Multiple Small-angle Neutron Scattering Research Articles

Correlation effects in multiple small-angle neutron scattering at the surface layers of inhomogeneities

The influence of spatial correlations on the angular distribution of multiple small-angle neutron scattering (MSANS) at the surface layers of inhomogeneities is studied. Calculations are carried out by taking instrumental distortions into account when observing multiple small-angle neutron scattering by means of methods of a double-crystal diffractometer and a small-angle diffractometer with a position-sensitive detector. Within the framework of the eikonal approximation, the MSANS line is calculated, and the influence of the surface-layer thickness and the inhomogeneity concentration on its width is studied.

Investigation of condensed matter by means of elastic thermal-neutron scattering

The application of elastic thermal-neutron scattering in investigations of condensed matter that were performed at the Institute for Theoretical and Experimental Physics is described. An account of diffraction studies with weakly absorbing crystals, including studies of the anomalous-absorption effect and coherent effects in diffuse scattering, is given. Particular attention is given to exposing the method of multiple small-angle neutron scattering (MSANS). It is shown how information about matter inhomogeneities can be obtained by this method on the basis of Moliere’s theory. Prospects of the development of this method are outlined, and MSANS theory is formulated for a high concentration of matter inhomogeneities.

Investigation of multiple ultrasmall-angle neutron scattering with the aid of a double-crystal diffractometer

A method of multiple small-angle neutron scattering (MSANS), used to obtain information about inhomogeneities of substances, is considered. Experimental schemes and theory of a double-crystal diffractometer intended for measuring multiple small-angle neutron scattering are described. Methods used to approximate MSANS angular distributions at a low concentration of inhomogeneities and based on Moliere’s theory are reviewed. Their applicability is demonstrated for the examples ofMSANS spectra of samples from ferromagnetic iron-nickel alloys, aluminum powders, and high-Tc superconductor ceramic materials. Theoretical and experimental investigations of interference effects that manifest themselves in multiple small-angle neutron scattering on systems containing high concentrations of scatterers are reported.

Effect of the concentration of inhomogeneities on the multiple small-angle neutron scattering

The interference effects manifested during multiple small-angle neutron scattering (MSANS) on a chaotically arranged close-packed ensemble of scatterers have been studied. MSANS measurements have been performed for mixtures of Al and Ti-Zr alloy powders. It is shown that the results can be satisfactorily described based on a theory that takes into account spatial correlations in the arrangement of powder grains.

Development of methods for processing spectra of multiple small-angle neutron scattering

A method has been developed for processing spectra of multiple small-angle neutron scattering (MSANS) to obtain information about substance heterogeneities, namely, their size and concentration. A method has been proposed for constructing the dependence of the MSANS line width on the sample thickness starting from the angular neutron distribution measured for one sample. The standard method for processing this dependence has been improved for application at any scattering multiplicity and complete account for the instrumental line of the double-crystal spectrometer. The method has been tested for the MSANS spectra of the samples of the Fe-Ni ferromagnet, Al powders, and HTSC ceramics.

Multiple small-angle neutron scattering in media with a high concentration of inhomogeneities

Multiple small-angle neutron scattering (MSANS) on a polydisperse system of scatterers was considered taking into account interparticle interference. The effect of the scatterer’s size distribution on the MSANS spectrum was studied. The exponential and log-normal distributions were analyzed. It was shown that the MSANS linewidth decreases at high scatterer concentrations due to the contribution of interparticle interference. The dependence of this effect on the scattering multiplicity and scatterer’s size dispersion was studied in detail.

Multiple small angle neutron scattering: A new two-dimensional ultrasmall angle neutron scattering technique

We report on the demonstration experiment of the multiple small angle neutron scattering (MSANS) technique at a 5.6m long neutron beam line, leading to a q resolution of 3×10−4Å−1. The MSANS technique is based on two two-dimensional multihole apertures placed at the front end of the collimator and close to the sample, respectively. By choosing the proper MSANS geometry, individual diffraction patterns are superimposed leading to a large gain in intensity. Using MSANS as an option for standard small angle neutron scattering beam lines, the q resolution could be increased to 10−5Å−1 without dramatically sacrificing intensity.

Small-angle neutron scattering study of the role of feedstock particle size on the microstructural behavior of plasma-sprayed yttria-stabilized zirconia deposits

The microstructures of thick plasma-sprayed yttria-stabilized zirconia (8% mass fraction yttria) deposits were studied in a series of Porod small-angle neutron scattering (SANS) and multiple small-angle neutron scattering (MSANS) experiments. Three main void components were identified in the deposits: intrasplat cracks, interlamellar planar pores, and globular pores. The SANS and MSANS measurements were analyzed using the traditional theory for Porod scattering and a recently developed three-component model for MSANS evaluation. The average size, volume fraction, internal surface area, and orientation distribution for each void component within the deposits were determined. This study focused on gaining a better understanding of the effects of initial feedstock particle size and annealing temperatures on the microstructure of deposits sprayed under equivalent particle-impact conditions. Quantitative results are presented for each of four deposit samples: one prepared using the as-received feedstock particle wide-size distribution and three prepared from feedstock powder of different and relatively narrow particle size ranges with average sizes of 32, 47, and 88 μm. Except for the coarse (88 μm) feedstock powder, only mild monotonic variations were found in the microstructural anisotropies, the porosities (13 ± 1%), and the internal surface areas in the as-sprayed deposits. The internal surface area was independent of the feedstock particle size, even with the coarse feedstock. When the deposits were annealed at high temperatures (1100 and 1400 °C), the microstructures were altered with a reduction of the total internal surface area and a mild coarsening of the voids. These changes in the microstructural evolution were well-captured and described by the three-component model. The results were compared and related with those obtained from scanning electron microscopy images and elastic moduli measurements.

Characterisation of thermally sprayed metallic NiCrAlY deposits by multiple small-angle scattering

The technique of multiple small-angle neutron scattering (MSANS) was applied to thermally sprayed metallic deposits. The samples are technologically relevant Ni-based NiCrAlY coatings manufactured by different spray techniques (atmospheric and water-stabilised plasma spraying, flame spraying). MSANS measurements were made in directions parallel and perpendicular to the surface plane. Based on empirical considerations and on the analysis of SEM micrographs of coating cross-sections, the complex microstructures were modelled in terms of three distinct void systems. Employing a recent MSANS formalism, the experimental beam-broadening as a function of incident wavelength was used to derive the model parameters under the constraints of MSANS anisotropy, total measured porosity, and total internal surface area. The surface area was obtained from small-angle neutron scattering analysis in the Porod regime.

Multiple small-angle neutron scattering studies of anisotropic materials

Building on previous work that considered spherical scatterers and randomly oriented spheroidal scatterers, we describe a multiple small-angle neutron scattering (MSANS) analysis for nonrandomly oriented spheroids. We illustrate this with studies of the multi-component void morphologies found in plasma-spray thermal barrier coatings.

Multiple small-angle neutron scattering

Abstract Over the past decade, a multiple small-angle neutron scattering (MSANS) formalism has been developed to enable researchers to derive microstructural parameters from multiply-scattered small-angle neutron data. The MSANS formalism is particularly useful in ceramic science and materials research because it is applicable to samples that are thicker (> 2 mm) and have larger scattering volume fractions (> 2%) than are commonly used in small-angle neutron scattering studies. At the same time, the microstructural size range within which microstfuctures are determined is extended from 10–1000 A for small-angle neutron scattering to 800 A-10 μm for MSANS. This extended size range is precisely the size regime where significant materials microstructure exists. Finally, the rapidity with which MSANS data can be accumulated (on the order of minutes) compared to the typical time for small-angle neutron scattering data accumulation (on the order of hours) offers an opportunity to explore the kinetics of micro-s...

Authors' response to the comment by Mazumder and Sequeira on “probing porous ceramics using small-angle scattering”

We regret that Mazumder and Sequeira do not feel we gave their work recognition in our Neutron News article [1]. We considered that the purpose of this brief Scientific Review was to summarize our own work in this field. and place it in the context of the ongoing experimental research of ourselves and our collaborators. Clearly, such a brief article cannot be a comprehensive review of the multiple small-angle neutron scattering (MSANS) field.

Asymptotic behavior of neutron small-angle multiple scattering spectra

The asymptotic behavior of the spectra for large values of the scattering vector for the case of elastic multiple small-angle neutron scattering (SANS) is investigated theoretically and experimentally. An expansion of the spectrum in terms of the reciprocal of the magnitude of the momentum transfer is obtained taking account of the influence of the instrumental line. It is shown that, to within some factor, the leading term of the expansion is identical to the differential single-scattering cross section averaged over a statistical ensemble of particles; several subsequent terms in the expansion are calculated and the range of applicability of the resulting expressions is determined. The asymptotic behavior of the multiple SANS spectrum is measured, using a two-crystal neutron spectrometer, for samples of an HTSC ceramic, the alloy Fe-Ni, and Al powder. The agreement between the experimental results and the theoretical predictions is analyzed.

Probing porous ceramics using small-angle scattering

Small–angle neutron scattering (SANS) has a significant role in metallurgy, polymer science, biology, chemistry, geology, and condensed matter physics. It is of increasing interest to extend its application to other technologically–important materials, such as partially sintered ceramics and gels, plasma–sprayed deposits, and reinforced composites. These materials contain concentrated heterogeneous microstructures in the 0.1 μm − 10 pm scale regime. The SANS from such coarse microstructures is usually dominated by multiple scattering. Indeed, for partially–sintered ceramics and plasma-sprayed deposits, multiple SANS (MSANS) causes observable beam-broadening, with no unscattered transmitted beam surviving passage through the sample. However, with complementary information on the sample density and the scattering morphology, the beambroadening can be related to the mean scatterer size. The broadening itself brings this information within range of standard SANS instruments. where traditional single scatter SANS experiments face a maximum scatterer size limitation of ∼ 100 nm.

New Developments in Multiple Small-Angle Neutron Scattering Studies of Advanced Ceramics

ABSTRACTAn enhanced multiple small-angle neutron scattering (MSANS) formulation has been developed to interpret the beam-broadening, arising from coarse, concentrated pore/grain microstructures in porous ceramics and similar materials. Prolific scattering from such systems precludes single-scattering studies (apart from Porod surface determinations). Previous MSANS techniques, which have been developed to extract the mean pore dimensions, either treat a range of scattering morphologies, while assuming that the scattering is in the diffraction limit, or they consider refraction effects, while assuming that the scattering features are spherical. Many systems of interest violate both these assumptions. In the enhanced formulation, the previous method, which allowed fully for refraction, is extended to non-spherical scattering morphologies. Applications of the MSANS formulation to sintering studies of Si3N4 and silica gels, and to the microstructural characterization of plasma-spray coatings are currently of interest.

Multiple Small Angle Neutron Scattering Characterization of the Densification of Alumina

ABSTRACTMultiple small angle neutron scattering (MSANS) was used to follow the evolution of the pore size distribution in α-Al2O3through the intermediate and final stages of sintering. This technique makes it possible to determine microstructure morphology in the 0.08 to 10 μm size regime under conditions where the total scattering cross-section is dominated by elastic incoherent multiple scattering, as is often the case for ceramics. The MSANS results indicate an initial decrease in the effective pore radius from 0.19 μm at 57% of theoretical density (TD) to 0.17 μm at 79% TD. As the sample density further increased, there was a transition region after which the effective pore radius grew rapidly to ≤0.5 μm at 98% TD. Standard Porod analysis on scattering by the same samples also indicates a transition between the intermediate and final stages of processing. Both sets of results support a topological model of sintering in which the interconnected pore network in the intermediate stage of sintering decays in a stable manner. The pores become fewer, while retaining the same diameter, as densification proceeds. In the final stage, isolated pores remain.

Porosity in Spinel Compacts Using Small‐Angle Neutron Scattering

Unfired spinel (MgAl2O4) compacts and sintered materials with small hard agglomerates (<5 μm) were studied using small‐angle neutron scattering (SANS) techniques. The SANS results were compared with those from mercury porosimetry and gas adsorption. The results from green‐state samples are consistent with interconnected “ink‐bottle”‐type porosity. In the latter stages of densification the average void size is significantly larger than that found in the unfired compact. The presence of the hard agglomerates affects the observed SANS scattering much more in the partially densified samples than in the unfired compacts. It was demonstrated that the use of multiple SANS techniques to study large voids (<0.1 μm) and large pore fractions (45%) is a useful, sensitive, nondestructive diagnostic probe for the evaluation of porosity during sintering.