Abstract
A method of simulating the neutron scattering by a textured polycrystal is presented. It is based on an expansion of the scattering cross sections in terms of the spherical harmonics of the incident and scattering directions, which is derived from the generalized Fourier expansion of the polycrystal orientation distribution function. The method has been implemented in a Monte Carlo code as a component of the McStas software package, and it has been validated by computing some pole figures of a Zircaloy-4 plate and a Zr-2.5Nb pressure tube, and by simulating an ideal transmission experiment. The code can be used to estimate the background generated by components of neutron instruments such as pressure cells, whose walls are made of alloys with significant crystallographic texture. As a first application, the effect of texture on the signal-to-noise ratio was studied in a simple model of a diffraction experiment, in which a sample is placed inside a pressure cell made of a zirconium alloy. With this setting, the results of two simulations were compared: one in which the pressure-cell wall has a uniform distribution of grain orientations, and another in which the pressure cell has the texture of a Zr-2.5Nb pressure tube. The results showed that the effect of the texture of the pressure cell on the noise of a diffractogram is very important. Thus, the signal-to-noise ratio can be controlled by appropriate choice of the texture of the pressure-cell walls.
Highlights
Neutron and X-ray scattering are extensively used in materials science for many purposes, in particular to analyse the structure of phases, quantifying their volume fractions and determining the state of stress and the crystallographic texture
Because of the low flux of neutrons compared with X-rays, in neutron laboratories the instruments are optimized for a particular set of scientific applications, which implies looking for the highest flux on the sample while keeping the resolution required by the technique to ensure a reasonable signal-tonoise ratio (SNR)
We present expressions for the differential and total elastic coherent cross sections in terms of the generalized Fourier coefficients of the orientation distribution function (ODF), which are suitable for implementation in Monte Carlo programs
Summary
Neutron and X-ray scattering are extensively used in materials science for many purposes, in particular to analyse the structure of phases, quantifying their volume fractions and determining the state of stress and the crystallographic texture. The paper is organized as follows: in Section 2 we give a brief description of the ODF, to state clearly the conventions used in this work; in Sections 3 and 4 we present, respectively, the expressions used to compute the differential and total neutron cross sections for coherent elastic scattering by a polycrystalline material; in Section 5 we describe in detail how the method is implemented in the McStas Monte Carlo code; in Section 6 we analyse the effects of the truncation of the Fourier series; in Section 7 we present the results of simulations performed to validate the code; and in Section 8 we discuss, as a first application, an estimation of the SNR of an experiment involving a pressure cell with a sharp texture, comparing it with the SNR associated with a pressure cell of the same characteristics and a uniform texture. Some details of the computations and other useful information are provided in the appendices
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