Extended flexibility of neutron Larmor diffraction for increased diffraction range in mosaicity measurements

Magnetised foils as white beam π/2 flippers for polarised neutrons

Spin echo small-angle neutron scattering (SESANS) is a novel technique that measures correlation functions in real space. Recent theoretical study on SESANS has enabled the interpretation of this correlation function. It has also revealed the range of applications and limitations of the SESANS technique. On a two-dimensional SESANS instrument, the experimental correlation function is the pair-distance distribution function of the scattering particle. On a one-dimensional instrument, the correlation function is an integral function of the pair-distance distribution function. SESANS is suitable for studying particles from a nanometer to a few tens of micrometers in size, a range that is similar to that covered by the traditional Bonse-Hart ultra-small-angle neutron scattering instrument. The greatest advantage of SESANS lies in the fact that it can use divergent neutron beams, thus drastically increasing the counting rate. The resolution of a SESANS instrument is limited by the integrated Larmor precession field and by the neutron wavelength. Because any SESANS instrument will have a limited momentum transfer coverage, truncation errors can result in the measured correlation functions. The effect of the inhomogeneity of the Larmor field can be handled as smearing. On a one-dimensional SESANS instrument, the off-plane scatterings also result into smearing effects.

Spin-echo small angle neutron scattering (SESANS) provides a new experimental tool for structural investigation. Due to the action of spin-echo encoding, SESANS measures a spatial correlation function in real space, as opposed to the structure factor S(Q), I(Q), in momentum (Q) space measured by conventional small angle neutron scattering. To establish the usefulness of SESANS in structural characterization, particularly for interacting colloidal suspensions, we have previously conducted a theoretical study of the SESANS correlation functions for model systems consisting of particles with uniform density profiles [X. Li, C.-Y. Shew, Y. Liu, R. Pynn, E. Liu, K. W. Herwig, G. S. Smith, J. L. Robertson, and W.-R. Chen J. Chem. Phys. 132, 174509 (2010)]. Within the same framework, we explore in the present paper the prospect of using SESANS to investigate the structural characteristics of colloidal systems consisting of particles with nonuniform intraparticle mass distribution. As an example, a Gaussian model of interacting soft colloids is used to investigate the manifestation of structural softness in a SESANS measurement. The exploration shows a characteristically different SESANS correlation function for interacting soft colloids, in comparison to that of a uniform hard sphere system. The difference arises from the Abel transform imbedded in the mathematical formalism bridging the SESANS spectra and the spatial autocorrelation function.

Using a neutron scattering technique that measures a statistically-averaged density correlation function in real space rather than the conventional reciprocal-space structure factor, we have measured correlations between poly(methyl-methacrylate) (PMMA) colloidal particles of several sizes suspended in decalin. The new method, called Spin Echo Small Angle Neutron Scattering (SESANS) provides accurate information about particle composition, including the degree of solvent penetration into the polymer brush grafted on to the PMMA spheres to prevent aggregation. It confirms for particles, between 85 nm and 150 nm in radius that inter-particle correlations closely follow the Percus-Yevick hard-sphere model when the colloidal volume-fraction is between 30% and 50% provided the volume-fraction is used as a fitted parameter. No particle aggregation occurs in these systems. When small amounts of polystyrene are added as a depletant to a concentrated suspension of PMMA particles, short-range clustering of the particles occurs and there is an increase in the frequency of near-neighbor contacts. Within a small range of depletant concentration, near-neighbor correlations saturate and large aggregates with power law density correlations are formed. SESANS clearly separates the short- and long-range correlations and shows that, in this case, the power-law correlations are visible for inter-particle distances larger than roughly two particle diameters. In some cases, aggregate sizes are within our measurement window, which can extend out to 16 microns in favorable cases. We discuss the advantages of SESANS for measurements of the structure of concentrated colloidal systems and conclude that the method offers several important advantages.

Line integral corrections in spin-echo small angle neutron scattering instrument

A novel spin echo small-angle neutron scattering (SESANS) concept based on a rotationally symmetric magnetic field geometry is introduced. The proposed method is similar to the conventional linear SESANS technique but uses longitudinal precession fields and field gradients in a radial direction, as typically found in neutron spin echo (NSE) spectrometers. Radial SESANS could thus be implemented as an add-on to NSE setups. The neutron trajectory through the instrument is encoded with the help of radial gradients generated by radial shifters, which are coils placed in the beam area similar to Fresnel coils. The present work introduces the setup of the instrument and explores its performance and the relationship between the encoded momentum transfer and the precession angle. The results indicate that radial SESANS is only sensitive to scattering along the radial direction and thus measures the projected correlation function along this direction as a function of the spin echo length, defined similarly to linear SESANS. For an evaluation of the performance of the setup, the case of scattering from solid spheres is considered and the results calculated for the radial and linear SESANS cases are compared. Also discussed is the implementation of the radial magnetic field geometry in spin echo modulated small-angle neutron scattering.

Structural insights into soft matter materials via spin echo small angle neutron scattering and small angle neutron scattering

Several single-modal Debye correlation functions to approximate part of the overall Debey correlation function of liquids are closely examined for elucidating their behavior in the corresponding spin echo small angle neutron scattering (SESANS) correlation functions. We find that the maximum length scale of a Debye correlation function is identical to that of its SESANS correlation function. For discrete Debye correlation functions, the peak of SESANS correlation function emerges at their first discrete point, whereas for continuous Debye correlation functions with greater width, the peak position shifts to a greater value. In both cases, the intensity and shape of the peak of the SESANS correlation function are determined by the width of the Debye correlation functions. Furthermore, we mimic the intramolecular and intermolecular Debye correlation functions of liquids composed of interacting particles based on a simple model to elucidate their competition in the SESANS correlation function. Our calculations show that the first local minimum of a SESANS correlation function can be negative and positive. By adjusting the spatial distribution of the intermolecular Debye function in the model, the calculated SESANS spectra exhibit the profile consistent with that of hard-sphere and sticky-hard-sphere liquids predicted by more sophisticated liquid state theory and computer simulation.

The application of the spin-echo small angle neutron scattering (SESANS) technique for structural characterization of interacting colloidal suspensions is considered in this work. The framework to calculate the theoretical SESANS correlation function is briefly laid out. A general discussion regarding the features of the SESANS correlation functions obtained from different model systems is presented. In comparison with conventional elastic scattering tools operating at the same length scale, our mean-field calculations, based on a monodisperse spherical colloidal system, show that the real-space measurement provided by SESANS presents a powerful probe for studying the intercolloid potential. The reason of this sensitivity is discussed from the standpoint of way, in which how the spatial correlations are manifested in different neutron scattering implementations. This study leads to a better understanding regarding the distinction between SANS and SESANS.

The results of the first experiments with a spin-echo small-angle neutron scattering (SESANS) device built at the VVR-M reactor at the St. Petersburg Institute of Nuclear Physics (Gatchina) are presented. SESANS utilizes the possibilities of the spin-echo method for determining the structural characteristics of materials in real space with on the 10–104-nm length scale. Validation measurements are conducted using SiO2 colloidal particles. Samples of SiO2 spheres with a diameter determined through scanning electron microscopy and synchrotron-radiation ultra-small-angle scattering are used for calibration of the device. Approximation of the data obtained with the SESANS device was conducted using the autocorrelation function for dilute monodisperse spheres. The sizes of the spheres determined via SESANS are in agreement with those determined by other methods within the experimental error.

Structure of hard-sphere colloid observed in real space by spin-echo small-angle neutron scattering

Spin-echo small-angle neutron scattering (SESANS) technique is a method to measure the correlation function of the structural organization of materials from nano- to micrometer length scales. As this method does not require neither highly collimated beams nor high incident intensity it can be easily and effectively used at the low flux sources, such as compact accelerator-driven neutron sources. Here we describe an important science case for SESANS setup designed at the compact neutron source DARIA. It was shown that SESANS method is a sensitive tool to study the packaging of DNA in the nuclei of biological cells. The sensitivity of the SESANS signal crucially depends on the neutron wavelength. The pulse character of the compact neutron source suits ideally to these investigations as it implies changeable neutron wavelength in the range from 0.2 to 1.0 nm. Such option allows one to study in great detail the internal structure of the biological cell in the length scale from 10 nm to 100 μm.

We discuss the present status and the prospects of Spin-Echo Small-Angle Neutron Scattering (SESANS) against the background of the available expertise and the neutron source PIK at PNPI (Gatchina). Two options for SESANS instruments are reviewed: (1) monochromatic with π-flipping permalloy foils and (2) with adiabatic radio frequency spin flippers in a white beam, combined with time-of-flight data collection. A software tool for quantitative prediction of the technical properties of option (2) is developed. For both options, we show that a SESANS instrument which can compete with instruments elsewhere, is realistic. For option (2), we suggest a perspective of spin-echo-length range such that neutron interference experiments become feasible.

SESANS studies of colloid phase transitions, dairy products and polymer fibres

Spin-echo small-angle neutron scattering (SESANS) is a real-space [1] scattering technique that does not need any collimation to obtain high resolution. In this article, we present the SESANS instrument at the Delft University of Technology [2], which measures microstructures on length scales between 20 nm and 20 μm. In order to discuss the technical issues with the choice of precession devices, we will present the principle in this article in reciprocal space. We have applied the technique to a wide variety of samples, amongst which are colloidal phase transitions [3] and aggregation processes in dairy products [4]. In this article we show two other examples: artificial lattices [5] and cream cheese [6].