ODF: Orientation Distribution Function
Definition:A three dimensional representation of the crystallite orientation density in a polycrystalline material.
Explanation:In order to describe the texture of a polycrystalline specimen, the orientations of the grains relative to the sample coordinate system need to be determined. In this respect, a distribution function is introduced with three variables (e.g. Euler angles), since at least three parameters are necessary to give a distinct description. Such function can either be determined from single orientation measurements or from pole figure data. Finally, an ODF describes the volume fraction of a specimen with a certain orientation compared to a sample with randomly distributed orientations.

The most common way to represent an ODF is the Euler space defined by three orthogonal vectors that correspond to the Euler angles φ1, Φ, φ2 needed to describe uniquely an orientation. It is common practice to represent ODFs in form of equal distance sections along one of the axes (usually φ2). To display the intensity distribution in these sections, lines of equal intensity are used.
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(a) Three dimensional illustration of the ODF (Euler space). (b) ODF displayed in equal distance (5°) sections along φ2
SFB-Link:The crystallographic texture determines the anisotropy of materials’ properties. ODFs are used to display and analyze the texture evolution of high manganese steels during deformation and heat treatment. Additionally, the measured texture data is used as both input data for and validation of process simulations.
References:V. Randle und O. Engler, Introduction to Texture Analysis, CRC Press, 2000
G. Gottstein, Physikalische Grundlagen der Materialkunde, Berlin: Springer, 2007