Let us first begin with some constructed ODFs to be analyzed below
A bimodal ODF:
A fibre ODF:
An ODF estimated from diffraction data
Modal Orientations
The modal orientation of an ODF is the crystallographic preferred orientation ori_pref
of the texture. It is characterized as the maximum of the ODF. In MTEX it is returned as the second output argument of the command max
Lets mark this preferred orientation in the pole figures
Texture Characteristics
Texture characteristics are used for a rough classification of ODFs into sharp and weak ones. The two most common texture characteristics are the entropy and the texture index. The texture index of an ODF \(f\) is defined as:
\[ t = \int_{SO(3)} f({R})^2 dR\]
We may either compute this integral using the command sum
directly by
or, more efficiently, by the command norm
The entropy of an ODF \(f\) is defined as:
\[ H = - \int_{SO(3)} f({R}) \ln f({R}) dR\]
Volume Portions
Volume portions describes the relative volume of crystals having a certain orientation. The relative volume of crystals having a orientation close to a given orientation is computed by the command volume
and the relative volume of crystals having a orientation close to a given fibre is computed by the command fibreVolume
The relative volume in percent of crystals with misorientation maximum 30 degree from the preferred orientation ori_pref
:
The relative volume of crystals with misorientation maximum 20 degree from the preferred fibre in percent: