V.O. de Haan

Genetic algorithms used in model finding and fitting for neutron reflection experiments

Abstract A fitting procedure based on genetic algorithms is described. This procedure is used to find scattering length density profiles that correspond to measured neutron reflectivity data. It gives parameters of a model that fits the data, without any a priori knowledge about the sample. It can give different parameter sets of a model, that yield equally good fits to the data, which stresses the nonuniqueness of the solutions.

ROG, the neutron reflectometer at IRI, Delft

Abstract A description is given of an optimally designed neutron reflectometer. The background to the design is explained, calibration measurements are discussed and data handling procedures are described. Finally, the possibilities of the reflectometer are shown with several reflectivity measurements.

Observation of the Zeeman splitting for neutrons reflected by magnetic layers

Abstract The Zeeman splitting was measured for neutrons specularly reflected from a magnetic layer in a particular geometry. The neutron spins were quantized along an external magnetic field H, and the reflecting layer was magnetized in a different direction, causing some of the reflected neutrons to flip spin. The laws of conservation of energy and momentum for the spin-flipped neutrons impose the condition θf2 = θi2 ± 1.47 × 10−7 Hλ2, where θi, θf are, respectively, the incident and reflected angles in radians, H is expressed in kOe and λ (the neutron wavelength) in A. Spin-flipped neutrons are reflected at an angle significantly different from the angle of incidence even in fields of a few kOe, although the Zeeman splitting energy amounts to less than 10−7 eV.

ROG, the new neutron reflectometer at IRI, Delft

Abstract A description is given of the neutron reflectometer ROG, recently installed at IRI. The neutron wavelength is determined by time of flight. Wavelengths from 0.08 to 0.8 nm can be used. First experimental results are presented.

Testing a multilayer mirror system in use for polarised neutrons

Abstract The transmission of a curved system of multilayers is investigated theoretically as well as experimentally. The new feature of this work is the consideration of different indices of reflection on both sides of the mirrors. It appears that the experimental result is systematically by about 30% lower as theoretically expected, which most probably is due to the imperfect planeness of the mirror.

On the use of a multilayer monochromator in neutron reflectometry

Abstract In neutron reflectometry experiments, the intensity reflected from the sample under investigation is determined as a function of the wave-vector transfer. One way of doing this is to start with a monochromatic beam and perform the so-called θ/2θ scans. The monochromatic beam can be produced by Bragg reflection from a single crystal, or from a multilayer system. In this paper, we experimentally investigate the performance of a multilayer monochromator. We demonstrate that the large-wavelength contamination, intrinsically present, may lead to large errors in the obtained reflectivity at large values of the wave-vector transfer.

The average number of reflections in a curved neutron guide

Abstract Analytic expressions are given for the average number of both garland and zigzag reflections for trajectories through a curved guide as a function of wavelength. Expressions are obtained for cases when the concave surface and the convex surface of the guide have the same and different coatings.

Dynamical theory: Application to spin-echo resolved grazing incidence scattering from periodic structures

Neutron spin-echo resolved grazing incidence scattering (SERGIS) measurements performed on a silicon diffraction grating with a rectangular profile were shown in our previous publications to be well explained by dynamical theory calculations. The theory is based on a Bloch wave expansion of the neutron wavefunction in the periodic layer of the grating, which includes all multiple scattering within that layer. Calculations show that the spin-echo polarization should be very sensitive to the scattering geometry (i.e., incident angle, sample alignment and beam divergence) and the sample specifications (i.e., grating period, groove depth). To test these predictions, SERGIS measurements have been performed on a set of gratings with different specifications in various scattering geometries. In all cases, simulations based on the dynamical theory, with all the parameters set to their known values, are in good agreement with the collected data.

Instrument control and data acquisition for a time-of-flight neutron reflectometer

Abstract A description is given of the integrated instrument control and data-acquisition electronics and the software of the neutron reflectometer ROG. For the data acquisition, VME electronics is developed to perform time-of-flight and stroboscopic measurements, using a single 3He detector or a two-dimensional position-sensitive detector. For the latter pixel-dependent discrimination is implemented. The instrument control is performed via a distributed (field bus) system. A flexible integrated software system controls the complete instrument.

Comparison of dynamical theory and phase-object approximation for neutron scattering from periodic structures

Dynamical theory (DT) calculations have been successfully developed toexplainneutronspin-echoresolvedgrazing-incidencescatteringfromdiffractiongratings. The theory, without any adjustable parameters, has been shown inprevious publications to accurately reproduce the sensitivity of the spin-echopolarization signal to sample specifications and scattering geometry. The phase-object approximation (POA), which is computationally less demanding than theDT, has also been used to analyze neutron spin-echo polarization data obtainedfrom diffraction gratings. In this paper, POA and DT calculations are comparedfor neutron scattering from various diffraction gratings in different geometricalsettings. POA gives a good description of the data for transmission cases, wherethe neutron beam is incident at large angles to the average grating surface.However, for the grazing-incidence reflection cases that were studied, the POAdoes not fit the data using the independently determined dimensions of themeasured gratings. On the other hand, the good agreement between dynamicaltheory and the data from gratings with known profiles paves the way for its useto extract profile information from periodic samples with unknown structures.1. IntroductionSince the early use of scattering techniques to study crystalproperties, many theories have been developed to explain thescattering data. These theories simulate scattering based onthe characteristics of the scattering potential as well as thoseof the scattered radiation. By fitting a theoretical model to themeasured scattering, unknown properties of the sample areextracted. For perfect crystals, a two-beam dynamical theorywas proposed by Bethe (1928) to describe dynamical scat-tering effects of electrons. However, this theory is fairlycomplicated and when more than two diffracted beams had tobe considered the calculations were tedious, especially withthelimitedcomputationalpoweravailablethen.Moreover,formost samples (e.g. crystals with defects) it is not easy todescribe the individual scattering events accurately. Hence,alternative scattering theories involving further approxima-tions were proposed to make calculation schemes easier toevaluate. The challenge has always been to find an approx-imation thatboth reasonably modelsthe scattered wave and isreadily computed.In 1957, Cowley & Moodie (1957) proposed a new‘physical-optics’ approach to interpret the diffraction ofelectrons by thin crystals. The authors assumed that, when anelectron traverses a region with a varying electrostaticpotential, the electron wave at the exit suffers an amplitudemodification (due to inelastic scattering) and a phase modifi-cation (due to elastic scattering) relative to the incident wave.In the limit where the scattering is perfectly elastic, the effectis due solely to a ‘phase-object’. Later, Jap & Glaeser (1978)used a Feynman path formulation to explain the scattering ofhigh-energy electrons from thin specimens with an evensimpler approximation, in which the accumulated phase of anelectron is calculated along a single classical path parallel tothe incident beam direction. This straight-line path approx-imation is known as the phase-object approximation (POA).A higher-order POA, which involves zigzag as well as straight-line paths, has been also derived (Jap & Glaeser, 1978) andwas found, in the case of forward scattering, to be theapproximation of Cowley and Moodie.The POA has been recently applied to small-angle neutronscattering from micrometre-scale silicon diffraction gratings(de Haan et al., 2007). The theoretical approximation allowsgood fits to the experimental data in the case of transmissionbut cannot reproduce reflection data without adjustment ofsome parameters (groove depth and/or period of the grating)(Plomp, 2009; Plomp et al., 2007). This poses a question