Polarization-analyzed small-angle neutron scattering. II. Mathematical angular analysis

2012 ◽  
Vol 45 (3) ◽  
pp. 554-565 ◽  
Author(s):  
Kathryn Krycka ◽  
Julie Borchers ◽  
Yumi Ijiri ◽  
Ryan Booth ◽  
Sara Majetich
Keyword(s):  
Neutron Scattering ◽  
Small Angle ◽  
Small Angle Neutron Scattering ◽  
Magnetic Moments ◽  
Magnetic Scattering ◽  
Directional Sensitivity ◽  
Angular Analysis ◽  
Structural Contribution ◽  
Anisotropic Systems ◽  
Simplified Procedures

Polarization-analyzed small-angle neutron scattering (SANS) is a powerful tool for the study of magnetic morphology with directional sensitivity. Building upon polarized scattering theory, this article presents simplified procedures for the reduction of longitudinally polarized SANS into terms of the three mutually orthogonal magnetic scattering contributions plus a structural contribution. Special emphasis is given to the treatment of anisotropic systems. The meaning and significance of scattering interferences between nuclear and magnetic scattering and between the scattering from magnetic moments projected onto distinct orthogonal axes are discussed in detail. Concise tables summarize the algorithms derived for the most commonly encountered conditions. These tables are designed to be used as a reference in the challenging task of extracting the full wealth of information available from polarization-analyzed SANS.

A small-angle neutron scattering model for polydisperse spherical particles with diffusion zones and application to soft magnetic metallic glass

2000 ◽  
Vol 33 (6) ◽  
pp. 1386-1392 ◽  
Author(s):  
André Heinemann ◽  
Helmut Hermann ◽  
Albrecht Wiedenmann ◽  
Norbert Mattern ◽  
Klaus Wetzig
Keyword(s):  
Neutron Scattering ◽  
Small Angle ◽  
Small Angle Neutron Scattering ◽  
Scattering Length ◽  
Spherical Particles ◽  
Magnetic Scattering ◽  
Soft Magnetic ◽  
Polarized Neutrons ◽  
Regression Procedure ◽  
Polarized Neutron Scattering

An analytical expression for the small-angle neutron scattering intensity of diluted systems of polydisperse spherical particles, with diffusion zones, embedded in a matrix is presented. It is used within a nonlinear regression procedure to analyse small-angle neutron scattering experiments with polarized neutrons on an Fe73.5Si15.5B7CuNb3alloy. The results for the nuclear and magnetic scattering length densities allow verification of the inhibitor concept introduced for the explanation of the limited sizes of precipitates developing during nanocrystallization. In the case of amorphous Fe73.5Si15.5B7CuNb3alloy, the observed nanocrystals of the Fe3Si type are surrounded by an Nb-enriched shell, which stops the growth of the precipitates. With the results of polarized neutron scattering experiments, it is shown that magnetic and nuclear small-angle neutron scattering signals have the same origin. Additionally, the precision of the fits is improved by complementary use of polarized neutrons.

scholarly journals Multiple magnetic scattering in small-angle neutron scattering of Nd–Fe–B nanocrystalline magnet

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Tetsuro Ueno ◽  
Kotaro Saito ◽  
Masao Yano ◽  
Masaaki Ito ◽  
Tetsuya Shoji ◽  
...  
Keyword(s):  
Neutron Scattering ◽  
Small Angle ◽  
Small Angle Neutron Scattering ◽  
Magnetic Scattering

Small-angle neutron scattering analysis of a water-based magnetic fluid with charge stabilization: contrast variation and scattering of polarized neutrons

2009 ◽  
Vol 42 (6) ◽  
pp. 1009-1019 ◽  
Author(s):  
Mikhail V. Avdeev ◽  
Emmanuelle Dubois ◽  
Guillaume Mériguet ◽  
Elie Wandersman ◽  
Vasil M. Garamus ◽  
...  
Keyword(s):  
Neutron Scattering ◽  
Magnetic Fluid ◽  
Small Angle ◽  
Small Angle Neutron Scattering ◽  
Scattering Length ◽  
Magnetic Scattering ◽  
Contrast Variation ◽  
Polarized Neutrons ◽  
Scattering Length Density ◽  
Charge Stabilization

Structure analysis of a magnetic fluid (nanoparticles of maghemite dispersed in water with charge stabilization and without surfactant) by means of small-angle neutron scattering is presented. A combination of the contrast variation technique and scattering of polarized neutrons was applied. In the first case, the scattering curves obtained for the unmagnetized fluid with variation of the heavy water content in the carrier are treated in terms of the basic functions approach. The almost homogeneous character of the nanoparticles with respect to the nuclear scattering length density makes it possible to separate information about their characteristic nuclear and magnetic radii. Polarized neutrons are then used to separate and analyze independently the nuclear and magnetic scattering contributions for the fully magnetized fluid. Both methods reveal a significant excess of the apparent nuclear size over the magnetic one, which is explained by a difference in the nonmagnetic and magnetic interactions in the system. The results indicate that from the viewpoint of magnetic interaction the studied fluid behaves under a magnetic field as a purely superparamagnetic system of independent particles. The magnetic scattering length density of the maghemite nanoparticles is found to be ∼25% less than the bulk value, which is in agreement with the data of the magnetization analysis.

Structure of water-based ferrofluids with sodium oleate and polyethylene glycol stabilization by small-angle neutron scattering: contrast-variation experiments

2010 ◽  
Vol 43 (5) ◽  
pp. 959-969 ◽  
Author(s):  
Mikhail V. Avdeev ◽  
Artem V. Feoktystov ◽  
Peter Kopcansky ◽  
Gabor Lancz ◽  
Vasil M. Garamus ◽  
...  
Keyword(s):  
Polyethylene Glycol ◽  
Neutron Scattering ◽  
Sodium Oleate ◽  
Small Angle ◽  
Small Angle Neutron Scattering ◽  
Colloidal Particles ◽  
Micelle Formation ◽  
Magnetic Scattering ◽  
Contrast Variation ◽  
Water Based

Contrast variation in small-angle neutron scattering (SANS) experiments is used to compare the structures of a water-based ferrofluid, where magnetite nanoparticles are stabilized by sodium oleate, and its mixture with biocompatible polyethylene glycol, PEG. The basic functions approach is applied, which takes into account the effects of polydispersity and magnetic scattering. Different types of stable aggregates of colloidal particles are revealed in both fluids. The addition of PEG results in a reorganization of the structure of the aggregates: the initial comparatively small and compact aggregates (about 40 nm in size) are replaced by large (more than 120 nm in size) fractal-type structures. It is postulated that these large structures are composed of single magnetite particles coated with PEG, which replaces sodium oleate. Micelle formation involving free sodium oleate is observed in both fluids. The structures of the fluids remain unchanged with increasing temperature up to 343 K. New and specific possibilities of SANS contrast variation with respect to multicomponent systems with different aggregates are considered.

Evaluation of Nanosize NbC Precipitates in HSLA Steel through Microstructural Analysis and Small Angle Neutron Scattering

2018 ◽  
Vol 941 ◽  
pp. 141-146
Author(s):  
Haruo Nakamichi ◽  
Katsumi Yamada ◽  
Kaneharu Okuda ◽  
Toshinori Ishida ◽  
Masato Ohnuma
Keyword(s):  
Neutron Scattering ◽  
Small Angle ◽  
Small Angle Neutron Scattering ◽  
Hsla Steel ◽  
Microstructural Analysis ◽  
Magnetic Scattering ◽  
Precipitate Size ◽  
Steel Matrix ◽  
Orientation Relationships ◽  
Hardening Mechanism

Nano size precipitate morphologies are very important for considering the precipitate hardening mechanism of HSLA steels. Systematic analysis of precipitates from nano scale to bulk scale were carried out using Nb bearing hot rolled steels through transmission electron microscopy (TEM) observations and chemical analysis of precipitates by solvent extraction. A small angle neutron scattering (SANS) experiment was also performed using a Hokkaido Univ. compact neutron source to understand average precipitate size. Results show that both changes in hardness and the amount of precipitates (under 20nm in size) have the same tendency. Precipitate is recognized as NbC plates, which have coherency with the steel matrix by Baker-Nutting orientation relationships. A row of precipitates, formed on the interface between austenite and ferrite during transformation, is also apparent. The SANS profile shows that small size precipitate formation is detected even though the amount of precipitation is small. In addition, the magnetic scattering component of the SANS profile has high sensitivity to NbC precipitates compared with that of the nucleus scattering component. By comparing precipitate data from comprehensive experiments, we consider the relationship between precipitate behavior and the hardening mechanism.

scholarly journals Critical Consideration of Precipitate Analysis of Fe–1 at.% Cu Using Atom Probe and Small-Angle Neutron Scattering

2010 ◽  
Vol 17 (1) ◽  
pp. 26-33 ◽  
Author(s):  
M. Schober ◽  
E. Eidenberger ◽  
P. Staron ◽  
H. Leitner
Keyword(s):  
Neutron Scattering ◽  
Small Angle ◽  
Small Angle Neutron Scattering ◽  
Volume Fraction ◽  
Search Algorithm ◽  
Atom Probe ◽  
Magnetic Scattering ◽  
Model Alloy ◽  
Chemical Compositions ◽  
Heat Treated

AbstractAn Fe–1 at.% Cu model alloy was examined by atom probe (3DAP) and small-angle neutron scattering (SANS) to verify the accordance of the gained results. The Fe-Cu alloy was heat-treated for various times at 500°C, forming Cu-rich precipitates within the Fe matrix. The chemical compositions of the precipitates and matrix found by 3DAP were used to calculate the magnetic scattering contrast. Additionally, a magnetic moment of the precipitates that contain a significant amount of Fe was taken into account for the calculation of magnetic scattering contrast. This in turn is used for the evaluation of the magnetic scattering curves gained by SANS. Both the 3DAP data as well as the scattering curves were analyzed with regard to radius, number density, and volume fraction of the precipitates as a function of aging time. The results yielded by both techniques are in good agreement and correspond to the development of the hardness of the alloy. Minor differences can be related to the cluster search algorithm used for the analysis of the 3DAP data as well as Fe overestimation based on different field phases.

Spin-echo small-angle neutron scattering for magnetic samples

2006 ◽  
Vol 39 (2) ◽  
pp. 252-258 ◽  
Author(s):  
Sergey V. Grigoriev ◽  
Wicher H. Kraan ◽  
M. Theo Rekveldt ◽  
Timofey Kruglov ◽  
Wim G. Bouwman
Keyword(s):  
Neutron Scattering ◽  
Small Angle ◽  
Small Angle Neutron Scattering ◽  
Spin Echo ◽  
Real Space ◽  
Magnetic Scattering ◽  
Neutron Spin ◽  
Magnetic Contribution ◽  
Nuclear Scattering ◽  
Density Correlation

A novel real-space scattering technique, spin-echo small-angle neutron scattering for magnetic samples, is described. Previously, this method has been exploited for non-magnetic samples only, in order to measure the nuclear density correlation function. Magnetic scattering is different from nuclear scattering as in the former a partial neutron spin-flip that affects the phase accumulation of the Larmor precession occurs just at the moment of scattering. Because of this intrinsic property of magnetic scattering, one can use a magnetic sample as a flipper in the spin-echo technique. This enables the separation of the magnetic contribution from other sources of scattering. Particular features of the technique are pointed out. Some model examples are considered. The similarity and the differences of magnetic SESANS with respect to the technique of three-dimensional neutron depolarization are discussed. The theoretical description is proven by experiments.

scholarly journals A Small Angle Neutron Scattering Investigation of the Kinetics of Phase Separation in an Fe-27.5 AT.% Cr-5.6 AT.% Ni Alloy

1990 ◽  
Vol 205 ◽  
Author(s):  
J. E. Epperson ◽  
V. S. Rainey ◽  
C. G. Windsor ◽  
K. A. Hawick ◽  
Haydn Chen
Keyword(s):  
Neutron Scattering ◽  
Small Angle ◽  
Small Angle Neutron Scattering ◽  
Magnetic Scattering ◽  
Diffuse Maximum ◽  
Dynamical Scaling ◽  
Peak Intensity ◽  
Ni Alloy ◽  
Dependent Component

AbstractThe small angle neutron scattering has been investigated in situ at 450° and 500°C for a polycrystalline, duplex Fe-27.5 at.% Cr - 5.6 at.% Ni steel. A broad diffuse maximum in the scattering function is the signature of the α' phase formation, and this maximum is superimposed on a strong, temperature-dependent component due mainly to critical magnetic scattering. The time dependence of the shift in the peak intensity position to lower scattering vectors and the increase in peak intensity obey power law scaling behavior. Furthermore, the structure function exhibits dynamical scaling, after about three hours annealing. It is suggested that this behavior could be utilized to predict the microstructure, and hence some of the properties, after significantly longer annealing times.

scholarly journals Magnetic scattering in the simultaneous measurement of small-angle neutron scattering and Bragg edge transmission from steel

2016 ◽  
Vol 49 (5) ◽  
pp. 1659-1664 ◽  
Author(s):  
Yojiro Oba ◽  
Satoshi Morooka ◽  
Kazuki Ohishi ◽  
Nobuhiro Sato ◽  
Rintaro Inoue ◽  
...  
Keyword(s):  
Neutron Scattering ◽  
Small Angle ◽  
Simultaneous Measurement ◽  
Small Angle Neutron Scattering ◽  
Microstructural Characterization ◽  
Magnetic Scattering ◽  
Nuclear Scattering ◽  
Steel Microstructure ◽  
Scattering Contribution ◽  
Pure Cu

Pulsed neutron sources enable the simultaneous measurement of small-angle neutron scattering (SANS) and Bragg edge transmission. This simultaneous measurement is useful for microstructural characterization in steel. Since most steels are ferromagnetic, magnetic scattering contributions should be considered in both SANS and Bragg edge transmission analyses. An expression for the magnetic scattering contribution to Bragg edge transmission analysis has been derived. The analysis using this expression was applied to Cu steel. The ferrite crystallite size estimated from this Bragg edge transmission analysis with the magnetic scattering contribution was larger than that estimated using conventional expressions. This result indicates that magnetic scattering has to be taken into account for quantitative Bragg edge transmission analysis. In the SANS analysis, the ratio of magnetic to nuclear scattering contributions revealed that the precipitates consist of body-centered cubic Cu0.7Fe0.3and pure Cu, which probably has 9R structure including elastic strain and vacancies. These results show that effective use of the magnetic scattering contribution allows detailed analyses of steel microstructure.

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