Texture (crystalline)

In materials science, texture is the distribution of crystallographic orientations of a polycrystalline sample (it is also part of the geological fabric). A sample in which these orientations are fully random is said to have no distinct texture. If the crystallographic orientations are not random, but have some preferred orientation, then the sample has a weak, moderate or strong texture. The degree is dependent on the percentage of crystals having the preferred orientation. Texture is seen in almost all engineered materials, and can have a great influence on materials properties. Also, geologic rocks show texture due to their thermo-mechanic history of formation processes.Four circles diffractometer, or Eulerian cradle, for texture measurement with X-ray diffractionχ mode for reflection measurementΩ mode for transmission measurement In materials science, texture is the distribution of crystallographic orientations of a polycrystalline sample (it is also part of the geological fabric). A sample in which these orientations are fully random is said to have no distinct texture. If the crystallographic orientations are not random, but have some preferred orientation, then the sample has a weak, moderate or strong texture. The degree is dependent on the percentage of crystals having the preferred orientation. Texture is seen in almost all engineered materials, and can have a great influence on materials properties. Also, geologic rocks show texture due to their thermo-mechanic history of formation processes. One extreme case is a complete lack of texture: a solid with perfectly random crystallite orientation will have isotropic properties at length scales sufficiently larger than the size of the crystallites. The opposite extreme is a perfect single crystal, which likely has anisotropic properties by geometric necessity. Texture can be determined by various methods. Some methods allow a quantitative analysis of the texture, while others are only qualitative. Among the quantitative techniques, the most widely used is X-ray diffraction using texture goniometers, followed by the EBSD method (electron backscatter diffraction) in Scanning Electron Microscopes. Qualitative analysis can be done by Laue photography, simple X-ray diffraction or with a polarized microscope. Neutron and synchrotron high-energy X-ray diffraction are suitable for determining textures of bulk materials and in situ analysis, whereas laboratory x-ray diffraction instruments are more appropriate for analyzing textures of thin films. 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. These directions define the so-called sample reference frame and are, because the investigation of textures started from the cold working of metals, usually referred to as the rolling direction RD, the transverse direction TD and the normal direction ND. For drawn metal wires the cylindrical fiber axis turned out as the sample direction around which preferred orientation is typically observed (see below). 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. The full 3D representation of crystallographic texture is given by the orientation distribution function ( O D F {displaystyle ODF} ) which can be achieved through evaluation of a set of pole figures or diffraction patterns. Subsequently, all pole figures can be derived from the O D F {displaystyle ODF} . The O D F {displaystyle ODF} is defined as the volume fraction of grains with a certain orientation g {displaystyle {oldsymbol {g}}} . The orientation g {displaystyle {oldsymbol {g}}} 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 O D F {displaystyle ODF} . The orientation distribution function, O D F {displaystyle 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 O D F {displaystyle ODF} from the pole figures or data in general. They can be classified based on how they represent the O D F {displaystyle ODF} . Some represent the O D F {displaystyle ODF} as a function, sum of functions or expand it in a series of harmonic functions. Others, known as discrete methods, divide the O D F {displaystyle ODF} space in cells and focus on determining the value of the O D F {displaystyle ODF} in each cell.