Chapter 12: X-Ray Diffraction: Intensities

The treatment begins with single-electron scattering described by Thomson scattering theory and polarization considerations, then progresses to atomic-level phenomena where the atomic scattering factor quantifies how scattering amplitude diminishes at higher diffraction angles due to constructive and destructive interference within electron clouds. The structure factor emerges as a central mathematical construct, representing the vector sum of scattered waves from all atoms within a unit cell and encompassing both amplitude and phase information determined by atomic coordinates and identity. The chapter demonstrates how specific lattice geometries—body-centered and face-centered arrangements—and symmetry operations including screw axes and glide planes generate systematic absences or extinction conditions that uniquely identify the crystallographic space group of a material. Notable structural examples such as cesium chloride, sodium chloride, and diamond illustrate practical applications of structure factor calculations and their consequences for observed diffraction patterns. Friedel's law and its implications for centrosymmetric and non-centrosymmetric structures receive detailed treatment. The chapter concludes by bridging theoretical predictions with experimental powder diffraction observations through intensity correction factors including the Lorentz-polarization correction that accounts for the geometric relationship between crystal and detector, multiplicity effects arising from symmetry-equivalent planes, absorption phenomena within crystal samples, and the Debye-Waller factor that describes intensity reduction from thermal motion of atoms at elevated temperatures. Together, these concepts enable researchers to extract quantitative structural information from measured diffraction intensities and validate crystallographic models against experimental data.