Fabric analysis by orientation distribution functions

Abstract

Abstract Crystalline materials (natural or artificial) may consist of several phases (minerals) the crystal structures and relative amounts of which will generally be known. In order to fully characterize such a material, also the form and spatial distribution of the phases, the grain structure, and lattice defects and their distribution must be specified by appropriate distribution functions. Among these, the Orientation Distribution Function (texture, fabric structure) plays an important role. It can be deduced from experimental pole figures by series expansion methods. In textured materials two different symmetries can be distinguished, the crystal symmetry and the statistical sample symmetry. Special consideration must be given to the inversion centre as an element of either of these symmetries and in Friedels' law. A complete description of all possible sample symmetries can be given in terms of black—white symmetry groups. The determination of the odd part of the texture function is strongly related to these groups and the various kinds of the inversion centre. Each combination of a certain crystal symmetry group with a certain sample symmetry group induces a certain space group in the orientation space, the proper consideration of which minimizes the required amount of numerical calculations. The texture function (ODF) is the most important factor in the relation between anisotropic properties of single crystals and the polycrystalline material. Changes of the ODF can be used as a sensitive indicator for solid state processes having occurred in the material.