Pole figure

A pole figure is a graphical representation of the orientation of objects in space.

For example, pole figures in the form of stereographic projections are used to represent the orientation distribution of crystallographic lattice planes in crystallography and texture analysis in materials science.

The orientation of the object is fully determined by the use of poles of two planes that are not parallel.

"Texture" in the context of Materials Science means "crystallographic preferred orientation".

If a polycrystalline material (i.e. a material composed of many different crystals or grains, like most metals, ceramics or minerals) has "texture" then that means that the crystal axes are not randomly (or, more correctly, uniformly) distributed.

The full determination of the texture requires the plot of two pole figures corresponding to planes that are not parallel and that do not have the same diffraction angle (thus different interplanar distances).

Poles of the faces of a cube
Stereographic projection of a pole
Wulff net, step of 10°
Wulff net, pole and trace of a plane
Pole figure of a diamond lattice in 111 direction .
Pole figures displaying crystallographic texture of gamma-TiAl in an alpha2-gamma alloy, as measured by high energy X-rays. [ 1 ]
Pole figure and diffraction figure