An optimized single-crystal to polycrystal model of the neutron transmission of textured polycrystalline materials

The attenuation coefficient of textured materials presents a complex dependence on the preferred orientation with respect to the neutron beam. Presented here is an attenuation coefficient model to describe textured polycrystalline materials, based on a single-crystal to polycrystalline approach, aiming towards use in full-pattern least-squares refinements of wavelength- resolved transmission experiments. The model evaluates the Bragg contribution to the attenuation coefficient of polycrystalline materials as a combination of the Bragg-reflected component of a discrete number of imperfect single crystals with different orientations, weighted by the volume fraction of the corresponding component in the orientation distribution function. The proposed methodology is designed to optimize the number of single-crystal orientations involved in the calculation, considering the instrument resolution and the statistical uncertainty of the experimental transmission spectra. The optimization of the model is demonstrated through its application to experiments on calibration samples presenting random crystallographic textures, measured on two imaging instruments with different resolutions. The capability of the model to simulate textured samples in different orientations is shown with a copper sample used as a reference in texture studies of archaeological objects and a 316L stainless steel sample produced by laser powder-bed fusion. The ability of the model to predict the attenuation coefficient of polycrystalline textured materials on the basis of a reduced number of texture components opens the possibility of including it in a least-squares fitting routine to perform crystallographic texture analysis from wavelength-resolved transmission experiments.