Robust method of approximating the orientation distribution function by canonical normal distributions

Abstract

The problem of the restoration of an orientation distribution function (ODF) of polycrystalline materials from experimental pole figures (PFs) using the modified method of components is considered. As the components, central normal distributions on the rotation group SO(3) are used. To find the parameters of the model, the regularization method is employed. The code constructed permits one to calculate the model parameters from complete or incomplete pole figures obtained by X-ray or neutron scattering method. In this case, no preliminary normalization is required. Based on the parameters found, both the ODFs and any other PFs can be restored. The validity of the method is demonstrated on the example of the restoration of the hot-rolling texture of magnesium proceeding from PFs that were obtained at the Laboratory of Neutron Physics, Joint Institute of Nuclear Research, Dubna, Moscow oblast. To find the parameters of the model, two of the six PFs measured have been used. The other four PFs that have not been employed in calculations were restored from the parameters found. They are used for the estimation of the adequacy of the model and, as follows from the calculations, have the same level of accuracy of the approximations as those that were used for the calculation of PFs.