Texture (crystalline)
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In materials science, texture is the distribution of crystallographic orientations of a sample. A sample in which these orientations are fully random is said to have no texture. If the crystallographic orientations are not random, but have some preferred orientation, then the sample has a weak, strong, or moderate texture. The degree is dependent on the percentage of crystals that have the preferred orientation. Texture is seen in almost all engineered materials, and it can have a great influence on material properties. Also geologic rocks show texture due to their thermo-mechanic history due to formation processes.
One extreme case is a complete lack of texture: a solid with perfectly random crystallite orientation, which will have isotropic properties at length scales sufficiently larger than the size of the crystallites. The opposite extreme is a perfect single crystal, which has anisotropic properties by geometric necessity.
[edit] Characterization and representation
Texture can be determined by different method. Some of them allow a quantitative analysis of the texture others are only qualitative. Among the quantitative techniques the most widely used is X-ray diffraction using texture goniometers, followed by EBSD-method (electron backscatter diffraction) in Scanning Electron Microscopes. For qualitative analysis it can be done by Laue photography, simple X-ray diffraction or with the polarized microscope. neutron and synchrotron high-energy X-ray diffraction allow to access textures of bulk material and in-situ whereas laboratory x-ray diffraction instrument are more appropriate for thin film textures.
Texture is often represented using a pole figure, in which a specified crystallographic axis (or pole) from each of a representative number of crystallites is plotted in a stereographic projection, along with directions relevant to the material's processing history such as the rolling direction and transverse direction or the fiber axis (see below).
 Four circles diffractometer, or Eulerian cradle, for texture measurement with X-ray diffraction |
 χ mode for reflection measurement |
 Ω mode for transmission measurement |
The full 3-dimensional representation of crystallographic texture is given by the orientation distribution function (ODF) which can be achieved through evaluation of a set of pole figures or diffraction spectra. Subsequently, all pole figures can be derived from the ODF.
[edit] ODF analysis
The ODF is defined as the volume fraction of grain oriented along a certain direction g.
ODF(g) = 1/V dV(g)/dg
the direction g is normally identified using three Euler angles. The orientation distribution function, ODF, cannot be measured directly by any technique. Traditionally both X-ray diffraction and EBSD may collect pole figures. Different methodologies exist to obtain the ODF from the pole figures or data in general. They can be classify at first based on how they represent the ODF. Some use to represent the ODF as a function, sum of functions or expand it in series of harmonic functions. Others, known as discrete methods, divide the ODF space in cells and focus on determine the value of the ODF in each cell.
[edit] 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 steel sheet for transformer cores (to reduce magnetic hysteresis) and of aluminium cans (since deep drawing requires extreme and relatively uniform plasticity).
Texture in ceramics usually arises because the crystallites in a slurry have shapes that depend on crystalline orientation, often needle- or plate-shaped. These particles align themselves as water leaves the slurry, or as clay is formed.
Casting or other fluid-to-solid transitions (i.e., thin-film deposition) produce textured solids when there is enough time and activation energy for atoms to find places in existing crystals, rather than condensing as an amorphous solid or starting new crystals of random orientation. Some facets of a crystal (often the close-packed planes) grow more rapidly than others, and the crystallites for which one of these planes faces in the direction of growth will usually out-compete crystals in other orientations. In the extreme, only one crystal will survive after a certain length: this is exploited in the Czochralski process (unless a seed crystal is used) and in the casting of turbine blades and other creep-sensitive parts.
