Orientation density distribution function
The orientation density distribution function (OVF, engl .: o RIENTATION d istribution f unction (ODF)) is used for quantitative description of the texture of a much crystalline solid .
Presentation and meaning
For each crystallite, the sample-fixed coordinate system is symbolically transferred into the crystal-fixed coordinate system. This is done by three consecutive rotations around the orthogonal Euler angles . The set of all orientations spans the so-called Euler or G space. The function value OVF ( g ) indicates the volume fraction of crystallites with the orientation in an infinitesimal sample volume. It is usually represented on right-angled coordinate axes as a set of sections through the three-dimensional Euler space. With a corresponding symmetry, a part of the Euler space is sufficient for a complete mapping.
The position and expression of maxima of the ODF are of particular practical importance . For example, characteristic ODF plots for a cube, roll or fiber texture or combinations thereof result. This allows a detailed prediction of the anisotropic deformation behavior of the material. It is also important to determine the random part of the texture, i.e. the part of the randomly oriented crystallites in the overall texture, the so-called phon.
Experimental determination
The ODF can be determined by individual orientation measurements ( TEM , SEM , to a limited extent also by light microscopy ) or statistically with diffraction methods ( X-ray diffraction , neutron diffraction ). When selecting the method, it is important to examine a representative sample volume with sufficient statistical certainty with as little effort as possible.