Crystallite Orientation in Materials Having Fiber Texture. II. A Study of Strained Samples of Crosslinked Polyethylene

Abstract

Diffraction data obtained for a crosslinked polyethylene sample crystallized at fixed strain are utilized to demonstrate the practicality of the method of analysis for samples having fiber texture which was presented in a previous paper. Plane-normal distributions qi(ζi) reconstructed using data for twelve reflections reproduce the features of the measured distributions quite satisfactorily. The series termination error is only appreciable for planes having a sharply peaked distribution, and fortunately it then appears mainly as false oscillations of small amplitude in the low-density region, which do not distort the principal features of the distribution. As a test of the accuracy of plane-normal distributions constructed for unmeasured reflections, qi(ζi) was recalculated for the (200) plane with omission of the intensity data for this plane. Deviations from the experimental distribution are again trivial. Thus, the procedure permits one to calculate the plane-normal distributions for the (002) and (401) planes, for which experimental measurements are not feasible. The crystallite orientation distribution G(ξ, φ) is calculated using the diffraction data for twelve reflections. This may be presented as a contour map or, if plotted in stereographic projection, as the inverse pole figure diagram. The most probable crystallite orientation for this sample, having relative elongation α=4.58, inclines the a, b, and c axes from the fiber direction by 41°, 90°, and 49°, respectively. The series termination error does not displace the peak positions, but it creates small areas of negative density in the low-density region. It is demonstrated that data for four planes suffice to reveal the qualitative aspects of the crystallite distribution. The approximate relation used to estimate the standard deviation of the truncated series is tested and verified. Diffraction data were also obtained for three additional samples covering a range of elongation α from 2.20 to 6.67. The (h0l) plane-normals orient most strongly toward the fiber axis, the (h/l) ratio of the plane exhibiting the best alignment decreasing continuously as α is increased. The implication that the b axis tends to orient perpendicular to the fiber axis is verified by the plane-normal distribution, which becomes more sharply peaked about χ=90° as α is increased. The maximum in the a-axis distribution shifts from χ=0° to larger values of χ as α is increased, while the c-axis distribution undergoes a more complex transformation.