Internal optimization of the texture component approximation method

Abstract

The component approximation method for the reconstruction of orientation distribution function (ODF) is based on the assumption that the texture could be presented as a weighted linear combination of distributions depending on the parameters, which are related to the position of bell shaped function in orientation space and to the dispersion. The method uses a minimization procedure to obtain the values of ODF parameters. Traditionally, the mean- square deviation of the measured and recalculated pole figures is minimized. However, the quantitative measure of the fit is RP value which differs from the mean-square deviation. In the present work it is suggested to minimize the RP value to obtain ODF parameters. We are using Trust Region method for solving a non-linear optimization problem. The convergences of the proposed method for different minimized functional are compared. We also illustrate a usage of the different objective function on modeling data for the cubic crystalline symmetry. This study is fulfilled using new RIGAKU software for quantitative texture analysis.