[11] Small-angle x-ray scattering

TLDR: In this article, the authors discussed small-angle scattering experiments with particles in solution and showed that the correlation between the distance distribution function and the structure of the particle is also discussed.

Abstract: Publisher Summary This chapter discusses small-angle scattering experiments with particles in solution—i.e., the particles are nonoriented. A large number of particles contribute to the scattering and the resulting spatial average leads to a loss in information. The information contained in the three-dimensional electron density distribution is thereby reduced to the one-dimensional distance distribution function. This function is proportional to the number of lines with length, which connect any volume element i with any volume element k of the same particle. The spatial orientation of these connection lines is of no account to the function. The connection lines are weighted by the product of the number of electrons situated in the volume elements i and k , respectively. The correlation between the function and the structure of the particle is also discussed in the chapter. The connection between the distance distribution function and the measured experimental scattering curve is also shown. It is observed that the each distance between two electrons of the particle, which is part of the function, leads to an angular-dependent scattering intensity. This physical process of scattering can be mathematically expressed by a Fourier transformation, which defines the way in which the information in “real space” (distance distribution function) is transformed into “reciprocal space” (scattering function). The chapter also discusses monochromatization and the camera type developed in Graz.