Small-Angle Neutron Scattering of Precipitates in Ni-Rich Ni–Ti Alloys. II. Methods for Analyzing Anisotropic Scattering Data

Abstract

Methods for analyzing small‐angle neutron scattering data for single crystals with anisometric precipitates and anisotropic arrangement are described. A method for projecting the measured scattering intensity in a (110) plane and obtaining the anisotropic correlation function is described. The method uses an indirect Fourier transformation with Hermitian functions as the basis. The correlation function gives model‐independent information on the precipitate form and arrangement. A modified paracrystal cluster model is also introduced and size polydispersity is included in a local monodisperse approximation. The size distribution is obtained by least‐squares fitting. The correlation function and the cluster model give consistent results for the morphology of precipitates in Ni‐rich Ni–Ti single crystals.

Determination of displacements from nanoprecipitates in a Cu–Ni–Fe single crystal using anomalous small-angle and large-angle X-ray scattering

“…4 of Lyon et al (2000) and Fig. 1 of Pedersen et al (1997)]. Each set corresponds to one of the three possible families of precipitates, piled up along one of the h100i directions.…”

“…During the past ten years, an increasing number of experiments have been performed on single crystals in order to highlight this anisotropic effect (see e.g. Guilarducci et al, 1987;Sato et al, 1988;Fratzl et al, 1993;Lyon & Simon, 1994, hereinafter referred to as paper I; Pedersen et al, 1997). However, very few experiments have been attempted to determine the associated displacements: in the case of the plate-like Guinier±Preston (GP) zones formed in an Al±Cu alloy, Matsubara & Cohen (1983) have measured its large-angle scattering, i.e.…”

Soluble complexes in aqueous mixtures of low charge density comb polyelectrolyte and oppositely charged surfactant probed by scattering and NMR

“…For each instrumental setting the ideal model cross section was smeared by the appropriate resolution function when the model scattering intensity was compared to the measured one by means of least-square methods [28]. The parameters in the models were optimized by conventional least-square analysis and the errors of the parameters were calculated by conventional methods [29].…”

Chitosan-N-poly(ethylene oxide) brush polymers for reduced nonspecific protein adsorption

“…For each instrumental setting the ideal model cross section was smeared by the appropriate resolution function when the model scattering intensity was compared to the measured one by means of least-square methods [33]. The parameters in the models were optimized by conventional least-square analysis and the errors of the parameters were calculated by conventional methods [34]. …”