Determination of the texture of polycrystalline materials using an algorithm of object-vector representation of reflection planes and visualization of the results in Rodrigues space

The article deals with the method of search and analysis of textural components using direct polar figures with due account for the symmetry of a cubic crystal and a sample. The algorithm is based on the representation of reflection planes by a polar complex of vectors. Search of orientation is made by moving the axis of a polar complex over the unit hemisphere followed by the rotation of a polar complex relative to this axis. Then the position of stereographic projections of the polar complex vectors on a discrete direct pole figure is determined. Orientation is found when the projections of at least three polar complex vectors are located in the area with non-zero intensity. For each orientation a Rodrigues vector is calculated. In addition, Euler angles and Miller indices are determined. Textural components are allocated interactively by clustering the data in Rodrigues space. Using the covariance matrix the eigenvalues and eigenvectors are determined characterizing the spatial dispersion of textural components. Pole figures of an aluminum foil after various textural transformations are investigated in the article. Obtained textural components are displayed in Rodrigues space.