polefigurer

Polefigurer, or pole figures, are graphical representations that show how crystallographic directions are distributed with respect to a material’s sample reference frame. They describe the texture of a polycrystalline material, meaning the preferred orientation of its grains.

They are produced from diffraction- or diffraction-like measurements. Techniques such as X-ray diffraction, neutron diffraction, and electron backscatter diffraction collect data on how often specific crystal directions align with the sample axes. Each measured orientation is projected from the crystal coordinate system onto a pole on the unit sphere, and the results are displayed on a stereographic or equal-area projection. The figure uses intensity or contour levels to indicate the probability of a given direction appearing in the sample.

Pole figures are interpreted to assess texture and anisotropy in materials. High intensity for a particular pole indicates a favored orientation of that crystal direction relative to the sample. In cubic materials common poles include (100), (110), and (111); in hexagonal materials, directions like (0001) are often important. Multiple pole figures for different directions are typically analyzed together to capture the overall texture.

They are a key input for texture analysis and for estimating the orientation distribution function (ODF), which describes the probability density of all orientations in the material. This information helps predict anisotropic properties such as mechanical strength, formability, diffusion, and diffusion, and informs processing steps like rolling, annealing, or recrystallization.

Limitations include the projection nature of pole figures, which can obscure some orientation information, and the need to combine several figures with symmetry considerations to resolve ambiguities. Pole figures are widely used in materials science and geology to characterize crystalline textures.