Abstract

The relationship between crystal orientations in polycrystalline materials influences many macroscopic properties including plastic deformation and phase transitions. This talk considers the geometry of crystal orientations with special attention paid to crystal symmetry. In particular, the geometry of the space of misorientations between orientations with arbitrary crystal symmetry will be discussed. It will be shown that important orientation relationships can be interpreted as vertices in misorientation space. From the geometry of the misorientation spaces we deduce formulas for the uncorrelated angle and axis distribution functions for any combination of symmetries.

The talk will be illustrated by visualizations generated with the texture analysis toolbox MTEX and will include and introduction to the toolbox. MTEX is a universal, free and open souce MATLAB toolbox for analyzing crystallographic orientation data. It provides basic functionalities to compute with orientations, misorientations, pole figure data, EBSD data, distribution functions, tensorial properties, elastic and plastic deformations. MTEX is highly extendable and everybody is welcome to contribute code.