Quantitative information from x‐ray diffraction of nylon‐6 yarns. I. Development of a model for the analytical description of equatorial x‐ray profiles

A wide‐angle x‐ray method has been developed by which quantitative structural information can be obtained on nylon‐6 yarns. To this end, experimental equatorial diffractometer scans measured in transmission were fitted to a mathematical model describing the profiles as the envelopes of three bell‐shaped functions. Four different models were investigated using, respectively, Gauss, Lorentz (Cauchy), Logistic, and Pearson‐VII functions. The last model, which can be regarded as a generalized Lorentz function, gave the best fit. On the basis of a statistical analysis of the results of well‐separated x‐ray peaks, two parameters could be fixed. Another reduction of the number of parameters was achieved by interrelating the peak areas of the two outer reflections. These reductions widened the applicability of a computer program based on the aforementioned model to highly overlapping x‐ray peaks. So the whole variety of x‐ray scans, which can be obtained from nylon‐6 yarns made under widely varying process conditions, can be well described. The fitting procedures provide unique solutions and hence objectively determined parameters.