Real-Space Distributions from Small-Angle Scattering Data: Structure Interference Method versus Indirect Transformation Method

Abstract

The indirect transformation method (program ITP) developed by Glatter since 1977 is still one of the most popular methods for obtaining real-space information from small-angle scattering data. In order to validate the novel structure interference method (SIM), a comparison of the two methods has been performed with both simulated and experimental data. Although no explicit smoothing criterion is used in SIM, the solutions are less influenced by oscillations, termination effects are smaller and higher real-space resolution is obtained compared with ITP. It has been found that the structure interference method is very robust even in the case of incomplete data (h iRma x > re) where the indirect transformation method fails to find a physically meaningful solution.

Improvements and considerations for size distribution retrieval from small-angle scattering data by Monte Carlo methods

“…These only have a positivity constraint and have so far been limited to size distributions of sphereshaped scatterers. These methods can be used to extract the particle size distribution function of systems of scatterers whose shape is known or assumed, and not affected by concentration effects (Krauthä user et al, 1996;Martelli & Di Nunzio, 2002;Di Nunzio et al, 2004). The MC variant approaches the optimization by trial and error, whereas the SIM uses a conjugate gradient approach (Krauthauser, 1994).…”

Particle Size Distribution of Nanospheres by Monte Carlo Fitting of Small Angle X-Ray Scattering Curves

“…The MCF method was applied to determine the PSD function of SiC nanoparticles both as a loose powder in the as-synthesised state and as reinforcing agent after dispersion inside a PMMA matrix nanocomposite. The same scattering curves were also analysed with the SIM program [14] to cross-check the results of the two similar procedures. In the first example, the result of the SAXS analysis is compared with the PSD function derived from transmission electron microscopy (TEM) images.…”

“…A general feature of these models is the introduction of an additional constraint on the smoothness of the PSD in order to achieve the best compromise between a regular solution in real space and the approximation of the resulting computed scattering curve to the experimental data. The ITM approach has subsequently been further improved [14] by the structure interference method (SIM). The SIM could relax the regularity constraint and provide a more accurate solution for PSDs less influenced by oscillations and termination effects.…”

Analysis of two-dimensional energy and relaxation-time distributions from temperature-dependent broadband dielectric spectroscopy

“…For such kinds of problems the structure-interference method has been developed, originally to obtain 1D size distributions from x-ray data. 13 It is based on the idea that a physically meaningful solution must be independent of the discretization. Solutions belonging to different random discretizations…”

“…14 By comparing the results of our 2D method with TSDC data we have given independent experimental evidence for the existence of a (W,ln o ) distribution associated with a ␤ mechanism. The 2D dielectric analysis is based on ͑i͒ a stable method for the solution of inverse problems, 13 ͑ii͒ a broadband measurement technique of high precision due to temperature-dependent calibration. 3 No a priori assumptions on the shape of G(W,ln o ) are made; i.e., in principle, the algorithm is applicable to discrete and continuous distributions.…”