Diffraction from Crystals
This chapter develops diffraction from crystals in the Laue formulation, using both the Born approximation from Chap. 4, and a general formulation for the scattering of any wave from a potential. The concept of the reciprocal lattice is presented, and discussed in detail for cubic crystals. Structure factor rules are derived for cubic crystals, and extinctions of diffractions are related to crystal symmetry. The structure factor discussion is extended to superlattice diffractions and their dependence on chemical order. The shape factor is developed in Cartesian coordinates, and the broadening of diffractions is described for small crystals of various shapes. The Ewald sphere is defined with the Laue condition, and related to the Bragg condition for diffraction. Effects on diffraction intensities from tilting the Ewald sphere or tilting the crystal are explained geometrically. Laue zones and diffraction fine structure are explained with the help of the Ewald sphere.