Evaluation of double-crystal SANS data influenced by multiple scattering

Evaluation of small-angle neutron scattering (SANS) data is often complicated by multiple scattering effects if large particles of relatively high volume fraction have to be studied and dilution or contrast reduction is impossible. The use of pin-hole SANS instruments is often limited due to the contradictory requirements of high resolution and short wavelength needed to keep scattering contrast as low as possible. Double crystal (DC) SANS diffractometers of Bonse-Hart and bent-crystal type are useful alternatives in such cases, as they permit reaching very high resolution with thermal neutrons. A method for SANS data evaluation suited to DC instruments is presented. It includes the common scheme of the indirect Fourier transformation method, but takes multiple scattering into account. The scattering medium is described by the frequency function g(x) defined as the cosine Fourier transform of slit-smeared data. Although a simplistic model of polydisperse spheres is used to represent g(x), resulting g(x) function and some integral parameters are independent of this model. Tests on simulated data show, that the method reproduce well true values of microstructural parameters, though systematic errors are observed in the cases when the unscattered part of incident beam completely disappears. If the scattering power <N> is known and kept fixed during fitting, then other parameters are reproduced well also in the regime of strong multiple scattering. The evaluation procedure permits simultaneously fitting to several sets of data measured for different Q-regions, resolutions and sample thicknesses. It has proved to provide reliable results for particle sizes ranging from about 100 Angstrom to several microns and <N> < 10.