  The functionality of materials is determined by their composition and
microstructure, that is, the distribution and orientation of crystalline
grains, grain boundaries and the defects within them. The characterisation of
the material's microstructure is therefore critical for materials applications
such as catalysis, energy storage and buildings. Until now, characterization
techniques that map the distribution of grains, their orientation, and the
presence of defects have either been limited to surface investigations, to
spatial resolutions of a few hundred nanometres, or to systems of thickness
around one hundred nanometres, thus requiring destructive sample preparation
for measurements and preventing the study of system-representative volumes or
the investigation of materials under operational conditions. Here, we present
X-ray linear dichroic orientation tomography, a quantitative, non-invasive
technique that allows for an intra- and inter-granular characterisation of
extended polycrystalline and amorphous materials in three dimensions (3D). We
present the detailed characterisation of a polycrystalline sample of vanadium
pentoxide (V2O5), a key catalyst in the production of sulfuric acid. In
addition to determining the nanoscale composition, we map the crystal
orientation throughout the polycrystalline sample with 73 nm spatial
resolution. We identify grains, as well as twist, tilt, and twin grain
boundaries. We further observe the creation and annihilation of topological
defects promoted by the presence of volume crystallographic defects in 3D. Our
method's non-destructive and spectroscopic nature opens the door to in-operando
combined chemical and microstructural investigations of functional materials,
including energy and mechanical materials in existing industries, as well as
quantum materials for future technologies.
