An evaluation method of incoherent small-angle neutron scattering from softmatter in a parallel-plate shape is proposed. Both transmission and incoherent scattering intensity are uniquely determined as a function of the cross-sections and the sample thickness by taking account of multiple scattering from hydrogen. The validity of the method is examined for mixtures of H 2 O and D 2 O, polyethylene having various sample thicknesses, and polymer solutions in D 2 O.

Evaluation of Incoherent Neutron Scattering from Softmatter

Measurements and calculations of beam attenuation and background scattering for common materials placed in a neutron beam are presented over the temperature range of 300–700 K. Time-of-flight (TOF) measurements have also been made, to determine the fraction of the background that is either inelastic or quasi-elastic scattering as measured with a 3He detector. Other background sources considered include double Bragg diffraction from windows or samples, scattering from gases, and phonon scattering from solids. Background from the residual air in detector vacuum vessels and scattering from the 3He detector dome are presented. The thickness dependence of the multiple scattering correction for forward scattering from water is calculated. Inelastic phonon background scattering at small angles for crystalline solids is both modeled and compared with measurements. Methods of maximizing the signal-to-noise ratio by material selection, choice of sample thickness and wavelength, removal of inelastic background by TOF or Be filters, and removal of spin-flip scattering with polarized beam analysis are discussed.

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Survey of background scattering from materials found in small-angle neutron scattering

The H atom has a large incoherent scattering cross section and is a major source of incoherent scattering intensity, (dΣ/dΩ)inc, in small-angle neutron scattering. By taking account of multiple scattering from H atoms, a useful method (the transmission method or T method) is proposed for the estimation of (dΣ/dΩ)inc for various types of hydrogen-containing systems. The incoherent scattering intensity is calculated simply from the transmission, T, and the thickness of the sample, t, i.e. (dΣ/dΩ)inc ≅ [exp(Σtott) − 1]/(4πt) = (1 − T)/(4πtT), where Σtot ≡ −(lnT)/t is the macroscopic total cross section per unit volume. This method provides a reasonably accurate value of incoherent scattering intensity for various systems. The validity and the extent of applicability of the T method are examined for several samples, including light/heavy water mixtures, polymer gels and surfactant aqueous dispersions.

Evaluation of incoherent scattering intensity by transmission and sample thickness

Solution small-angle neutron scattering (SANS) combined with contrast variation provides information about the size and shape of individual components of a multi-component biological assembly, as well as the spatial arrangements between the components. The large difference in the neutron scattering properties between hydrogen and deuterium is key to the method. Isotopic substitution of deuterium for some or all of the hydrogen in either the molecule or the solvent can greatly alter the scattering properties of the biological assembly, often with little or no change to its biochemical properties. Thus, SANS with contrast variation provides unique information not easily obtained using other experimental techniques.If used correctly, SANS with contrast variation is a powerful tool for determining the solution structure of multi-component biological assemblies. This chapter discusses the principles of SANS theory that are important for contrast variation, essential considerations for experiment design and execution, and the proper approach to data analysis and structure modeling. As sample quality is extremely important for a successful contrast variation experiment, sample issues that can affect the outcome of the experiment are discussed as well as procedures used to verify the sample quality. The described methodology is focused on two-component biological complexes. However, examples of its use for multi-component assemblies are also discussed.

Designing and Performing Biological Solution Small-Angle Neutron Scattering Contrast Variation Experiments on Multi-component Assemblies.

Monte Carlo codes such as MCNP and Geant4 rely on a combination of physics models and evaluated nuclear data files (ENDF) to simulate the transport of neutrons through various materials and geometries. The grid representation used to represent the final-state scattering energies and angles associated with neutron scattering interactions can significantly affect the predictions of these codes. In particular, the default thermal scattering libraries used by MCNP6.1 and Geant4.10.3 do not accurately reproduce the ENDF/B-VII.1 model in simulations of the double-differential cross section for thermal neutrons interacting with hydrogen nuclei in a thin layer of water. However, agreement between model and simulation can be achieved within the statistical error by re-processing ENDF/B-VII.I thermal scattering libraries with the NJOY code. The structure of the thermal scattering libraries and sampling algorithms in MCNP and Geant4 are also reviewed.

The effects of nuclear data library processing on Geant4 and MCNP simulations of the thermal neutron scattering law

Light water is frequently used as a standard for calibrating small-angle neutron scattering (SANS) data. The intensities collected for 1 and 2 mm of light water in standard quartz cells may differ by up to about 50% due to the presence of multiple and inelastic scattering [Rennie & Heenan (1993). Proceedings of ISSI Meeting, Dubna, pp. 254–260, Report E3-93-65; Teixeira (1992). Structure and Dynamics of Strongly Interacting Colloids and Supramolecular Aggregates in Solution, edited by S. H. Chen, pp. 625–658. Dordrecht: Kluwer Academic Publishers]. Multiple scattering increases with the thickness of the sample. The use of only elastically scattered neutrons may lead to an absolute intensity of the SANS data of about a factor of 2 higher than that obtained by taking into account all of the neutrons on the detector [Ghosh & Rennie (1990). Inst. Phys. Conf. Ser. 107, 233–244]. However, it is shown here that the scattering intensities collected with different ratios of sample-to-beam dimension do present large differences as a function of sample thickness. In particular, ratios smaller and larger than unity are considered and the results are discussed and compared with Monte Carlo simulations.

Sample geometry effects on incoherent small-angle scattering of light water

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Sample geometry effects on incoherent small-angle scattering of light water