Calculation of two-dimensional scattering patterns for oriented systems

Abstract

A versatile procedure to calculate two-dimensional scattering patterns of oriented systems is presented. The systems are represented by a set of dummy atoms with different scattering length densities, which allows the construction of very complex shapes either for single particles or for sets of particles. By the use of oriented pair distance distribution functions it is possible to perform a fast calculation of the scattering intensity from the oriented system in a given direction in the scattering vector (q) space and generate the two-dimensional scattering pattern on a given q plane. Several examples of the calculations are presented, demonstrating the method and its applicability. The presented results open new possibilities for the analysis of scattering patters obtained from oriented systems.

Calculation of Small-Angle Scattering Patterns

“…The data treatment of the scattering data includes normalization of the intensity, background subtraction, and normalization to absolute scale among several steps, which depends on the specific characteristics of the experimental setup. The overall data treatment process and necessary procedure for proper reduction of the scattering data are described in many articles and books in the literature and will not be presented here [7,12,14,15,[23][24][25][26][27][28][29]. In this chapter we will focus on methods for calculation of the SAS intensity, either for oriented or randomly oriented particles.…”

“…This simulation method can also describe models with variable scattering length contrasts and interparticle interactions (structure factor). Several examples can be found in the original article [15].…”

“…Several examples demonstrating the precision of the method are described in the original article [15]. This new method opens a large number of possibilities for the calculation of scattering intensity for oriented particles.…”

“…In order to overcome these limitations, Alves and collaborators [15] recently proposed an innovative procedure to solve this problem. Inspired by the histogram approach used in the optimized Debye equation Eq.…”

“…Having the histograms, the intensities are easily calculated. One strategy proposed by Alves et al [15] is to divide the 2D scattering image in angular slices and compute the histograms for each direction. As shown by the authors, the calculation can be further optimized by the use of parallel computing.…”