Learned Peak Shape Functions for Powder Diffraction Data

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Abstract
An algorithm is described for the determination of an experimental (learned) peak shape function, which has been used succesfully in crystal structure refinements from powder data. The function gives an optimal fit to almost any peak shape since it is not based on an analytical expression. It is determined from a single peak in a pattern by first fitting this peak with the proposed algorithm which ensures that the function is smooth and has only one maximum and two inflection points. The learned function is then normalised and decomposed into a symmetric and an asymmetric part. These are stored in tabulated form, permitting linear interpolation. As with an analytical function, a FWHM and asymmetry function describing the 26 dependence of the peak shape can be applied.

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