SMALL-ANGLE SCATTERING OF NEUTRONS ON Sr2FeMoO6–δ SAMPLES WITH DIFFERENT-DEGREE SUPERSTRUCTURAL ORDERING OF Fe/Mo CATIONS

Single-phase Sr2FeMoO6-δ samples with different-degreesuperstructiral ordering Fe/Mo cations superstructural ordering (P, 76, 86 and 93 %) were obtained by the solid-phase technique. Based on the results of measuring the magnetic characteristics in the samples, we found that an increase in magnetization (26.41, 32.36 and 42.66 A·m2·kg–1), magnetic moment (1.33, 3.07 and 3.58 μB/f.u.) and Curie temperatures (422, 428 and 437 K) withparameter P (76, 86 and 93 %) can be explained by the presence of antistructural defects, as well as antiferromagnetic inclusions. This determines the redistribution of electron density, which is accompanied by the change in electronic configuration of a part of Fe/Mo cations. Based on the temperature dependences of the magnetic moment of the samples measured in ZFC and FC modes, and on small-angle polarized neutron scattering (SANS), we found that the samples are in a magnetically inhomogeneous state. An important result to mention is that we detected the difference between the slope of the SANS curves of samples with different oxygen content, which demonstrates a different microstructure of inhomogeneities. The main inhomogeneities are magnetic inclusions with the dimensions depending on the superstructural ordering of Fe/Mo cations. According to the Porod law, it was shown that the Sr2FeMoO6-δ samples with wave vector values 0.1 > q > 0.002 Å–1 contain polydisperse grains with a smooth surface. For q > 0.1 Å–1 a deviation from the Porod law is observed, confirming the presence of magnetic inhomogeneities with a diameter < 6 nm in the grains.

Simple inversion formula for the small-angle X-ray scattering intensity from polydisperse systems of spheres

A practical inversion method to calculate the size distribution of colloidal homogeneous particles from small-angle scattering experiments is presented. It is based on the analysis of the deviations of the scattering signal from the Porod law. The resulting inversion formula provides a reliable way to assess complex size distributions such as power-law, multimodal or very broad distributions. It is particularly suitable for colloidal dispersions that have a substantial fraction of very small particles. These cases correspond to large deviations from the Porod law over a broad range of scattering vector values,q. Shannon's theorem gives a way to obtain the maximum amount of information concerning the size distribution, without requiring an arbitrary extrapolation of the data beyond the availableqrange. It is demonstrated that this protocol yields a calculated distribution of particle sizes that is stable.

Small angle scattering in the Porod region from hydrated paper sheets at varying humidities

The microscopic changes in the structure of paper at different equilibrium moisture contents were examined using the novel technique of contrast variation small angle neutron scattering (SANS). Contrast variation, by appropriate selection of the H2O:D2O ratio, was used to simplify the scattering from hydrated paper to a two-phase approximation. The two phases were paper polymers (cellulose, lignin and hemicelluloses) and a phase consisting of water and voids. The two-phase approximation is justified by consideration of the chemistry and density of each of the polymer species belonging to paper, and by matching the scattering length density of the sorbed moisture to air. The neutron intensity at the higher scattering angles examined was successfully fitted using the Porod law, which is applicable to scattering from a two-phase system at the high scattering angle limit. This limit is related to the specific surface area between the two phases. The limiting scattered intensity of neutrons was found to increase with increasing moisture content for a range of paper materials. It is concluded that the sorption of water increased the limiting intensity because water disrupted polymer-polymer bonding. The Porod law also predicts the slope of the intensity/scattering angle curve at the high scattering angle limit.

Illustration of the anisotropic Porod law

A simple derivation of the leading asymptotic term of small-angle scattering intensities relevant to anisotropic particulate samples is reported. The result is illustrated for the case of ellipsoidal particles. It is discussed under what circumstances the anisotropic Porod law can be applied to scattering intensities collected by a two-dimensional detector.

Small-angle X-ray scattering analysis of craze-fibril structures

Load-bearing craze fibrils are fundamental to the ability of many polymer materials to support applied tensile stress. Three models of the scattering from craze-fibril structures have been compared through a rigorous analysis procedure. The results indicate that a diffuse-boundary model provides a more accurate description of scattering from the fibril structure than the standard Porod-law technique. Previously reported methods for determining fibril diameters were found to be inappropriate for high-impact polystyrene (HIPS) materials, overestimating the fibril diameters by as much as 60%. Indirect transforms using regularization theory of the fibril scattering data provide confirmation of the fibril diameters obtained from a power-law diffuse-boundary model, which is developed specifically for the craze-fibril structure of interest.