X-ray Diffraction

Abstract

Crystalline structures are deduced by the diffraction of known radiation incident from solid materials. The three-dimensional regularity of unit cells in crystalline materials results in coherent scattering of the radiation. The directions of the scattered beams are a function of the wavelength of the radiation and the specific interatomic spacing (d _hkl ) of the plane from which the radiation scatters. The intensity of the scattered beam depends on the position of each atom in the unit and on the orientation of the crystal relative to the direction of the incident X-ray beam. Those beams that scatter in a constructive manner result in allowed reflections, i.e., the intensity is a nonzero value. Those beams that scatter in a destructive manner result in unallowed reflections, i.e., the intensity has a minimal value. Each of the constructively scattered beams depends directly on the wavelength of the incident radiation. Having said this, we must address the issue: Why is the wavelength important? One of the requirements for diffraction is that the wavelength of the incident radiation λ must be smaller than the distance between scattering sites. Typically, in crystalline solids, we desire to measure atomic spacing on the order of the lattice constants, e.g., 0.2–0.4 nm. Hence, we must use radiation with wavelengths less than 0.2 nm. This range of wavelength includes those of X-rays and high-energy electrons. Another criteria is that the scattering occurs in a coherent manner, i.e., the energy of the incident radiation equals the energy of the scattered radiation.