X-ray Diffraction (XRD) is the definitive technique for determining the crystal structure, phase composition, and microstructural properties of solid materials. It exploits the constructive interference of monochromatic X-rays scattered by the periodic arrangement of atoms in a crystal lattice. XRD is indispensable in materials science, geology, pharmaceuticals, and solid-state chemistry for identifying unknown crystalline phases and quantifying their relative abundances.
The fundamental relationship governing XRD is Bragg’s law: nλ = 2d sinθ, where n is an integer (the order of diffraction), λ is the X-ray wavelength, d is the interplanar spacing of the crystal lattice, and θ is the incident angle. When a monochromatic X-ray beam strikes a crystalline sample at angle θ, scattered X-rays from successive crystal planes interfere constructively only when the path-length difference equals an integer multiple of the wavelength. Each set of crystal planes (hkl) produces a diffraction peak at a specific 2θ angle.
A crystal lattice consists of a repeating three-dimensional arrangement of atoms, ions, or molecules defined by unit cell parameters (a, b, c; α, β, γ). The positions and intensities of diffraction peaks encode the lattice geometry, while the relative intensities encode the atomic positions (the structure factor). Powder XRD measures a polycrystalline sample where all crystallite orientations are present simultaneously, producing a diffractogram of intensity vs. 2θ. Single-crystal XRD measures a single, well-formed crystal and provides complete three-dimensional structural determination, including bond lengths and angles.
Phase identification is performed by comparing the measured diffraction pattern against reference patterns in databases such as the International Centre for Diffraction Data (ICDD) Powder Diffraction File (PDF). Modern search-match software automates this process, identifying phases by their characteristic peak positions and relative intensities. Quantitative phase analysis uses the Rietveld refinement method, which fits a calculated pattern (based on crystal structure models) to the observed pattern by least-squares optimization of structural, microstructural, and instrumental parameters.
The Scherrer equation relates the broadening of diffraction peaks to the average crystallite size (coherently scattering domain size): τ = Kλ / (β cosθ), where τ is the crystallite size, K is the shape factor (~0.9), and β is the full width at half maximum (FWHM) of the peak in radians. Peak broadening analysis is also used to assess microstrain. XRD finds extensive application in pharmaceutical polymorph screening (different crystal forms of the same drug can have different solubility and bioavailability), clay mineralogy (identifying expandable clays), cement chemistry (clinker phase quantification), and failure analysis (corrosion products and thin-film phase identification).
