Study of multiple small-angle neutron scattering by the warren method

A procedure for studying multiple small-angle neutron scattering using a double-crystal spectrometer is presented. It is based on measuring the linear coefficient of beam attenuation caused by smallangle scattering. The method has been substantiated theoretically, and the range of its applicability has been determined.     

Correlation effects in small-angle multiple neutron scattering

The dependence of the spectra of small-angle multiple neutron scattering on the volume fraction occupied by scattering grains is considered. The concentration expansion is used to develop scattering theory in the eikonal approximation. The leading term of the expansion reproduces the standard low-concentration theory (Mollier). Some properties of the first correction term are analyzed, and it is shown that the angular distribution narrows with an increase in concentration, in qualitative agreement with the experimental data.     

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. Zh. éksp. Teor. Fiz. 114, 2194–2203 (December 1998)     

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.     

Interparticle interference of neutrons in multiple small-angle scattering by a close-packed polydisperse system

Small-angle multiple neutron scattering by a disordered polydisperse system with various concentrations of scattering centers is studied experimentally and theoretically. The experiments show that, for high concentrations (specific volume of scatterers ≥30%), interparticle interference of neutron waves plays a significant role and strongly affects the angular distribution of scattered neutrons. The experimental results are qualitatively explained within the framework of the theory allowing for pair correlations in the spatial distribution of scatterers.     

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.     

富勒烯-PVP聚合物链团结构的中子小角散射实验研究

应用中子小角散射技术研究了水溶液中富勒烯-PVP聚合物的链团结构及其大小以及它们在不 同富勒烯含量下的变化.结果表明：当加入富勒烯后，不论是PVP单体分子链还是大分子链团 ，其相关长度与纯PVP溶液相比均变小，且大分子链团的变化更为明显；在不同富勒烯含量 情况下，高富勒烯含量的富勒烯-PVP分子链团的体积更小. 关键词： 中子小角散射 富勒烯 PVP聚合物     

Vortex lattices in type-II superconductors studied by small-angle neutron scattering

Here we review recent small-angle scattering studies of the vortex lattice in a range of type-II superconductors carried out by our group. Emphasis is placed on providing examples of the kind of information which can be obtained by such measurements, focusing in particular on studies of the vortex lattice structure and form factor in LuNi₂B₂C, TmNi₂B₂C, CeCoIn₅ and Ba(Fe_0.93Co_0.07)₂As₂.     

Determining the structural parameters of fractal and nonfractal objects in multiple small-angle neutron scattering experiments

An experimental procedure employing setups with standard resolution characteristics for multiple small-angle neutron scattering in fractal and nonfractal media is described. Specific features of the proposed method, which are related to a limited resolution of the spectrometer, are considered in the case of large-scale inhomogeneities with the characteristic size exceeding the inverse spatial resolution. A new approach to the extraction of information about the fractal dimension of the system studied is demonstrated, which takes into account the dependence of the attenuation and broadening of the transmitted neutron beam on the sample thickness.     

Distribution of transport current in a type-II superconductor studied by small-angle neutron scattering

We report small-angle neutron scattering measurements on the vortex lattice in a PbIn polycrystal in the presence of an applied current. Using the rocking curves as a probe of the distribution of current in the sample, we observe that vortex pinning is due to the surface roughness. This leads to a surface current that persists in the flux-flow region. We show the influence of surface treatments on the distribution of this current.     

Detection of submicron-sized raft-like domains in membranes by small-angle neutron scattering

Using coarse grained models of heterogeneous vesicles we demonstrate the potential for small-angle neutron scattering (SANS) to detect and distinguish between two different categories of lateral segregation: 1) unilamellar vesicles (ULV) containing a single domain and 2) the formation of several small domains or “clusters” (~10 nm in radius) on a ULV. Exploiting the unique sensitivity of neutron scattering to differences between hydrogen and deuterium, we show that the liquid ordered (lo) DPPC-rich phase can be selectively labeled using chain deuterated dipalymitoyl phosphatidylcholine (dDPPC), which greatly facilitates the use of SANS to detect membrane domains. SANS experiments are then performed in order to detect and characterize, on nanometer length scales, lateral heterogeneities, or so-called “rafts”, in ~30 nm radius low polydispersity ULV made up of ternary mixtures of phospholipids and cholesterol. For 1:1:1 DOPC:DPPC:cholesterol (DDC) ULV we find evidence for the formation of lateral heterogeneities on cooling below 30 °C. These heterogeneities do not appear when DOPC is replaced by SOPC. Fits to the experimental data using coarse grained models show that, at room temperature, DDC ULV each exhibit approximately 30 domains with average radii of ~10 nm.     

Analysis of the structure of aqueous ferrofluids by the small-angle neutron scattering method

The structures of several aqueous magnetic fluids stabilized by different combinations of surfactants have been compared using small-angle neutron scattering. The size distribution functions of colloidal particles in water have been determined. The degree of clustering of magnetic nanoparticles has been obtained from comparison with electron microscopy data. The combinations of surfactants that lead to a minimum clustering have been revealed.     

Internal structures of agar-gelatin co-hydrogels by light scattering, small-angle neutron scattering and rheology

Internal structures of agar-gelatin co-hydrogels were investigated as a function of their volumetric mixing ratio, $\ensuremath r=[\mathrm{AG}]:[\mathrm{Ge}]=0.5Internal structures of agar-gelatin co-hydrogels were investigated as a function of their volumetric mixing ratio, [Formula: see text] , 1.0 and 2.0 using dynamic light scattering (DLS), small-angle neutron scattering (SANS) and rheology. The degree of non-ergodicity ( X = 0.2 ± 0.02) , which was extracted as a heterodyne contribution from the measured dynamic structure factor data remained less than that of homogeneous solutions where ergodicity is expected (X = 10. The static structure factor, I(q) , results obtained from SANS were interpreted in the Guinier regime (low-q , which implied the existence of ≈ 250 nm long rod-like structures (double-helix bundles), and the power law (intermediate-q regions) yielded I (q) ~ q(?α) with α = 2.3 , 1.8 and 1.6 for r = 0.5 , 1.0 and 2.0. This is indicative of the presence of Gaussian chains at low r , while at r = 2 there was a propensity of rod-shaped structures. The gel strength and transition temperatures measured from frequency sweep and temperature ramp studies were suggestive of the presence of a stronger association between the two biopolymer networks at higher r . The results indicate that the internal structures of agar-gelatin co-hydrogels were highly dependent on the volumetric mixing ratio.     

Comparative analysis of the nucleosome structure of cell nuclei by small-angle neutron scattering

The nucleosome structure in native nuclei of normal (chicken erythrocyte and rat leukocyte nuclei) and anomalously proliferating (the human cervical adenocarcinoma cell line HeLa and the Chinese hamster fibroblast cell line A238) cells has been investigated using small-angle neutron scattering. The experimental results obtained allow one to make the inference that the parameters of the nucleosome structure for the chicken erythrocyte and rat leukocyte nuclei (on average over the nucleus) are close to the universally accepted values and that the distance distribution function is bimodal. The bimodality of the distance distribution function reflects a narrow distribution of distances between nucleosomes (on average over the nucleus) at the fibril level of the chromatin organization. The histone core of the nucleosome structure in the nuclei of the HeLa and A238 cells (on average over the nucleus) is considerably less compact than that in the chicken erythrocyte and rat leukocyte nuclei, and the distance distribution function does not exhibit indications of the bimodality.     

Analysis of the spatial structure of rigid polyphenylene dendrimers by small-angle neutron scattering

The analysis of the spatial structure of a rigid polyphenylene dendrimer G4-M of fourth generation by small-angle neutron scattering (SANS) is presented. This dendrimer is composed of phenyl units and is therefore devoid of any flexible unit. The scattering intensity of dilute solutions of the dendrimer was measured by SANS at different contrast which was adjusted by mixtures of protonated and deuterated toluene. Hence, the method of contrast variation could be applied and the data yield the scattering function extrapolated to infinite contrast. The comparison of this data with simulations demonstrates that the scaffold of the dendrimer is rigid as expected from its chemical structure. The positions of the various units setting up consecutive shells of the dendrimer are relatively well localized and the entire structure cannot be modeled in terms of spherically symmetric models. No backfolding of the terminal groups can occur and the model calculations demonstrate that higher generations of this dendritic scaffold must exhibit a dense shell and a congestion of the terminal groups. This finding is directly corroborated by recent solid-state NMR data. All results show that the rigid dendrimer investigated here presents the first example for a dendritic structure whose segment density does not have its maximum at the center. Rigid scaffolds are therefore the only way to achieve the goal of a “dense-shell” dendrimer whereas flexible scaffolds leads invariably to the “dense-core” case.     

Precipitate characterisation in metallic systems by small-angle X-ray or neutron scattering

Small-angle scattering enables the extraction of precise, quantitative information about nano-scale precipitate microstructures. It can be used with X-rays (SAXS) or neutrons (SANS). This paper presents simple methods for extracting information on the precipitate size and volume fraction from SAS spectra. The various possibilities for obtaining precipitate size are reviewed, and the meaning of their differences is discussed. Examples of applications for complex precipitate microstructure measurements are given in the following areas: kinetic in-situ measurements in Fe–Cu and Fe–Nb–C alloys, non-stoichiometric precipitation in an Al–Zn–Mg–Cu alloy studied by anomalous SAXS (ASAXS), and precipitation mapping in weld cross-sections.     

Scaling in the aggregation behaviour of zinc-free insulin studied by small-angle neutron scattering

Summary The aggregation behaviour of zinc-free insulin has been studied by small-angle neutron scattering as a function of protein concentration,pH, and ionic strength of the solution. The distance distribution functions for the 12 samples have been obtained by indirect Fourier transformation. The weight-averaged molecular mass and thez-averaged radius of gyration were determined. Both quantities vary systematically with the experimental conditions. They increase with decreasingpH and with increasing ionic strength. The radius of gyration scales as a power law of the weight-average mass with the exponent 0.44. A similar scaling is found for a set of oligomers structures based on the crystal structure of zinc-free insulin. The mass distribution between the oligomers was determined by a model based on these oligomers. The results from this model and the Fourier transformations have been compared to an equilibrium model recently introduced by Kadimaet al. The model takes into account the variation of the effective charge of the monomer withpH and ionic strength. The neutron scattering results agree well with the predictions of the model. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Structure of phase-inversion membranes from small-angle neutron scattering data

The structure of gradient-porous (asymmetric) membranes based on polyamide imide at different conditions of their formation has been investigated using small-angle neutron scattering. It has been shown that the membranes consist of rigid porous networks with well-defined interfaces between the polymer and the pores. It has been found that there are differences in the packings of structural elements of porous membranes-spherical pores with radii from 4 to 100 nm—depending on the membrane preformation time, drying regime, and the presence of fullerene C₆₀ for modifying the mechanical and selective properties of membranes. The membranes also contain larger pores of micrometer sizes. Differences in the rates of saturation of membranes with water and their limiting swelling ratios are found, which can be explained by the structure of the dense layers of membranes (skin layer) and their different hydrophilities (depending on the fullerene content).     

Investigation of the microstructure of activated carbons by the small-angle slow neutron scattering method

The porosity characteristics of the SKT-3 activated carbon (both pure and impregnated with a specific impregnator that increases the carbon absorbability to iodine) have been studied using small-angle neutron scattering. It has been established that the impregnation with an impregnator slightly affects the porosity characteristics of the SKT-3 carbon. The average size of the scattering object is estimated as R ～ 500 Å.