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.     

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.     

The microstructure of hydrogen- and deuterium-doped nanocrystalline palladium studied by small-angle neutron scattering

By means of small-angle neutron scattering the microstructure of two nanocrystalline Pd samples (prepared by inert gas condensation) has been studied at room temperature in a Q-range from [0pt] to [0pt] . An additional subsequent doping of the two samples with H as well as with D (concentrations < 4 at%) caused contrast variations that provided more detailed structural information. The measured scattering intensity was modeled by a Porod contribution from large heterogenities (e.g. pores) and a contribution from spherical grains with a log-normal distribution of their radii. To account for the presence of grain boundaries, the grains were considered to be surrounded by a shell with a reduced Pd density and a thickness half as large as the thickness of the grain boundaries. For the above model, the data of the H-doped, D-doped and undoped sample were simultaneously fitted with one single set of adjustable parameters. The fits yielded for the two samples volume-weighted mean grain radii of 10 nm and 13 nm. The values for the grain boundary thickness lie between 0.2 and 0.8 nm. Almost all of the H- and D-atoms are, at low hydrogen concentrations, located in the grain boundaries. Received 1 May 2000     

The magnetic behaviour of CeAl2 studied by neutron scattering

Diffuse neutron scattering experiments with unpolarized neutrons in zero field have been performed on a CeAl₂ single crystal in the temperature range 2.5 K to 300 K. At the lowest temperature we observe collective excitations in the system. At higher temperatures the energy spectra can be analysed in terms of quasielastic and inelastic lines due to the crystal field splitting of the Ce ions.     

Scaling concept applied to the defect formation caused by interactions between melittin and phosphatidylcholine (PC) model membranes

Summary A simple computer model of defection process caused by interactions between melittin and phosphatidylcholine (PC) model membrane has been proposed. It leads to a scaling formula which connects the average diameter (or linear size parameter) of the affected domain with the reciprocity of the number of such domains. Some preliminary investigations show the scaling exponent to be a small fractional number between ca. 0.3 and 0.1, depending on the number of possible infection directions and the type of lattice taken as a lipid matrix. Such small values of the scaling exponent can roughly be interpreted in terms of random tesselations on a plane (like random Voronoi networks), and the whole process displays a statistical self-similarity. The values obtained seem to be, however, small comparable to the scaling exponents characteristic for the faulting process occurring during the earthquake propagation. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Laser light scattering in micellar solutions

Summary The laser light scattering apparatus used for both total intensity and quasi-elastic light scattering experiments on micellar solutions is described in detail. The absolute calibration of the scattered intensity is obtained by exploiting the existence of a lower critical consolution point in a low-concentration aqueous solution of a nonionic amphiphile (C₁₂E₈). The obtained results suggest that micellar solutions may represent a very convenient light scattering standard for both static and dynamic experiments. Paper presented at the “Meeting on Lyotropics and Related Fields”, held in Rende, Cosenza, September 13—18, 1982.     

Elastic properties of polymer-doped dilute lamellar phases: A small-angle neutron scattering study

We investigate experimentally, using small-angle neutron scattering the elastic properties of polymer-doped dilute lamellar phases. In our system the polymer is water-soluble but nevertheless partially adsorbs onto the negatively charged surfactant bilayers. The effective polymer-mediated interaction between bilayers is less repulsive than the weakly screened electrostatic interaction that prevails at zero polymer content. It even becomes attractive in some regions of the phase diagram. Small-angle neutron scattering allows us to measure directly the Caillé exponent η characterizing the bilayer fluctuations in lamellar (smectic A) phases, and thus indirectly estimate the compression modulus as a measure of the strength of the bilayer-bilayer interactions. The compression modulus appears to be vanishing at a point located on the lamellar-lamellar phase separation boundary, a candidate critical point. Received: 7 August 2000     

Self—assembly behaviour of amphiphilic diblock copolymer in selective solvents studied by synchrotron small—angle x—ray scattering

The aggregation behaviour of styrene-vinyl benzoic acid (PS_m-b-PVBA_n) amphiphilic diblock copolymers in selective solvents with different m and n was investigated by synchrotron small-angle x-ray scattering (SAXS). We have carried out a detailed analysis of scattering intensity, dimension, shape and microstructure of the diblock copolymers of narrow distribution in water, methanol, ethanol and isopropanol selective solvents, respectively. We have found that the aggregation behaviour of the copolymer depends on the nature of the solvent and the micelle forms flat disc objects with the ratio of radius ω=0.4. The average radius gyration R_g of the copolymer decreases as solvents change from isopropanol to ethanol and to methanol, and increases with increasing pH in aqueous solution, but decreases with the addition of CoCl_2 in ethanol solvent. The scattering intensity of diblock copolymer micelle follows I(h)∝h^{-α} in different selective solutions, suggesting that the PS_m-b-PVBA_n coils have self-similar structure behaviour or a fractal structure in the selective solvents. All of these revealed that the aggregation behaviour of the diblock copolymer changes dramatically with experimental condition in the selective solvent. The increase of mass fractal dimension (D_m) from 2.12 to 2.47 indicates that the copolymer chain changes from a swollen coil to a rather compact disc in the course of changing solvents, decreasing surface fractal dimension (D_s) from 2.98 to 2.58 indicates that the copolymer micelle change from a rather rough surface to a smooth form in the course of increasing pH in aqueous solutions, and increasing D_m and D_s from 2.29 to 2.35 and 2.70 to 2.90, respectively, indicates the shrinkage of copolymer micelle to a rather compact and rough disc form by adding CoCl_2 in ethanol solvents.     

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.     

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     

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.     

Longitudinal polarization analysis in small-angle neutron scattering

Due to recent progress in the development of ³He spin filters, it has only now become possible to perform routinely longitudinal (one-dimensional) neutron-spin analysis (POLARIS) in small-angle neutron scattering (SANS) experiments. It is the purpose of this article to provide a brief introduction into the technique and to discuss first experimental data. In particular, for the most common scattering geometry where the applied magnetic (guide) field is perpendicular to the incident neutron beam, we write down the equations for the non-spin-flip and spin-flip SANS cross sections of a bulk ferromagnet, and we discuss the various angular anisotropies and asymmetries along with some selected experimental results on an FeCr based soft magnetic nanocrystalline alloy. In particular, we show that the analysis of the spin-flip data allows one to obtain the magnitude-squares of the three vector (Fourier) components of the magnetization.     

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.     

Erratum to: Structural aspects of human lactoferrin in the iron-binding process studied by molecular dynamics and small-angle neutron scattering

The European Physical Journal E - Until recently, natural gas encountered in tight shales, which provided the source and seal of the gas, was considered uneconomical to produce. Although...     

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.     

Ti-Mo合金氢化物微观缺陷的小角X射线散射研究

采用小角X射线散射(SAXS)方法对Ti-Mo合金氢化物的微观缺陷进行了研究.结果表明,氢化物样品中Mo含量为5at％时,所测定的SAXS强度在高散射角区明显低于其他样品的SAXS强度.氢化物中的晶粒及其内部的亚结构是引起SAXS现象的散射体,而这些亚结构是由合金氢化时引入的大量位错所产生.Mo 含量为5at％合金主要为hcp结构而其他合金为bcc结构,但两种合金氢化后都成为fcc结构的氢化物.据此,认为hcp结构与bcc结构Ti-Mo合金在氢化时氢化物结构相同但引入的位错缺陷特征不同. 关键词： Ti-Mo合金氢化物 小角X射线散射 微观缺陷     

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)     

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.