Supplementary Material from On three-dimensional misorientation spaces

Determining the local orientation of crystals in engineering and geological materials has become routine with the advent of modern crystallographic mapping techniques. These techniques enable many thousands of orientation measurements to be made, directing attention towards how such data are best analysed and plotted. Here, we provide a guide to the visualization of misorientation data in three-dimensional (3D) vector spaces, reduced by crystal symmetry, to reveal crystallographic orientation relationships. By choosing an appropriate vector space, domains for all point group symmetries become accessible and fundamental zones are presented for combinations of all Laue classes. An analysis methodology is then developed and applied to identify crystallographic relationships in examples from materials science and geology. These examples highlight key advantages of analysing misorientations as 3D vectors. In particular, identification of misorientation clusters highlights the presence of previously unknown orientation relationships and helps determining active deformation mechanisms. Evaluation of cluster spread and centre allows for a more accurate description of transformation processes and quantification of clusters can be used for arguments of a sample's provenance.