One-dimensional models for small-angle X-ray diffraction from crystalline polymers. II. Model with continuous density changes between phases

The small angle X-ray scatter from crystalline polymers is evaluated by using a one-dimensional model where the density between crystal and amorphous phases changes linearly over a finite transition range t, and where the sizes of the crystal and amorphous regions fluctuate according to independent Gaussian distributions. The calculation is based on the general model formulated in part I. Approximate expressions are derived for the width and area of the diffraction peaks. The dependence on t occurs in the factor sin² πst/(πst)² which affects only the peak intensities. An analysis is made to find how the factor will modify theoretical interpretations based on experimental intensity measurements.