Reconstruction of the Orientation Distribution Function for Materials with Low Lattice and Sample Symmetry Using the Harmonic Method

Abstract

Many properties of polycrystalline materials depend on their crystallographic texture, which can be fully described by the orientation distribution function (ODF). The main task of quantitative texture analysis is to reconstruct the ODF from its two-dimensional projections, which are obtained through X-ray or neutron diffraction methods. In this work, the results of ODF reconstruction for materials with low lattice and sample symmetry using the harmonic method are presented. The method is based on expanding the ODF in a Fourier series using three-dimensional symmetric spherical functions. Real functions which are linear combinations of corresponding complex spherical functions were used. A model single-component texture and the texture of a magnesium alloy sample subjected to equal-channel angular pressing were investigated. Both textures exhibit hexagonal lattice symmetry and triclinic sample symmetry. In both cases, the RP-factor values and the error of ODF calculation, used to check the adequacy of the solution, showed good agreement between the calculated and original data. It was also found that the ODF of the magnesium alloy sample contains two texture components (\(\bar {1}\)2\(\bar {1}\)6)[\(\bar {1}\)211] and (\(\bar {1}\)2\(\bar {1}\)6)[\(\bar {1}\)2\(\bar {1}\)1] with maximum intensities of 13.81 and 2.23, respectively. The obtained results can be used in texture studies of ceramics, rocks, and other nonmetallic materials with low symmetry.