The representation of orientation distributions

Textures are properly described as densities in a three-dimensional orientation space. The appropriate coordinates of this space are the Euler angles describing relative rotations or, equivalently, the location and azimuth of a vector on a sphere (a boat on the earth). The space spanned up by these angular coordinates has conventionally been chosen Cartesian, and the orientation distribution function (ODF) is then represented in two-dimensional (square) sections through this space, with contour lines. It is proposed that an alternative representation be used that maintains a closer connection to pole figures and inverse pole figures, which areprojections of orientation space. There are advantages if ODFsections are also plotted in polar coordinates. The equivalents to pole figures are ’partial pole figures’ or COD’s (crystal orientation distributions); the equivalents to inverse pole figures are partial inverse pole figures or SOD’s (sample orientation distributions). These representations are less distorted than conventional ODF’s and display the symmetry properties in a more obvious way. In addition, both projections and sections should be plotted inequal-area projection; then, equal volume elements in orientation space are displayed by equal area elements in the representations. Common operations with these diagrams are outlined and illustrated using a rolled copper sample.