An Analytical Method for the Quantitative Determination of the Volume Fractions in Fiber Textures

Abstract

In order to evaluate pole-figure measurements quantitatively, one needs the normalization factor which reduces measured intensity values to multiples of the random density. This factor may be determined experimentally by measuring the intensities of a random sample or it may be calculated by integrating over the whole pole-figure or its asymmetric unit. If pole-figure values are not available in the whole angular range 0≤φ≤90° (incomplete pole-figures), then the calculation is in general much more difficult and it usually presumes the knowledge of several pole-figures.In the case of fiber textures (axial symmetry), consisting of only a few strongly preferred orientations with the crystal directions 〈uvw〉i parallel to the axis of symmetry, the normalization factor and hence the volume fractions of the components i may be calculated in a rather simple way requiring only one, possibly incomplete, pole figure.