Multigrain crystallography and three-dimensional grain mapping

Conventionally, crystallography is based on two extreme sample morphologies: perfect single crystals and homogeneous powders. In the last decade, however, methods have been developed to treat polycrystalline specimens as an ensemble of individual crystals, creating the possibility to rigorously characterize such samples in terms of not just average properties, but of the distributions of those properties. In this way, crystallographic techniques developed for analysis of single-crystal data have been generalized to simultaneously characterize each of the crystals in the polycrystalline sample. Examples of application areas are structure solution and refinement, reciprocal-space mapping, and characterization of sizes and strains. Furthermore, now-established methods such as three-dimensional X-ray diffraction (3DXRD) microscopy and diffraction-contrast tomography enable 3D mapping of the morphology of the individual embedded grains, as well as 3D mapping of local crystallographic properties such as phase, crystallographic orientation and strain. Samples with up to 20 000 crystals have been characterized in this way and, as these methods are non-destructive, experiments can be carried out under in situ conditions and 3D movies of structural evolution can be acquired. In this chapter methods for multigrain crystallography and grain mapping are presented. A detailed treatment of the underlying mathematical formalism is given and a comprehensive survey of ways to represent orientation space – a topic central to the performance of algorithms – is included.