What Is X-ray Diffraction?

X-ray diffraction (XRD) is a technique for probing the internal structure of crystalline and semi-crystalline materials by measuring the angular distribution of X-rays scattered elastically from ordered atomic planes. When X-rays with wavelengths comparable to interatomic spacings, typically 0.05 to 0.25 nanometers, strike a periodic crystal lattice, they scatter from successive planes of atoms. At specific angles determined by the lattice spacing and wavelength, scattered waves reinforce one another constructively, producing diffraction peaks whose positions and intensities encode the geometry and atomic composition of the unit cell. The technique is non-destructive and requires minimal sample preparation for many specimen types.

X-ray diffraction was established as a practical analytical tool by William Henry Bragg and William Lawrence Bragg in 1913, for which they received the 1979 Nobel Prize in Physics. The field draws on classical wave optics, crystallography, solid-state physics, and materials science, and it underpins structural biology, geology, semiconductor technology, and pharmaceutical development.

Bragg's Law and Diffraction Geometry

The condition for constructive interference in a crystal is described by Bragg's law: n times the wavelength equals two times the interplanar spacing times the sine of the glancing angle, or nλ = 2d sinθ, where n is an integer order, λ is the X-ray wavelength, d is the spacing between parallel lattice planes, and θ is the angle of incidence. Each family of lattice planes in a crystal has a characteristic d-spacing, and a diffraction peak appears whenever the Bragg condition is satisfied for that family. As explained in the Nature article on the birth of X-ray crystallography, this insight transformed the determination of crystal structures from a theoretical exercise into a systematic experimental program. In practice, instruments vary the angle θ while recording scattered intensity, producing a diffractogram whose peak positions allow unambiguous identification of phases and whose peak widths carry information about crystallite size and lattice strain.

Powder and Single-Crystal Methods

Powder diffraction uses a finely ground polycrystalline sample in which crystallites are randomly oriented. Because all orientations are simultaneously present, every family of lattice planes that satisfies Bragg's law at the incident wavelength contributes a ring to the diffraction pattern; a one-dimensional detector records this as a set of peaks versus 2θ angle. Powder patterns are matched against reference databases such as the ICDD Powder Diffraction File to identify crystalline phases. Single-crystal diffraction orients a macroscopic crystal and records diffracted spots at precise three-dimensional angles, providing enough data to solve the complete atomic arrangement of the unit cell, including bond lengths and angles, to sub-angstrom precision. Synchrotron sources, which deliver X-ray beams many orders of magnitude brighter than laboratory tubes, reduce data collection for protein crystals from hours to seconds.

Applications in Materials Characterization

X-ray diffraction serves as the primary technique for phase identification and lattice parameter measurement in a broad range of material systems. In the semiconductor industry, high-resolution XRD measures epitaxial layer thickness, composition, and strain in compound semiconductor heterostructures to tolerances of a few parts per million. In pharmaceutical manufacturing, powder XRD distinguishes polymorphic crystal forms of active pharmaceutical ingredients, which can differ substantially in solubility and bioavailability. In structural materials, XRD quantifies residual stress by measuring shifts in diffraction peak positions relative to unstressed reference samples, a technique applied to welds, coatings, and machined surfaces. The American Chemical Society publication documenting the X-ray diffraction and Bragg equation provides a detailed treatment of the analytical derivation and its pedagogical use in materials characterization courses. An introduction to the broader principles underlying the technique, including reciprocal lattice geometry and structure factor calculations, is available in Portland State University's X-ray diffraction course notes.

Applications

X-ray diffraction has applications across a wide range of scientific and industrial disciplines, including:

• Crystal structure determination in chemistry, biology, and mineralogy
• Pharmaceutical polymorph identification and quality control
• Semiconductor thin-film characterization and strain measurement
• Cement, ceramic, and geological phase analysis
• Residual stress measurement in engineering components
• Battery electrode and electrolyte material analysis