direction around which preferred orientation is typically observed (see below). Common textures There are several textures that are commonly found in processed (cubic) materials. They are named either by the scientist that discovered them, or by the material they are most found in. These are given in Miller indices for simplification purposes. Cube component: (001)[100] Brass component: (110)[-112] Copper component: (112)[11-1] S component: (123)[63-4] Orientation distribution function The full 3D representation of crystallographic texture is given by the orientation distribution function () which can be achieved through evaluation of a set of pole figures or diffraction patterns. Subsequently, all pole figures can be derived from the . The is defined as the volume fraction of grains with a certain orientation . The orientation is normally identified using three Euler angles. The Euler angles then describe the transition from the sample’s reference frame into the crystallographic reference frame of each individual grain of the polycrystal. One thus ends up with a large set of different Euler angles, the distribution of which is described by the . The orientation distribution function, , cannot be measured directly by any technique. Traditionally both X-ray diffraction and EBSD may collect pole figures. Different methodologies exist to obtain the from the pole figures or data in general. They can be classified based on how they represent the . Some represent the as a function, sum of functions or expand it in a series of harmonic functions. Others, known as discrete methods, divide the space in cells and focus on determining the value of the in each cell. Origins In wire and fiber, all crystals tend to have nearly identical orientation in the axial direction, but nearly random radial orientation. The most familiar exceptions to this rule are fiberglass, which has no crystal structure, and carbon fiber, in which the crystalline anisotropy is so great that a good-quality filament will be a distorted single crystal with approximately cylindrical symmetry (often compared to a jelly roll). Single-crystal fibers are also not uncommon. The making of metal sheet often involves compression in one direction and, in efficient rolling operations, tension in another, which can orient crystallites in both axes by a process known as grain flow. However, cold work destroys much of the crystalline order, and the new crystallites that arise with annealing usually have a different texture. Control of texture is extremely important in the making of silicon