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Three-dimensional (3D) reconstructions from electron tomography provide important morphological, compositional, optical and electro-magnetic information across a wide range of materials and devices. Precession electron diffraction, in combination with scanning transmission electron microscopy, can be used to elucidate the local orientation of crystalline materials. Here we show, using the example of a Ni-base superalloy, that combining these techniques and extending them to three dimensions, to produce scanning precession electron tomography, enables the 3D orientation of nanoscale sub-volumes to be determined and provides a one-to-one correspondence between 3D real space and 3D reciprocal space for almost any polycrystalline or multi-phase material.

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 orientation data are best studied. Here, we provide a guide to the visualization of misorientation data in three-dimensional vector spaces, reduced by crystal symmetry, to reveal crystallographic orientation relationships. Domains for all point group symmetries are presented and an analysis methodology is developed and applied to identify crystallographic relationships, indicated by clusters in the misorientation space, in examples from materials science and geology. This analysis aids the determination of active deformation mechanisms and evaluation of cluster centres and spread enables more accurate description of transformation processes supporting arguments regarding provenance.

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