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 Molière’s theory. Prospects of the development of this method are outlined, and MSANS theory is formulated for a high concentration of matter inhomogeneities.     

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.     

Diffraction limit of the theory of multiple small-angle neutron scattering by a dense system of scatterers

Multiple small-angle neutron scattering by a high-density system of inhomogeneities has been considered. A combined approach to the analysis of multiple small-angle neutron scattering has been proposed on the basis of the synthesis of the Zernike–Prince and Moliére formulas. This approach has been compared to the existing multiple small-angle neutron scattering theory based on the eikonal approximation. This comparison has shown that the results in the diffraction limit coincide, whereas differences exist in the refraction limit because the latter theory includes correlations between successive scattering events. It has been shown analytically that the existence of correlations in the spatial position of scatterers results in an increase in the number of unscattered neutrons. Thus, the narrowing of spectra of multiple small-angle neutron scattering observed experimentally and in numerical simulation has been explained.     

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.     

Spin correlations and a mesoscopic structure in Ni-Mn-Ga

The mesoscopic structures of the Heusler alloys Ni_49.1Mn_29.4Ga_21.5 and Ni₂MnGa are studied by small-angle polarized neutron scattering in the temperature range 15 < T < 400 K. The characteristic temperatures of phase transformations (ferromagnetic, martensitic, and premartensitic transformations) and the characteristic sizes of mesoscopic inhomogeneities in them have been determined. Differences in the spin dynamics of these phases and magnetic-nuclear interference upon neutron scattering have been revealed. The evolutions of the mesoscopic structures in the nonstoichiometric and stoichiometric alloys are found to be substantially different.     

Multiple small-angle neutron scattering for an arbitrary value of the born parameter

Computer calculations are made of the intensity of multiple small-angle neutron scattering using the general Moliére formula [8] over a wide range of variation of the Born parameter, embracing the diffraction and refraction regimes, and a transition region between diffraction and reflection. A comparison is made with approximate formulas obtained earlier by Maleev et al. [9, 10] in the limiting cases of the Born parameter α ? 1 and α ? 1 for the diffraction and refraction regimes, respectively. It is shown that over a wide range of values of α the results of the calculations using the approximate and general formulas are the same. The theoretical conclusions were checked experimentally using data from measurements of small-angle neutron scattering for the domain structure of ferromagnets. Measurements were made of the neutron beam broadening for samples of different thickness and these were used to determine the effective domain sizes in pure iron and nickel exposed to thermal treatment and plastic deformation, and also in the Invar alloys Fe⁶⁵Ni³⁵and Fe³Pt. An analysis is made of the angular dependence of magnetic small-angle neutron scattering at the asymptote.     

Mesoscopic magnetic inhomogeneities in the low-temperature phase and structure of Sm1−x SrxMnO3 (x < 0.5) perovskite

Results are presented of studies of the ¹⁵⁴Sm_1?x Sr_xMnO₃ system using neutron powder diffraction and small-angle polarized neutron scattering. An analysis of the neutron diffraction spectra showed that at T < 180 K these exhibit typical Jahn-Teller distortions of the manganese-oxygen octahedrons which persist under further cooling and on transition of the sample to a metallic magnetically ordered state. The magnetic contribution to the diffraction is satisfactorily described using the (A _x (A _y )F _z ) model and is interpreted as the coexistence of ferromagnetic and antiferromagnetic phases. The exaggerated widths of the diffraction lines indicate an appreciable contribution from microdeformations evidently associated with the inhomogeneity of the system. Small-angle polarized neutron scattering showed that the Sm system for x = 0.4 and 0.25 is magnetically inhomogeneous in the low-temperature phase. Ferromagnetic correlations occur on scales of around 200 Å and having dimensions greater than 1000 Å which, combined with the temperature hysteresis of the magnetic small-angle scattering intensity observed for an x = 0.4 sample in the low-temperature phase, suggests that the transition is of a percolation nature.     

Description of small-angle neutron scattering data for nickel–chromium–aluminum alloy within quantum mechanics and classic polydisperse sphere model

The modified Yukawa potential is used to fit the nucleus model parameters to the data on small-angle neutron scattering on nickel—chromium—aluminum alloy for the product of the transferred momentum Q and the effective nucleus radius R, satisfying the condition QR ≤ ?. The analytical polydisperse sphere model is used to calculate the neutron scattering intensity and to determine the most probable macroscopic sphere radius R ₀ at QR ₀ ≥ 3?.     

Studying the structural features of oxide nanoclusters of cerium and titanium in a silicate glass by means of the small-angle neutron scattering

The features of the formation of Ce-Ti-O complex oxide nanoclusters in a silicate glass are studied by means of the small-angle neutron scattering technique. It is found that bounded regions of density fluctuation of the glass material are formed in the initial glass matrix without the addition of titanium and cerium oxides. These regions could serve as nucleation centers for oxide clusters of cerium and titanium upon their introduction into the matrix. The calculated average size of these inhomogeneities does not exceed 30 ± 1 nm, and their surface volume equals 0.72 ± 3 nm³. A structural mechanism for Ce-Ti-O oxide formation in a silicate glass, in which the nanoclusters are formed within a bounded region of glass material inhomogeneities at low concentrations of the initial cerium oxide (CeO₂), is proposed. At high cerium oxide concentrations, oxide nanocluster growth occurs predominantly on the surface of these inhomogeneities. This leads to a sharp change in the nanocluster sizes and their fractal dimension.     

Investigation of the closed porosity of functional ceramic materials by spin-echo small-angle neutron scattering

The closed porous structure in ceramic materials is investigated by spin-echo small-angle neutron scattering. A series of ceramic samples of oxygen–ion conductors based on bismuth molybdate with the general formula Bi_12.8 X _0.2Mo₅O_{34 ± δ} (X = Mg, Ba, Ca, Sr) is obtained by powder sintering for 6?45 h at a temperature close to the melting point. The samples are characterized by scanning electron microscopy and X-ray fluorescence analysis. It is found that they had a stoichiometric chemical composition, are singlephase, and contain clean pores between crystal grains. The pore size is determined by spin-echo small-angle neutron scattering and ranges from 2.2 to 3.5 μm. It is demonstrated that longer sintering times correspond to larger pores (the increase in their average diameter is as large as 30%). It is found that the studied materials lack a fractal pore structure.     

Long-wavelength magnetic excitations in the Zn0.55Mn0.45Fe2O4 ferrite

The small-angle neutron scattering energy spectra of the Zn_0.55Mn_0.45Fe₂O₄ ferrite are analyzed at different temperatures (both below and above T _C ? 390 K) and scattering angles. The thermal expansion coefficient α(T) is measured in the temperature range 80–600 K. It is revealed that inelastic neutron scattering is governed not only by spin waves of the Holstein-Primakoff type but also by the substantial contribution of additional long-wavelength magnetic excitations. The physical nature of these low-energy magnetic excitations is discussed.     

Study of the heavy-fermion compound CeRu<Subscript>2</Subscript>Si<Subscript>2</Subscript> by the small-angle neutron scattering method

In order to directly observe neutron scattering by heavy fermion quasiparticles at low temperatures, a CeRu₂Si₂ single crystal has been studied by the small-angle neutron scattering method. In the experiment, neutron scattering is observed at T = 0.85 K for momentum transfers q ≤ 0.04 Å^?1, which is treated as the orbital component of magnetic scattering by heavy fermion quasiparticles. It has been found that the application of a magnetic field H = 1 T leads to both an increase in the observed scattering and its anisotropy with respect to the field direction. Moreover, measurements in the magnetic field reveal additional scattering for q > 0.04 Å^?1, which is well described by a Lorentzian and is interpreted as neutron magnetic scattering by spin-density fluctuations with a correlation radius R_c ≈ 30 Å.     

Specific features of neutron scattering upon heat treatment of the Co67Fe31V2 alloy

This paper reports on the results obtained from small-angle neutron scattering investigations during annealing of two plates of the Co₆₇Fe₃₁V₂ alloy under heating the first and second samples to 360 and 500°C, respectively, as well as in applied weak magnetic fields (H ≈ 3 Oe). To elucidate the role of the vanadium impurity, measurements have also been performed on the Co₆₈F₃₂ alloy. It has been revealed using neutron diffraction that, at temperatures below 360°C, the Fe and Co atoms begin to undergo ordering in the samples, which results in a change in the space group of the crystal structure. With an increase in the temperature, a fine-dispersed phase is formed in the Co₆₇Fe₃₁V₂ alloy, which leads to a qualitative change in the small-angle neutron scattering pattern. It has been found that, after annealing and magnetization (H > 4 kOe) of the second sample, there is a strong difference in the integrated intensities of scattered neutrons for opposite directions of their spins in the primary beam.     

Small-angle neutron scattering and the Mössbauer effect in nitrogen austenite

Small-angle neutron scattering (SANS) in Fe-19%Cr-19%Mn-0.9%N and Fe-18%Cr-10%Mn-16%Ni-0.5%N (wt %) high-nitrogen austenites is investigated. The neutron diffraction patterns and Mössbauer spectra are measured and analyzed. The SANS curves are approximated in the framework of the Guinier and Porod models. The nature of small-angle neutron scattering in nitrogen austenite is explained in terms of microinhomogeneities whose structure depends on the alloying with nickel. The mean size and shape of inhomogeneities are evaluated. The effect of low-temperature annealing of the Fe-19%Cr-19%Mn-0.9%N austenite on small-angle neutron scattering and the parameters of the Mössbauer spectra is analyzed.     

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.     

Atomic and superatomic structures of solid solutions of zirconium and calcium oxides

Solid solutions of the ZrO₂-CaO system with 7, 9.6, and 20 mol % of calcium oxide are analyzed by X-ray and neutron diffraction and small-angle neutron scattering. Samples are synthesized by the sol-gel method and annealed at the temperature T = 600°C for 4 h. All samples have a tetragonal structure (P4₂/nmc space group). The size of crystallites is 10–20 nm. Small-angle neutron scattering curves are characterized by a peak near the momentum transfer q = 0.5 nm⁻¹. The existence of the peak is caused by correlation between solid nanoparticles in the samples. Density correlation functions are numerically computed from the experimental small-angle scattering cross-sections by the inverse Fourier transform. Correlation lengths, concentrations of scattering nanoparticles, and specific surface areas of the samples are determined.     

Studies of the structure of defects in In4Se3 crystals by small-angle neutron scattering

Small-angle neutron scattering is used to study the layered semiconductor In₄Se₃. It is observed that the samples contain inhomogeneities of colloidal dimensions, which are attributed to the precipitation of indium. Annealing reduces the concentration of inhomogeneities. Modeling the system using an ensemble of primary spherical inhomogeneities showed that a single cluster of a rectangular superlattice (2-2-6) contains 24 primary inhomogeneities of radius 13.5±1,5 Å and the distance between them is 70.9±1.5 Å.     

XRR and GISAXS study of silicon oxynitride films

Thin films of silicon oxynitride have largely replaced pure silicon oxide films as gate and tunnel oxide films in modern technology due to their superior properties in terms of efficiency as boron barrier, resistance to electrical stress and high dielectric strength. A single chamber system for plasma enhanced chemical vapor deposition was employed to deposit different films of SiO_xN_yH_z with 0.85 < x < 1.91. All films were previously characterized by Rutherford back-scattering and infrared spectroscopy to determine the stoichiometry and the presence of various bonding configurations of constituent atoms. We used X-ray reflectivity to determine the electron density profile across the depth, and we showed that the top layer is densified. Moreover, grazing incidence small-angle X-ray scattering was used to study inhomogeneities (clustering) in the films, and it is shown that plate-like inhomogeneities exist in the top and sphere-like particles at the bottom part of the film. Their shape and size depend on the stoichiometry of the films.