Кристаллдық бағдарларды стереографиялық бейнелеу

Way of visually representing the orientation of objects in 3D space
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 structure of a crystal is often represented by the pole figure of its crystallographic planes. A plane is chosen as the equator, usually the (001) or (011) plane; its pole is the center of the figure. Then, the poles of the other planes are placed on the figure, with the Miller indices for each pole. The poles that belong to a zone are sometimes linked with the related trace.

"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. To draw a pole figure, one chooses a particular crystal direction (e. g. the normal to the (100) plane) and then plots that direction, called a pole, for every crystal relative to a set of directions in the material. In a rolled metal, for example, the directions in the material are the rolling direction, transverse direction and rolling plane normal. If a large number of crystals are involved, then it is typical to make a contour plot, rather than plotting individual poles. 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).

Consider the diffraction pattern obtained with a single crystal, on a plane that is perpendicular to the beam, e. g. X ray diffraction with the Laue method, or electron diffraction in a transmission electron microscope. The diffraction figure shows spots. The position of the spots is determined by the Bragg's law. It gives the orientation of the plane. If the parameters of the optics are known (especially the distance between the crystal and the photographic film), it is possible to build the stereographic diagram from the diffraction diagram, i. e. to transform the diffraction pattern into a pole figure.