A novel method to obtain integral parameters of the orientation distribution function of textured polycrystals from wavelength-resolved neutron transmission spectra

Abstract

A novel method to estimate integral parameters of the orientation distribution function (ODF) in textured polycrystals from the wavelength-resolved neutron transmission is presented. It is based on the expression of the total coherent elastic cross section as a function of the Fourier coefficients of the ODF. This method is broken down in detail for obtaining Kearns factors in hexagonal crystals, and other material properties that depend on the average of second- and fourth-rank tensors. The robustness of the method against three situations was analyzed: effects of sample misalignment, of cutoff value l max of the series expansion and of experimental standard deviation. While sample misalignment is shown not to be critical for the determination of Kearns factors and second-order-rank properties, it can be critical for fourth-rank and higher-order tensor properties. The effect of the cutoff value on the method robustness is correlated to the standard deviation of the experimental data. In order to achieve a good estimation of the Fourier coefficients, it is recommended that the experimental standard deviation be around 3-5% of the total scattering cross section of the material for the method to be stable. The method was applied for the determination of Kearns factors from transmission measurements performed at the instrument ENGIN-X (ISIS) on a Zr-2.5 Nb pressure tube along two sample directions and was shown to be able to estimate Kearns factors with an error below 5%.