Approximation of the Pole Figures and the Orientation of Distribution of Grains in Polycrystalline Samples by Means of Canonical Normal Distributions

Abstract

The orientation distribution function (ODF) as determined from experimental pole figures (PF) in a polycrystalline sample by classical spherical harmonics analysis can have ghost effects and regions of negative values. The regions of negative values and the ghosts are a consequence of the loss of information on the “odd” part of ODF.In the present paper the canonical normal distributions (CND) on the rotation group SO(3) and on the sphere S2 in R3 used in texture analysis are discussed.The examples of CND on SO(3), S2 and their PF calculated for hexagonal lattice symmetry and for a rolling texture of beryllium are demonstrated.