Small angle neutron scattering

Abstract

Abstract. Small Angle Neutron Scattering (SANS) is a technique that enables to probe the 3-D structure of materials on a typical size range lying from ∼ 1 nm up to ∼ a few 100 nm, the obtained information being statistically averaged on a sample whose volume is ∼ 1 cm 3 . This very rich technique enables to make a full structural characterization of a given object of nanometric dimensions (radius of gyration, shape, volume or mass, fractal dimension, specific area. . . ) through the determination of the form factor as well as the determination of the way objects are organized within in a continuous media, and therefore to describe interactions between them, through the determination of the structure factor. The specific properties of neutrons (possibility of tuning the scattering intensity by using the isotopic substitution, sensitivity to magnetism, negligible absorption, low energy of the incident neutrons) make it particularly interesting in the fields of soft matter, biophysics, magnetic materials and metallurgy. In particular, the contrast variation methods allow to extract some informations that cannot be obtained by any other experimental techniques. This course is divided in two parts. The first one is devoted to the description of the principle of SANS: basics (formalism, coherent scattering/incoherent scattering, notion of elementary scatterer), form factor analysis (I(q→0), Guinier regime, intermediate regime, Porod regime, polydisperse system), structure factor analysis (2 nd Virial coefficient, integral equations, characterization of aggregates), and contrast variation methods (how to create contrast in an homogeneous system, matching in ternary systems, extrapolation to zero concentration, Zero Averaged Contrast). It is illustrated by some representative examples. The second one describes the experimental aspects of SANS to guide user in its future experiments: description of SANS spectrometer, resolution of the spectrometer, optimization of spectrometer configurations, optimization of sample characteristics prior to measurements (thickness, volume, hydrogen content. . . ), standards measurements to be made and principle of data reduction.Résumé. (La Diffusion de Neutrons aux petits angles (DNPA) est une technique permettant de sonder la structure 3-D de matériaux sur une gamme typique de taille comprise entre ∼1 nm) et ∼ quelques 100 nm, les informations obtenues étant statistiquement moyennées sur la taille de l'échantillon dont le volume est d'environ 1 cm 3 . C'est une technique très puissante car elle permet de faire une caractérisation complète de la structure d'un objet donné de dimensions nanométriques (rayon de giration, forme, volume, masse, dimension fractale, surface spécifique. . . ) grâce à la détermination du facteur de forme, ainsi que la détermination de la manière dont les objets sont organisés au sein d'un milieu continu, et donc de décrire les interactions entre les objets, par la détermination du facteur de structure. Les propriétés spécifiques de neutrons (possibilité de modul...

A novel methodology to study nanoporous alumina by small-angle neutron scattering

“…In particular, experimental conditions have to be chosen to cancel out MS, because it has a strong influence on the scattering intensity I(q). A simple approach to detect MS is to measure the neutron transmission (Tr = N tr /N 0 , with N tr the number of neutrons transmitted through the AAO and N 0 the number of neutrons of the incident beam) of the AAO (Cousin, 2015). Tr is defined as Tr = exp(Àn tot L), with n the number density [= (/M)N a , being the mass density, M the molar mass and N a the Avogadro number], tot = 17.25 barns the absorption cross section of alumina and L the AAO length.…”

Structural evolution at short and medium range distances during crystallization of a P2O5‐Li2O‐Al2O3‐SiO2 glass

“…The small-angle neutron scattering (SANS) experiments were carried out on the PAXY spectrometer at the Léon Brillouin Laboratory in CEA Saclay, France. [34] Measurements have been carried out in a q-range of 2.5.10 -2 nm -1 ≤ q ≤ 5nm −1 (q=4π sinθ/λ with 2θ the scattering angle and λ the neutron wavelength). To cover these q ranges, four different configurations were used (Table 2).…”

“…Detailed information on SANS formalism can be found in various reviews. [34][35][36] In a binary system of n rigid and centrosymmetric objects that contains N elementary scatterers homogeneously distributed within a surrounding medium, the measured intensity can be written:…”

H2O/D2O Contrast Variation for Ultra-Small-Angle Neutron Scattering to Minimize Multiple Scattering Effects of Colloidal Particle Suspensions

“…While a typical approach to reduce multiple scattering is either or both (a) reducing the particle concentration and/or (b) reducing the sample path length, they have obvious limitations in (i) using the behavior of less concentrated suspension to understand the more concentrated suspension; (ii) difficulty in proper feeding of a viscous suspension (in other words, heterogeneity as well as the impact of the sample cell geometry on the structure could affect the sample subjected to the beam and, thus, produce a misleading result); and (iii) the increasing volumetric effect of the surface perturbation of two cell faces on the decreasing bulk of thinner samples. On the other hand, for neutron scattering experiments, it is possible to optimize the scattering strength of a sample by decreasing the contrast between the two phases, particulate, and solvent (water) in a way that is analogous to the role of refractive index adjustment in light scattering [12]. In this study, we adjusted the scattering length density of the solvent by varying the H 2 O/D 2 O composition, i.e., by contrast variation (e.g., [13]).…”