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%.

Determination of crystallographic texture in polycrystalline materials from wavelength-resolved neutron transmission experiments: application to high-symmetry crystals

“…Similarly, for each pair (l, ), equation (10c) can be interpreted as a linear system for the unknowns C l , where both A SS l ðsÞ and k SS Ã l ðsÞ are already given. The proposed inversion method, originally presented by Vicente Alvarez et al (2021) and extended in this work, is a two-step procedure: first, the A SS l ðsÞ coefficients are determined from the measured elastic cross section spectra for the directions s 1 ; s 2 ; . .…”

“…In this section, we present the derivation of the Fourier expansion expression for the elastic coherent cross section as a function of neutron wavelength in the kinematic diffraction approximation. However, unlike in our previous work (Vicente Alvarez et al, 2021), here we express this quantity in terms of symmetrized functions that comply with the crystal and sample symmetry. This approach enables us to directly expand the elastic coherent cross section in terms of a set of independent functions whose coefficients are linked to the Fourier coefficients of the ODF of the sample.…”

“…As previously explained by Vicente Alvarez et al (2021), when considering a fixed beam direction, equation (10a) can be interpreted as an expansion of el;coh ð; sÞ as a linear combination of B CS l ðÞ functions, where the expansion coefficients correspond to the values of A SS l ðsÞ for each set of (l, ). One of the main advantages of the present formalism is that the B CS l ðÞ functions are independent by construction, allowing for a straightforward inversion of equation (10a) to obtain the A SS l ðsÞ parameters from the experimental data.…”

“…A novel methodology was recently proposed to obtain integral parameters of the ODF by combining the transmission data obtained for different beam directions based on the Fourier decomposition of the ODF. This method was described in a recent paper by Vicente Alvarez et al (2021) and is applicable to materials with spatially uniform texture. The proposed methodology relies on the expansion of el;coh ð; sÞ in terms of functions of , whose expansion coefficients depend only on the texture Fourier coefficients and the beam direction.…”

“…If the ODF is expanded using generalized spherical harmonics (or Wigner functions), this LI condition is not fulfilled due to crystal symmetry. In some cases, such as hexagonal crystal symmetry, the linearly dependent functions can be easily identified and eliminated, as explained by Vicente Alvarez et al (2021). However, in high-symmetry crystals (e.g.…”