Texture (crystalline) - 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 spectra. 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.