Crystals diffract X-rays
In a crystal, atoms sit on a regular repeating lattice. X-rays have wavelengths comparable to the spacings between atomic planes, so when a beam strikes a crystal, the waves scattered by successive planes interfere. In most directions they cancel. In particular directions they reinforce and produce a strong diffracted beam.
The condition for reinforcement is described by Bragg’s law: n times the wavelength equals twice the plane spacing times the sine of the angle, where the angle is measured between the beam and the planes. Because the wavelength of the X-ray source is known and the angle is measured, the spacing between planes can be calculated. Every crystalline substance has its own set of spacings, determined by its lattice type and dimensions, so its pattern of diffraction angles and intensities acts as a fingerprint.
The usual experiment
The most common arrangement is powder or polycrystalline diffraction. A sample, either ground to a fine powder or a solid piece with many small grains, sits in the beam. The detector sweeps through a range of angles and records intensity, producing a pattern of peaks on a background. Because the grains point in many directions, all plane orientations are represented, and a complete set of peaks appears.
For thin films and coatings, grazing-incidence geometry keeps the beam at a shallow angle so that it samples mostly the film rather than the substrate underneath. Single crystals are measured differently, often with a rocking scan around one peak.
Identifying phases
The simplest and most common use is phase identification. The measured peak positions and relative intensities are compared with reference patterns of known compounds from databases. A match indicates that a given crystalline phase is present.
This is valuable throughout materials work. It can show whether a sintered ceramic has the intended crystal form, which matters for zirconia, where different crystal forms behave differently and underlie zirconia toughening. It can identify unwanted secondary phases left from processing, and it can detect reaction products at the interface of a coating and substrate. In carbon materials, it separates diamond, graphite and other forms, which complements Raman spectroscopy: diffraction reports average crystal structure over a larger volume, while Raman probes bonding in a small spot.
Mixtures show overlapping patterns, and with careful analysis the relative amounts of phases can be estimated. Typically, a phase making up only a few percent of a sample can be hard to detect, and amorphous material gives no sharp peaks at all, only broad humps.
What peak shape tells you
Beyond which peaks appear, their exact shape carries information.
- Position. A shift in a peak means the lattice spacing differs from the reference. Uniform shifts can indicate strain or a change in composition, such as atoms dissolved into the lattice. Stress in a coating can be estimated by measuring peak shifts at different tilt angles, which links to residual stress.
- Width. Peaks broaden when crystals are very small or contain non-uniform strain and defects. Narrow peaks suggest large, well-ordered crystals. The Scherrer relationship gives a rough estimate of crystallite size from broadening, mainly for sizes up to about a few hundred nanometers, and it is only approximate.
- Intensity. If grains tend to line up in a preferred direction (texture), the relative peak intensities depart from the reference. In coatings, this reveals the growth direction of the crystals.
For diamond, the narrowness of peaks from a single crystal relates to crystal quality, and rocking-curve widths are used for high-quality plates. For polycrystalline films, peak intensity ratios show how orientation varies with growth conditions.
Strengths and limits
X-ray diffraction is nondestructive, quantitative with care, and sensitive to the structure rather than just chemistry. It cannot see amorphous phases well, struggles with minor phases at low concentration, and gives only an average over the illuminated volume. Very thin films give weak signals. Samples that are strongly textured or contain overlapping phases need expert interpretation.
For these reasons, diffraction is rarely used alone. Results are checked against microscopy, which shows how grains and phases are arranged, and against chemical and thermal analysis. Together these form part of the wider toolkit for materials testing.