Robust Monte-Carlo fitting of small-angle neutron scattering curves for determining cluster-size distributions

Reactor pressure vessel (RPV) steel, when exposed to fast neutron irradiation, leads to the formation of nano-sized clusters [1]. These clusters can cause an overall degradation in mechanical properties, which is a safety issue. Small-angle neutron scattering (SANS) is a commonly used technique to determine the irradiation-induced cluster volume fraction and cluster size distribution in the material.
However, in the case of modern RPV steels, standard data treatment [2] for back-transforming the SANS scattering curves to real space can lead to unstable results. These are highly dependent on renormalisation parameters to be chosen by the user.
Here, a Monte Carlo fitting (MCF) algorithm based on [3] is presented. No renormalisation parameter is needed. The algorithm is optimized to get a robust determination of small cluster volume fractions (≈ 0.01 %) and cluster radii (≈ 0.7 nm), which are typical for modern RPV steels. The significance of the resulting data can be evaluated by an automatic error analysis. Using simulated scattering curves, the MCF is able to deliver a good reconstruction of the cluster size distribution and volume fraction in the vicinity of the SANS detection limit. Furthermore, the algorithm is tested with experimental scattering curves of neutron-irradiated RPV steels. The MCF transformation yields in physical meaningful, non-divergent results. Comparisons between analyses performed by the standard methods [2] and the MCF algorithm are drawn. The stability of the results and the limits of information to be extracted from the experimental data are discussed.

References
[1] G.R. Odette, B.D. Wirth, Handbook of Materials Modeling, Springer Netherlands, 999–1037 (2005)
[2] S. Hansen, J.S. Pedersen, J.Appl.Crystallogr. 24, 541–548 (1991)
[3] S. Martelli, P.E. Di Nunzio, Part.Part.Syst.Char. 19, 247–255 (2002)