Small angle neutron scattering

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 cm3. 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 (2nd 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