Spin-echo Small-angle Neutron Research Articles

Resolution, truncation and smearing of the one-dimensional spin echo small-angle scattering instrument

The resolution of the spin echo small-angle neutron scattering (SESANS) instrument is limited by the precession Larmor fields and by the wavelength of the neutrons. It can reach to about a micrometer with thermal neutrons and to a few tens of micrometers with cold neutrons. Since a SESANS instrument will have a limited coverage in scattering angles or in neutron momentum transfers, there will be truncation errors in the measured correlation functions. These truncation errors increase with smaller scattering particles and they limit the smallest particle that can be effectively studied by the instrument. The off-plane scatterings in one-dimensional SESANS as well as the inhomogeneity of the precession fields cause smearing effects in the correlation functions. Desmearing procedures developed for the traditional small-angle scattering instruments can be used to restore the true parameters of the scattering particle.

Model calculations for the spin-echo small-angle neutron-scattering correlation function

Spin-echo small-angle neutron scattering (SESANS) is a new kind of SANS technique enabling measurements to be made directly in real space from a range of a few nanometres up to micrometres. In this paper it is shown by calculations on models that SESANS measures correlations directly. Furthermore, the effect of polydispersity and structure factor has been studied. An exact expression for the correlation function has been derived in the case of random systems, such as fractal systems.

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 functionG(Z), the meaning of which was unknown until now. Here a direct real-space interpretation ofG(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 ofG(Z) for non-interacting solid spheres, hollow spheres and Gaussian coils are derived. The case of solid spheres is compared with experimental data.

Magnetised foils as ?-flippers in spin-echo spectrometry

The use of π-flippers for correction of line integrals in Larmor-precession devices is described. The π-flippersconsist of magnetised foils of the proper thickness, magnetised by the field of the precession device itself. Application of such π-flippers in a spin-echo small angle neutron scattering set-up with fields perpendicular and parallel to the beam direction is discussed. It appears that such flippers avoid corrections for the inhomogeneity of the field-line integrals, for the main part, in both options.

First quantitative test of spin-echo small-angle neutron scattering

Spin-echo small-angle neutron scattering of dilute dispersions of mono-disperse polystyrene spheres is measured. The spheres have radii of 60 and 100 nm. The measurements agree well in shape and absolute intensity with calculations. Multiple scattering is significant in these experiments and is easily taken into account. This is the first time that quantitative analysis of real-space small-angle neutron scattering is possible. The calculations show that this technique will have most applications in systems with strong scattering, which usually implies larger length scales.

Magnetic design of a spin-echo small-angle neutron-scattering instrument

In a spin-echo small-angle neutron scattering instrument dipole magnets and guide field coils are used. The homogeneity of the fields should be sufficient to have linear labeling of the height with precession. Furthermore, the instrument must have a homogenous line integral over the beam cross-section. It is shown that line integral inhomogeneities are directly connected to field components perpendicular to the main field. The design parameters of these magnetic units of the setup are calculated.

Magnetized foils as π flippers in neutron spin-echo spectrometry

In neutron spin-echo spectrometry Larmor precession regions are used, in which the homogeneity of the field line integrals along the neutron paths play an essential role. In the application of this technique for small-angle scattering, the transmission angle encoding happens by strong precession gradients in a certain direction in a magnetic field. Here the use of magnetized foils as π flippers will be discussed. They appear to compensate very efficiently for field line inhomogeneities and moreover they create an effectively strong gradient in Larmor precession, needed for the small-angle scattering application. The π flippers consist of magnetized foils of the proper thickness, magnetized by the field of the precession devices itself. Application of such π flippers in a spin-echo small angle neutron scattering setup with fields perpendicular and parallel to the beam direction is discussed. It appears that such flippers avoid corrections for the inhomogeneity of the field line integrals for the main part in both options.

Concepts in spin echo small-angle neutron scattering

Two-dimensional spin echo small-angle neutron scattering experiments that measure the vector-length distribution function, or pair-distance distribution function, in real space are discussed. The proposed diffractometer uses two cylindrically symmetric magnetic fields with conically shaped front and end faces to enable experiments in two dimensions. It also features a π/2 neutron spin flipper to make the effective analyzing direction of the analyzer perpendicular to the polarizing direction of the polarizer. The theoretical aspect of one-dimensional spin echo small-angle neutron scattering experiments is also explored. The relationship between the correlation function from one-dimensional experiments and the vector-length distribution function is established, and interpretation of this correlation function in real space is presented.

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

A good polarization of the neutron beam is required for the spin-echo small-angle neutron scattering (SESANS) instrument. SESANS is a novel kind of small-angle neutron scattering (SANS) technique. The measured quantity in a SESANS experiment is the depolarization of the neutron beam due to elastic scattering by a sample. The amount of precession of a neutron along a path is proportional to the line integral of the magnetic field intensity along this path. The inhomogeneities in the magnetic field intensity due to fringing of the magnetic field lines near the magnet edges give rise to line integral differences. This causes extra depolarization that decreases the sensitivity of the instrument. The requirement on the homogeneity of the line integral is calculated. In first order, the line integral increases quadratically towards the magnet poles. This quadratic increase is compensated by correction coils which have an opposite quadratic dependence.

Test of magnetised foils as a polarisation rotator for a spin echo small-angle neutron scattering instrument

Magnetised foils are used as a polarisation rotator for a spin echo small-angle neutron scattering instrument (a novel technique to measure SANS in direct space). To find out which foil is suitable for this instrument, we made different foils and layers and tested them with depolarisation measurements in the neutron beam.

Spin-echo small-angle neutron scattering calculations

The expected signal for spin-echo small-angle neutron scattering experiments are calculated for a dilute system of particles consisting of concentric spherical shells. The calculations show that the signals are directly sensitive to the structure of the particles.

An analysis of magnetic field inhomogeneities in a spin-echo small-angle neutron scattering instrument

In a spin-echo small-angle neutron scattering instrument homogeneity of the magnetic field is of great importance. The maximum allowable variation of the magnetic field is calculated using a model whereby an inhomogeneity only in the vertical direction is taken into account.