X-Ray Diffraction and Scattering by Nanomaterials

Abstract

This chapter contains basic concepts and applications of wide-angle X-ray diffraction (XRD) and small-angle X-ray scattering (SAXS) to studies of nanostructured materials. The first part includes an introduction to the technique of X-ray powder diffraction (XPD), which is commonly applied to phase identification of powdered materials, characterization of unit cells, determinations of lattice parameters and, in some cases, also coordinates of atoms inside the unit cells. The main aspect described here is the analysis of the shape of X-ray diffraction peak profiles, which allows one to determine additional and also valuable structural information of nanomaterials, such as average crystallite sizes and crystallite microstrains. Detailed deductions of the equations used for different applications of X-ray diffraction and basic concepts of crystallography (such as those related to symmetries, Bravais and reciprocal lattices, etc.) are not described. The second part presents the basic equations related to the SAXS method and their applications to several biological systems (proteins in solution). Classical SAXS is an experimental procedure that is employed in transmission mode and is also applied to the study of many nanostructured inorganic materials. The third part includes two variants of the classical SAXS procedure, namely grazing incidence small-angle X-ray scattering (GISAXS) and anomalous small-angle X-ray scattering (ASAXS). The basic concepts of the GISAXS method and several applications to studies of nanostructured materials deposited on flat substrates and buried nanostructures are presented. The basic concepts of the ASAXS method are described, together with its applications to complex materials that cannot be properly studied using the classical SAXS technique, such as, for example, materials modeled by three phases with different electron densities. Most of the experiments described in this chapter were performed by the authors using X-ray beam lines of the National Synchrotron Light Laboratory (LNLS), Campinas, Brazil.