Approximation of pole figures for the determination of crystal orientation in polymeric solids

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Abstract
The approximation of experimentally measured angular intensity distributions of X-rays diffracted by oriented polycrystalline specimens is suggested as a method for the determination of orientation distribution characteristics for uniaxially oriented polymeric fibres. A non-linear optimization program based on a Hook–Jeeves algorithm is elaborated and incorporated into the method. As an example, the interpretation of the data from polyethylene specimens having various degrees of orientation is given. An important application of the method is the analysis of distributions (pole figures) using a superposition of two identical or similar functions with different parameters.

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