Study of the influence of the parameters of an experiment on the simulation of pole figures of polycrystalline materials using electron microscopy

Abstract

A two-dimensional mathematical model of a polycrystalline sample and an experiment on electron backscattering diffraction (EBSD) is considered. The measurement parameters are taken to be the scanning step and threshold grain-boundary angle. Discrete pole figures for materials with hexagonal symmetry have been calculated based on the results of the model experiment. Discrete and smoothed (by the kernel method) pole figures of the model sample and the samples in the model experiment are compared using homogeneity criterion χ², an estimate of the pole figure maximum and its coordinate, a deviation of the pole figures of the model in the experiment from the sample in the space of L₁ measurable functions, and the RP-criterion for estimating the pole figure errors. Is is shown that the problem of calculating pole figures is ill-posed and their determination with respect to measurement parameters is not reliable.