On Probability - Statistical Representation of Pole Figures for Materials with Hexagonal Symmetry

Abstract

A new method of computing of normal distributions [1] on rotation groups is suggested. Monte Carlo method allows to calculate the orientation of grains function (ODF) and correspondent pole figures (PFs) using approximation by normal distributions [2]. The developed Monte Carlo method is applied for construction of PFs mathematical statistical model corresponding to experimental measurement. This model is based on statistical simulation of normal distributions on SO(3) group for discrete representation of pole figures. It is possible to calculate effective physical properties of polycrystals using the given discrete representation. The mathematical simulation for texture with two components of polycrystalline sample with hexagonal symmetry is developed. Two experimental PFs } 0 1 10 { and } 0002 { for Be measured by X-ray experiment are being used. For this case the effective property as a tensor of elastic compliance was calculated. The mathematical simulation of PFs also allows to determine the statistical errors of pole figures measurement.