The Modified Maximum Entropy Method (MMEM) in QTA for Lower Symmetry Polycrystalline Aggregates

Abstract

A new algorithm of quantitative texture analysis (QTA), which is called the modified maximum entropy method (MMEM), has been proposed and applied to determination of textures in polycrystalline samples of lower crystal symmetry with overlapping diffraction peaks (Wang and Xu, 1995a). By introducing directly the maximum entropy principle into the least square procedure of pole figure inversion (Bunge, 1969), then both minimizing the differences between experimental and postulated pole figure data, and maximizing entropy may be satisfied simultaneously. Thus, the maximum entropy principle is applied to the entire process of QTA in frame of the harmonic method (HM). The detailed comparisons among the three pole figure inversion methods, i.e. the traditional HM, the primary maximum entropy method (MEM) and the MMEM, are given through a model example of simulated fiber texture. It is shown that the precise and stable solution of inverse pole figure for the polycrystalline samples with smooth or sharp textures will be obtained by the MMEM even using a less number of pole figures. The minimum range of polar angle and the least number of pole figures, which are needed in the QTA for pretended tetragonal materials by the MMEM, are discussed in detail.