Wim G. Bouwman

Spin-echo small angle neutron scattering in Delft

We describe two spin-echo instruments for neutron small angle scattering, which have been installed at the reactor institute in Delft. The first setup is using a monochromatic beam and magnetized foils as spin flippers, while the second uses resonant spin flippers in a pulsed neutron beam. The components that play an essential role for operation are described in some detail. Each setup has specific advantages in its range of spin-echo lengths that covers the range of correlation lengths that could be measured. This is demonstrated in a comparative measurement, the setup with magnetized foils measuring at spin-echo-lengths up to 20 μm and the setup with resonant flippers measuring in the range up to 0.5 μm.

Real-space interpretation of spin-echo small-angle neutron scattering

Spin-echo small-angle neutron scattering (SESANS) is a novel real-space scattering technique. SESANS measures a correlation-like function G(Z), the meaning of which was unknown until now. Here a direct real-space interpretation of G(Z) through the particle scattering density and pair correlation function is given. One-dimensional and two-dimensional SESANS are compared. The case of non-interacting particles is considered in detail with an explicit geometrical interpretation. General methods for the calculation of structural parameters, such as the total scattering length and the radius of gyration, are developed. Analytical expressions of G(Z) for non-interacting solid spheres, hollow spheres and Gaussian coils are derived. The case of solid spheres is compared with experimental data.

Analysis of spin‐echo small‐angle neutron scattering measurements

Spin-echo small-angle neutron scattering (SESANS) is, in contrast to conventional small-angle neutron scattering (SANS), a real-space technique. SESANS measures the projection of the density–density correlation function of a sample, rather than, as in SANS, its Fourier transform. This paper introduces a toolkit for interpretion and analysis of a SESANS measurement. Models that are used in SANS are discussed and translated into a SESANS formalism. These models can be used to analyse and fit the data obtained by SESANS. Dilute, concentrated, random, fractal and anisotropic density distributions are considered. Numerical methods used to calculate the projection from numerical data are presented, either by using Fourier transformation or via the real-space pair correlation function.

Double stacking faults in convectively assembled crystals of colloidal spheres.

Using microradian X-ray diffraction, we investigated the crystal structure of convectively assembled colloidal photonic crystals over macroscopic (0.5 mm) distances. Through adaptation of Wilsons theory for X-ray diffraction, we show that certain types of line defects that are often observed in scanning electron microscopy images of the surface of these crystals are actually planar defects at 70.5 degrees angles with the substrate. The defects consist of two parallel hexagonal close-packed planes in otherwise face-centered cubic crystals. Our measurements indicate that these stacking faults cause at least 10% of stacking disorder, which has to be reduced to fabricate high-quality colloidal photonic crystals.

Structural transitions of hard-sphere colloids studied by spin-echo small-angle neutron scattering

The structure of hard-sphere colloidal suspensions is measured at different concentrations using the recently developed spin-echo small-angle neutron scattering (SESANS) technique. It is shown that SESANS measures real-space correlations ranging from the size of a single particle for a dilute suspension to several particle diameters for a concentrated suspension, glass and crystalline state.

Fabrication of artificial opals by electric-field-assisted vertical deposition.

We present a new technique for large-scale fabrication of colloidal crystals with controllable quality and thickness. The method is based on vertical deposition in the presence of a DC electric field normal to the conducting substrate. The crystal structure and quality are quantitatively characterized by microradian X-ray diffraction, scanning electron microscopy, and optical reflectometry. Attraction between the charged colloidal spheres and the substrate promotes growth of thicker crystalline films, while the best-quality crystals are formed in the presence of repulsion. Highly ordered thick crystalline layers with a small amount of stacking faults and a low mosaic spread can be obtained by optimizing the growth conditions.

Development of spin-echo small-angle neutron scattering

A polarised neutron spin echo technique is used to build a novel kind of small angle neutron scattering (SANS) instrument. The basis of this instrument is a symmetric set-up with a spin flipper in the centre, which creates a spin echo, even with a divergent beam. The precession regions on either side of the spin flipper are shaped such as to produce a very sensitive relation between the vertical angle of the neutron path and the total precession angle. Any SANS of a sample placed in the instrument reduces the symmetry of the neutron path and therefore decreases the echo. Magnetised foils define the precession regions by rotating the neutron spin from being parallel to the magnetic field to perpendicular to the field, to start the precession. These foils and the flipper were built and tested. A spin echo SANS signal is measured with the complete set-up . It should be possible with this technique to measure within minutes a full correlation function in samples over distances from 5 to 1000 nm.

Multidimensional Nature of Fluidized Nanoparticle Agglomerates

We show that fluidized nanoparticle agglomerates are hierarchical fractal structures with three fractal dimensions: one characterizing sintered aggregates formed during nanoparticle synthesis, one that is also found in stored agglomerates and represents unbroken agglomerates, and one describing the large agglomerates broken during fluidization. This has been possible by using spin-echo small-angle neutron scattering-a relatively novel technique that, for the first time, allowed to characterize in situ the structure of fluidized nanoparticle agglomerates from 21 nm to ∼20 μm. The results show that serial agglomeration mechanisms in the gas phase can generate nanoparticle clusters with different fractal dimensions, contradicting the common approach that considers fluidized nanoparticle agglomerates as single fractals, in analogy to the agglomerates formed by micron-sized particles. This work has important implications for the fluidization field but also has a wider impact. Current studies deal with the formation and properties of clusters where the building blocks are particles and the structure can be characterized by only one fractal dimension. However, fluidized nanoparticle agglomerates are low-dimensional clusters formed by higher-dimensional clusters that are formed by low-dimensional clusters. This multifractality demands a new type of multiscale model able to capture the interplay between different scales.

Long-range ordering in anodic alumina films: A microradian X-ray diffraction study

A quantitative analysis of long-range order in the self-organized porous structure of anodic alumina films has been performed on the basis of a microradian X-ray diffraction study. The structure is shown to possess orientational order over macroscopic distances larger than 1 mm. At the same time, the interpore positional order is only short-range and does not extend over more than � 10 interpore distances. These positional correlations are mostly lost gradually rather than at the domain boundaries, as suggested by the divergence of the peak width for the higher-order reflections. In the direction of the film growth the pores have a very long longitudinal self-correlation length of the order of tens of micrometres.

Phase-object approximation in small-angle neutron scattering experiments on silicon gratings

The phase-object approximation for neutron scattering based on a one-dimensional dynamic forward scattering theory is discussed and used to calculate the differential cross section of an object. It is shown that this approximation is valid in ultra-small-angle neutron scattering (USANS) and spin-echo small-angle neutron scattering (SESANS) experiments on silicon gratings. In the weak scattering limit, the phase-object approximation reduces to the kinematic or first Born approximation. The spatial coherence function is used to describe instrumental resolution effects. Measurements on three different instruments are in good agreement with calculation results. In the experiment with a time-of-flight SESANS instrument, the effect of Pendellosung with object size is observed.