimentally acquired material textures (random, cube and Goss texture components) and illustrates how three-dimensional visualization can be used to gain insight about orientation distribution functions and orientation relations. The intrinsic symmetry of the Euler orientation representations is considered in detail and it is shown that a monoclinic magnetic space group properly describes the symmetry of Euler space.

Time-resolved (four-dimensional) and high-resolution data have been collected using X-ray diffraction contrast tomography (DCT) and the TriBeam from the same volume in a single strontium titanate sample. Methods presented for the merger of the reconstructions enable direct quantitative comparisons on a grain and voxel scale and can be extended to other multi-modal data sets.

X-ray diffraction contrast tomography is used to investigate the crystallographic, topological and morphological characteristics of the evolving microstructure in thermally aged strontium titanate samples. The analysis of the 3D structure shows a clear signature of the grain boundary anisotropy, which can be correlated to surface energy anisotropy: the grain boundary orientation distribution function shows an excess of 〈100〉-oriented interfaces with respect to a random structure.