Crystallographic Texture
Polycrystalline materials are composed of many individual grains, each with a distinct crystallographic orientation. The statistical distribution of these orientations is called the crystallographic texture, described by the orientation distribution function (ODF) f(g):
dV/V = f(g) dg, ∫_{SO(3)} f(g) dg = 1
The ODF quantifies the probability density of finding a grain with orientation g in the sample. Processing history — rolling, annealing, deformation — imprints characteristic texture components that govern anisotropic mechanical, thermal, and electromagnetic properties.
Diffraction Tomography Forward Model
In synchrotron 6D texture tomography, a pencil beam scans a specimen at many positions and rotation angles φ. Each detector frame records a diffraction pattern encoding the pole-figure intensity projected along that beam path. The forward model integrates the local ODF along the beam:
I(hkl, t, φ) = ∫ f(g; r(t,φ)) P_{hkl}(g) dl
where Phkl(g) is the pole-figure weight for reflection (hkl) at orientation g. Inverting this integral equation for all voxels simultaneously constitutes a large-scale tomographic reconstruction problem constrained by non-negativity and ODF normalisation.
In the Simulation
Load a pre-computed grain-orientation dataset and visualise the reconstructed texture as a 3D colour-coded grain map. Colour encodes the crystal orientation via the inverse-pole-figure colour key. Features include grain-map slicing, ODF φ₂ sections, pole figure output, and misorientation analysis between any two grains.