Indirect evaluation of orientation in polycrystalline materials

• Published in: Journal of polymer science 1961-10, Vol.54 (160), p.543-560
• Main Author: Sack, R. A.
• Format: Article
• Language: English
• ISSN: 0022-3832; 1542-6238
• DOI: 10.1002/pol.1961.1205416018

For a polycrystalline material with partial orientation, relations are established between the mean square cosines of the angles ρ between the axis of orientation and lines fixed with the lattice. Experimentally, the mean orientation f = for the normal to a lattice plane can be determined from the intensity distribution of the corresponding Debye‐Scherrer ring. As already shown by Wilchinsky, the mean orientation for any line can, in general, be expressed as a linear function of the values of f for five other lines, with coefficient depending on the directions of the lines within the lattice, but not on the degree of orientation of the material. For crystallites with monoclinic or higher symmetry or lamellar shape, or if all the lines considered lie within one lattice plane or along its normal, the number of independent determinations reduces to 3 or 2, for needle‐shaped crystallites even to 1. The same number of measurements are needed if the rings contain several unresolved reflections. If more than the minimum number of observations are available, more accurate results can be obtained by a least square formalism; with composite rings the strongest reflections do not necessarily possess the highest statistical weight. The accuracy of the calculated results is estimated in terms of the errors of the experimental data. The new formalism is applied to a fresh analysis of the measurements by J. J. Hermans, P. H. Hermans, Vermaas, and Weidinger on regenerated cellulose.