Calculation Of Orientation Distribution Function Research Articles

Direct determination of physical properties from continuous orientation distributions

Traditionally, the orientation distribution function (ODF) of textured materials has been derived by a deconvolution of pole figures using the harmonic method. Recently, other methods of ODF calculation have been proposed which require a modification of procedures. We describe here a combined method for deriving harmonic coefficients from any ODF, using as an example the WIMV method [S. Matthies and G. W. Vinel, Phys. Status Solidi B 112, K111 (1982)] applied to calcite with orthorhombic specimen and trigonal crystal symmetries. The results demonstrate that elastic properties derived from the harmonic and WIMV results are indistinguishable. Furthermore, we document that the ODF contribution which is not implicit in pole figures (odd coefficients) can be obtained by WIMV with fair accuracy for a complex simulated texture.

ODF Calculation by Series Expansion from Incompletely Measured Pole Figures Using the Positivity Condition Part I—Cubic Crystal Symmetry

The calculation of orientation distribution functions (ODF) from incomplete pole figures can be carried out by an iterative procedure taking into account the positivity condition for all pole figures. This method strongly reduces instabilities which may occasionally occur in other methods.

Texture representation of deformed dolomite rocks

The determination of the Orientation Distribution Function (ODF) from pole-figures measurements and from individual crystal measurements is illustrated for trigonal crystal and triclinic specimen symmetry with an example of the rhombohedral carbonate mineral dolomite. We emphasize methodology of fabric analysis, taking into account some new aspects about the significance of the inversion center in ODF calculations. The odd coefficients of the harmonic expansion which can not be easily derived from pole-figure measurements, have been determined with Universal stage data of c-axes and f-twin lamellae. Their contribution to the ODF is 20–30% and therefore necessary in any quantitative representation of textures.