M. Theo Rekveldt

Novel SANS instrument using Neutron Spin Echo

Abstract Following a recent report by Keller et al. in Neutron News 6, no. 3 (1995), the application of neutron spin echo as a small angle neutron scattering instrument (SESANS) using dc magnetic fields is discussed. The principle is based on the difference in Larmor precession angle in a coil with changing transmission angle, caused by scattering from a sample. A scattering object between two identical coils with opposite precessions causes depolarisation. The latter as a function of the precession field yields a real space correlation function. A modification of this principle of SESANS is introduced enabling to suppress the contribution of inelastic scattering, which changes the precession angle too. The application of this technique is very promising for systems with large correlation lengths and may enable one to measure time dependent effects in correlation lengths with a time resolution of a few seconds. The latter corresponds to the time needed to measure a complete spectrum from which a correlation function in real space is derived.

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.

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.

Optimization of neutron scattering instrumentation using neutron spin echo: Application to the discrimination of diffuse scattering in neutron reflectivity experiments

We describe a method, based on the neutron spin-echo technique, to achieve good resolution in many neutron-scattering experiments, without sacrificing signal intensity. By “good resolution” we do not mean the ∼10−6 energy resolution usually associated with neutron spin-echo spectrometers, but rather the level of resolution traditionally obtained by collimation or monochromatization of neutron beams, often on specialized instruments, and almost always at some penalty in measured intensity. The method we discuss allows good resolution to be achieved in any chosen direction in the vector space defined by the neutron scattering wave vector, Q, and the energy transfer, E. Although the method has general applicability to many neutron scattering measurements, we discuss in detail its application to the problem of separating diffuse scattering from specular reflection in neutron reflectometry. The technological basis of the method is the availability of thin films of magnetic or easily magnetizable material that ...

Neutron reflectometry and SANS by neutron spin echo

Abstract The application of neutron spin echo as a small-angle neutron scattering instrument (SESANS) using DC magnetic fields is discussed. Its principle is based on the difference in Larmor precession angle in a coil system with changing transmission angle. A scatterer between two identical coils with opposite precessions causes depolarisation. The latter as a function of the precession field yields a real space correlation function. A modification of this principle of SESANS implemented into a polarised neutron reflectometer using a linear position-sensitive detector, is proposed, which enables one to measure with a full divergent beam. From two measurements with zero and maximum spin-echo field, the fraction of off-specular reflection can be determined at each point of the detector. Moreover, from a field-dependent measurement the full correlation function of the roughness perpendicular to the sample plane causing the off-specular reflection can be determined, when desired also in a direction with the momentum transfer in the plane of the sample by rotating the spin-echo coils over 90°. The sensitivity of SESANS is up to the micron range.

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.

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.

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 ...

Spin-echo small-angle neutron scattering in neutron reflectometry

A new method to perform neutron reflectometry measurements is discussed. The method is based on Larmor precession of polarized neutrons in the spin-echo mode. Two different modes of application are discussed, giving successively information about the structure perpendicular to and parallel to the sample plane. After describing the method, simulated results of the perpendicular mode are compared with those obtained by conventional neutron reflectometry methods. In this comparison, first the results obtained by the SESANS method are translated to those obtained by conventional methods. After that, more specific applications of the new method are considered. In the comparison, attention is focused on measuring statistics and resolution as readily comparable quantities.