Yd. Wang et al., Natural partitioning of orientation elements and determination of the ODF from individual orientations according to the maximum-entropy principle, J APPL CRYS, 32, 1999, pp. 404-408
The orientation distribution function (ODF) of a polycrystalline material i
s usually constructed from individual orientations by the harmonic method o
n the assumption of a certain function distribution in the Euler space arou
nd each orientation. In the present paper, a new method is developed to det
ermine 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 ele
ments are directly estimated by the volumes of the orientation elements and
the number of grains (or measured points) in each orientation element. The
n, the texture vector is further refined using the maximum-entropy method w
ith the preliminary orientation densities as constraints. The validity of t
his method is exemplified by the texture analysis of a cubic material from
individual orientations modelled by Gaussian distribution.