Natural partitioning of orientation elements and determination of the ODF from individual orientations according to the maximum-entropy principle

The orientation distribution function (ODF) of a polycrystalline material is usually constructed from individual orientations by the harmonic method on the assumption of a certain function distribution in the Euler space around each orientation. In the present paper, a new method is developed to determine the ODF from individual orientations. A natural partitioning of the orientation elements in the Euler space around some clustered orientations is proposed. Thus, the preliminary values of orientation density in the elements are directly estimated by the volumes of the orientation elements and the number of grains (or measured points) in each orientation element. Then, the texture vector is further refined using the maximum-entropy method with the preliminary orientation densities as constraints. The validity of this method is exemplified by the texture analysis of a cubic material from individual orientations modelled by Gaussian distribution.