Small-angle neutron scattering at fractal objects

The calculation of the correlation function of an isotropic fractal particle with the finite size ξ and the dimension D is presented. It is shown that the correlation function γ(r) of volume and surface fractals is described by a generalized expression and is proportional to the Macdonald function (D–3)/2 of the second order multiplied by the power function r ^(D–3)/2. For volume and surface fractals, the asymptotics of the correlation function at the limit r/ξ < 1 coincides with the corresponding correlation functions of unlimited fractals. The one-dimensional correlation function G(z), which, for an isotropic fractal particle, is described by an analogous expression with a shift of the index of the Macdonald function and the exponent of the power function by 1/2, is measured using spin-echo small-angle neutron scattering. The boundary case of the transition from a volume to a surface fractal corresponding to the cubic dependence of the neutron scattering cross section Q ^?3 leads to an exact analytical expression for the one-dimensional correlation function G(z) = exp(?z/ξ), and the asymptotics of the correlation function in the range of fractal behavior for r/ξ < 1 is proportional to ln(ξ/r). This corresponds to a special type of self-similarity with the additive law of scaling rather than the multiplicative one, as in the case of a volume fractal.     

Small-angle neutron scattering from micellar solutions

Micellar solutions are the suspension of the colloidal aggregates of the sur-factant molecules in aqueous solutions. The structure (shape and size) and the interaction of these aggregates, referred to as micelles, depend on the molecular architecture of the surfactant molecule, presence of additives and the solution conditions such as temperature, concentration etc. This paper gives the usefulness of small-angle neutron scattering to the study of micellar solutions with some of our recent results.     

Small-angle neutron scattering investigation of the nanostructure of ferritic-martensitic 12%-chromium steels

The nanostructure (nanoparticle distribution) of ferritic-martensitic 12%-chromium steels EK-181 (Fe-12Cr-2W-V-Ta-B) and ChS-139 (Fe-12Cr-2W-V-Ta-B-Nb-Mo) subjected to different modes of mechanical and heat treatments and neutron irradiation has been investigated using small-angle neutron scattering. The samples have been studied in the initial state and after neutron irradiation (IVV-2M reactor) at a temperature of 80°C with fluences of 10¹⁸, 10¹⁹, and 5 × 10¹⁹ cm^?2 (E ≥ 0.1 MeV). The nanostructure of the steels is characterized by precipitations of nanoparticles with two characteristic sizes of 1.0–1.5 and 7–8 nm. The dependence of the nanostructure parameters on the composition of the steels and on the conditions of heat treatment and irradiation has been discussed.     

Small-angle neutron spin-flip scattering in ferromagnetic films

This paper reports on the results of reflectometric measurements of anisotropic (Co₆₇Fe₃₁V₂) and almost isotropic (Fe) films prepared by magnetron sputtering. Nonspecular reflections and the corresponding peaks of the intensities of refracted neutrons have been observed for the alloy samples in magnetic fields H ≤ 7 Oe applied in the film plane along the easy magnetization axis. For iron films, angular splitting of the reflected neutron beam becomes observable only at H > 100 Oe and increases with an increase in the magnetic field. A general scheme has been proposed for this small-angle scattering with allowance made for different variants of changes in the Zeeman energy of neutrons. This scheme has allowed us to identify the magnetic structures of Co-Fe films. The magnetization of 0.15-μm-thick films with uniaxial and unidirectional textures leads to the formation of unidirectional textures characterized by different intensity distributions, for which the qualitative differences are retained with an increase in the magnetic field from 7 to 800 Oe. It has been revealed that, for 2.5-μm-thick films with the initial unidirectional texture, the oppositely magnetized states are nonequivalent.     

Small-angle neutron scattering study of dynamically polarized polyethylenes

We carried out a small-angle neutron scattering (SANS) study of dynamically polarized polyethylene (PE) samples doped with 2,2,6,6-tetramethylpiperidine 1-oxyl (TEMPO). The transmission of the PE with almost fully polarized neutrons (98.5%) increased with increasing the proton polarization, P. The incoherent scattering cross section decreased with increasing P. The effect of P on the polarized neutrons’ transmission and the incoherent scattering cross section agreed well with the theory. The q-dependence of the coherent scattering, which reflects a two-phase structure of PE composed of crystalline and amorphous domains, was kept unchanged by the proton polarization, but the intensity increased by a factor of 3 and 6 for P=+23% and −23%, respectively. The results mean that the contrast between the two phases was successfully enhanced by a dynamic nuclear polarization (DNP) technique. However, the enhancement is only 1/13–1/16 of the enhancement calculated by assuming a homogeneous polarization through the PE sample. The discrepancy suggests that P in amorphous domains (25%) should be higher than that in crystalline domains (22%) by 3%, which in turn may suggest the partial depolarization of proton spins on the way of the spin diffusion from amorphous domains, where TEMPO radicals localize, to crystalline domains.     

Small-angle neutron scattering studies of nonionic surfactant: Effect of sugars

Micellar solution of nonionic surfactantn-dodecyloligo ethyleneoxide surfactant, decaoxyethylene monododecyl ether [CH₃(CH₂)₁₁(OCH₂CH₂)₁₀OH], C₁₂E₁₀ in D₂O solution have been analysed by small-angle neutron scattering (SANS) at different temperatures (30, 45 and 60° C) both in the presence and absence of sugars. The structural parameters like micelle shape and size, aggregation number and micellar density have been determined. It is found that the micellar structure significantly depends on the temperature and concentration of sugars. The micelles are found to be prolate ellipsoids at 30° C and the axial ratio of the micelle increases with the increase in temperature. The presence of lower concentration of sugar reduces the size of micelles and it grows at higher concentration of sugar. The structure of micelles is almost independent of the different types of sugars used.     

Small-angle neutron and dynamic light scattering study of gelatin coacervates

The state of intermolecular aggregates and that of folded gelatin molecules could be characterized by dynamic laser light and small-angle neutron scattering experiments, which implied spontaneous segregation of particle sizes preceding coacervation, which is a liquid-liquid phase transition phenomenon. Dynamic light scattering (DLS) data analysis revealed two particle sizes until precipitation was reached. The smaller particles having a diameter of ～50 nm (stable nanoparticles prepared by coacervation method) were detected in the supernatant, whereas the inter-molecular aggregates having a diameter of ～400 nm gave rise to coacervation. Small-angle neutron scattering (SANS) experiments revealed that typical mesh size of the networks exist in polymer dense phase (coacervates) [1]. Analysis of the SANS structure factor showed the presence of two length scales associated with this system that were identified as the correlation length or mesh size, ξ = 10.6 Å of the network and the other is the size of inhomogeneities = 21.4 Å. Observations were discussed based on the results obtained from SANS experiments performed in 5% (w/v) gelatin solution at 60°C (ξ = 50 Å, ζ = 113 Å) and 5% (w/v) gel at 28°C (ξ = 47 Å, ζ = 115 Å) in aqueous phase [2] indicating smaller length scales in coacervate as compared to sol and gel.     

Small-angle neutron scattering in aqueous solutions of fullerene-containing oligopropylene oxides

Propylene-oxide oligomers in heavy water (their molecular mass is ～500, and the concentration C varies from ～0.6 to 5.0 g/dL) and similar systems with C₆₀ and C₇₀ fullerenes and C₆₀(OH) _x fullerenols (x ～ 20), i.e., functionalized oligopropylene oxides, are studied via small-angle neutron scattering. The initial oligomers are found to create spherical micelles (～40 molecules) in the solution. It is ascertained that, in oligopropylene-oxide solutions, the C₆₀, C₇₀, and C₆₀(OH) _x derivatives (～1 wt % of fullerene relative to the oligomer) modify its molecular organization, acting as physical bonds whereby micelles are joined into large-scale linear, twisted, and branched chain superstructures.     

Small-angle neutron scattering studies of aqueous solutions of short-chain amphiphiles

We present small angle neutron scattering measurements on binary aqueous solutions of some short-chain amphiphiles (diols, triols, glycols and diglycols) at room temperature. The spectra were analysed in terms of the Teubner-Strey phenomenological formula which allows to obtain a measure for the amphiphilicity strength of each system (amphiphilicity factor f _a). In some systems, however, other models, valid for micellar solutions, give also a good representation of the spectra. As a result, we find that, independently of the type of hydrophilic group side (oxydrilic or oxirane), these systems cover the entire accessible amphiphilicity scale ( -1 < f _a < 1). Some disordered systems ( f _a > 1) presumably are able to form micelle-like aggregates. Received 12 June 2002 Published online: 16 April 2003 RID="a" ID="a"e-mail: giovanni.darrigo@uniroma1.it     

Small-angle neutron scattering contrast variation on magnetite-myristic acid-benzene magnetic fluid

A magnetic fluid with magnetite dispersed in D-benzene and stabilized by myristic acid is investigated using the contrast variation technique in small-angle neutron scattering. The results obtained are interpreted within a new approach to the basic functions for polydisperse multicomponent and superparamagnetic systems. Myristic acid is considered an alternative to oleic acid, which is commonly used in these fluids. The parameters characterizing the particle size distribution function and the thickness of the myristic acid layer are determined. The data obtained are in good agreement with the results derived from previous investigations with the use of polarized neutrons.     

Small-angle neutron scattering study on the cold rolled steel sheets

The effect of cold rolling on the small-angle neutron scattering (SANS) pattern was investigated for low-carbon steels. Several cold rolled steel samples with different reduction ratios and annealed samples after cold rolling were respectively measured by SANS. The cold rolled samples presented anisotropic two-dimensional (2D) SANS patterns. From the 2D SANS patterns two kinds of 1D pattern were calculated: one was for the Q⊥RD (rolling direction), the other for the Q//RD. The scatterer sizes calculated from the 1D patterns by using a model fitting increased with the reduction ratio, for the Q⊥RD section only. The annealed sample presented an isotropic SANS pattern. It can be concluded that the dislocations produced during the cold rolling process accumulated around the precipitates and then caused anisotropic 2D SANS patterns.     

Small-angle neutron scattering study of radiation defects in synthetic quartz

The superatomic structure of synthetic quartz single crystals with dislocation densities ρ = 54 and 570 cm^?2 was studied in the initial state and after irradiation with fast neutrons with energies E _n > 0.1 MeV in a WWRM reactor (St. Petersburg Nuclear Physics Institute) in the fluence range F = 0.2 × 10¹⁷?5.0 × 10¹⁸ neutrons/cm². Weak irradiation with F = 0.2 × 10¹⁷ neutrons/cm² causes only slight structural changes, whereas appreciable generation of defects with radii of gyration r _g ～ 1–2 nm and R _G ～ 40–50 nm occurs at F = 7.7 × 10¹⁷?5.0 × 10¹⁸ neutrons/cm². As the fluence increases further, the number and volume fraction of point defects, as well as extended (channels ～2 nm in radius) and globular (amorphous phase nuclei) defects, increase.     

Small-angle neutron scattering of nanocrystalline terbium with random paramagnetic susceptibility

We report magnetic small-angle neutron scattering (SANS) data for the nanocrystalline rare earth metal Terbium in its paramagnetic state. Whereas critical scattering dominates at large momentum transfer, q, the (magnetic-) field response of the scattering at small q arises from the spatial nonuniformity of the paramagnetic susceptibility tensor. The finding of an interrelation between SANS and the susceptibility suggests a way for characterizing the nonuniform magnetic interactions in hard magnets by neutron scattering.     

Two-dimensional spatially ordered system of nickel nanowires probed by polarized SANS

Structural and magnetic properties of two-dimensional spatially ordered system of ferromagnetic nickel nanowires embedded into Al₂O₃ matrix have been studied using polarized small-angle neutron scattering. The small-angle diffraction pattern exhibits many diffraction peaks, which corresponds to the scattering from highly correlated hexagonal structure of pores and magnetic nanowires. Magnetic contribution to the scattering has complex behavior and cannot be explained without taking into account stray fields located between magnetized nanowires.     

Small-angle neutron scattering by fractal clusters in aqueous dispersions of nanodiamonds

We considered how the choice of a model affects the treatment of data of small-angle neutron scattering by aqueous dispersions of detonation nanodiamonds. The scattering curves were analyzed using a general approach that combines the structure of nanodiamonds, the fractal organization of their clusters, and the interaction of clusters. The effect of the interaction between clusters on scattering was treated within the Guinier approximation.     

Contours of constant phonon energies in thebc-plane of sapphire (Al2O3) by means of inelastic neutron scattering

By means of inelastic neutron scattering the contoursv=const. have been determined for the transverse acoustic phonon branch which is polarized in the mirror plane (bc-plane). The results show that in all directions effects of dispersion can be neglected forq0.5q _max.     

XRD and Mössbauer spectroscopy investigation of Fe2O3–Al2O3 nano-composite

Fe₂O₃–Al₂O₃ nano-composites were synthesized by sol–gel means. The properties of samples sintered at various thermal treatment temperatures were investigated by X-ray diffraction (XRD) and Mössbauer spectroscopy (MS). The experimental results show that the γ- to α-Al₂O₃ transformation occurs at lower temperature after iron oxide doping. The samples obtained at 1173 K contained poorly crystallized γ-Al₂O₃ phase and an amorphous iron oxide. When the temperature of heating was increased to 1373 K, the sample was composed of α-Fe₂O₃/α-Al₂O₃ nano-composite and some solid solution. A superparamagnetic phenomenon was observed until the thermal treatment temperature reached 1373 K.