X-ray diffraction (XRD): principle, how to read a pattern, and what it tells you

A crystal is built from repeating unit cells, and its atoms lie on families of parallel planes. X-rays scattered by these planes reinforce one another only in particular directions, given by Bragg’s law, nλ = 2d sin θ, where λ is the X-ray wavelength, θ the angle between the beam and the planes, d the spacing between planes and n the order of diffraction (Wang et al. 2026). In practice only first-order reflections are used: a second-order reflection from the (100) planes is the same as a first-order reflection from (200) (Wang et al. 2026).

The size and shape of the unit cell set the directions in which constructive interference occurs (Abid et al. 2023), so each crystalline compound gives its own set of peak positions. A laboratory powder diffractometer scans θ–2θ and collects a whole suite of hkl reflections in one run; the common Bragg–Brentano arrangement uses a divergent beam so that many crystallites diffract at once (Cline et al. 2015).

Single-crystal XRD (SCXRD) uses one crystal and determines the full atomic arrangement of an unknown structure, but needs a well-formed crystal larger than about 100 μm; when only a powder is available, structures can be solved from high-resolution powder data with computation (Abid et al. 2023).

A powder pattern is a plot of intensity against 2θ. Read it in three parts:

• Peak positions give d-spacings through Bragg’s law and identify the phase: compare them with published or database patterns. Shifts of peaks can point to internal stress, twin boundaries, stacking faults, chemical heterogeneity, a small crystal size or structural defects (Abid et al. 2023).
• Peak widths carry size and strain. Micron-sized crystals give sharp, narrow peaks and nanocrystals give broad, short ones (Abid et al. 2023). For crystals below about 100 nm the mean crystallite size can be estimated with the Scherrer equation, D = Kλ / (β cos θ), with β the full width at half maximum and K a shape factor of about 0.89–0.94 (Abid et al. 2023). Micro-strain also broadens peaks (Cline et al. 2015).
• Peak intensities depend on the crystal structure. Whole-pattern Rietveld refinement fits a calculated pattern to the measured one, optimising structural, instrumental and sample parameters together (Wang et al. 2026); typical refined terms include lattice parameters, sample displacement and transparency, background, scale factors and atomic parameters (Cline et al. 2015). Peak shapes are usually modelled with Voigt or pseudo-Voigt functions (Wang et al. 2026).

A crystalline material with no long-range order in one direction shows it in the pattern: a highly porous carbon made from graphene oxide showed no graphite-like (002) reflection, only broad (100)/(101) features, indicating that it was not built from stacked multilayer graphene (Shulga et al. 2021).

• Grind to a fine, homogeneous powder. For quantitative powder work, crystallites of about 0.1–1 μm are recommended; larger or smaller crystallites can still be used when only phase identification is needed (Abid et al. 2023).
• Get the height right. In Bragg–Brentano geometry both the diffraction angle and the sample position matter; specimen displacement and X-ray transparency of the sample shift and distort peaks (Cline et al. 2015).
• Use a standard. An internal standard mixed into the sample corrects peak positions for displacement and transparency, which an external standard cannot do; NIST Standard Reference Materials such as the LaB₆ SRM 660 series calibrate the instrument (Cline et al. 2015).
• Protect sensitive crystals. Crystals that react with light, air or moisture can be sealed in thin-walled glass capillaries under inert gas before single-crystal measurement (Abid et al. 2023).
• Collect enough points. Choose a step size that gives at least five points above the FWHM if you plan a Rietveld refinement (Cline et al. 2015).

Porous frameworks. For metal–organic frameworks such as ZIF-8, HKUST-1 or UiO-66, XRD is the first check after synthesis: it confirms that the intended framework formed and that it is phase-pure before any other measurement (Abid et al. 2023). Adding a modulator such as benzoic acid to a Zr framework grew larger crystals, seen both in electron micrographs and as narrower XRD peaks (Abid et al. 2023). Pair XRD with SEM for crystal size and shape and with BET gas sorption to check that the pores are open after activation.

Carbon and 2D materials. Peak positions and widths show whether layers are stacked: a high-surface-area carbon derived from graphene oxide lacked the graphitic (002) peak and had coherent scattering domains of about 2.8 nm by the Scherrer formula (Shulga et al. 2021). Compare with graphene and Raman spectroscopy for disorder.

Battery electrodes. Operando energy-dispersive XRD can follow composition and lattice parameters inside working cells during cycling (Wang et al. 2026), an approach suited to battery materials such as LiFePO₄ and NMC cathodes.

Other crystalline solids. The same phase-identification logic applies to zeolites and perovskites. For surface chemistry, which XRD does not see, use XPS; for local structure at the nanoscale use TEM. All methods are compared on the characterisation techniques hub.

• Treating the Scherrer size as particle size. Scherrer gives the size of coherently diffracting crystallites, not of particles: polycrystalline particles make the two differ, and the shape constant K is uncertain for polydisperse samples (Jeong et al. 2008). Compare with TEM images.
• Ignoring instrument broadening and aberrations. The observed peak maximum does not necessarily reflect the true hkl spacing on a laboratory diffractometer; calibrate with a standard reference material before quoting precise lattice parameters (Cline et al. 2015).
• Reading a shifted peak as a new phase. Sample displacement shifts all peaks systematically; an internal standard separates this from real lattice changes (Cline et al. 2015).
• Forgetting that powder XRD is an average. PXRD reports an average over all the crystallites in the beam, not the structure of any one grain, and extremely small crystals (below about 10 nm) are better studied by small-angle X-ray scattering (Abid et al. 2023).
• Thin films on substrates. Strong substrate reflections can swamp a thin film’s pattern; high-resolution TEM is an alternative check of crystallinity (Abid et al. 2023).
• Ignoring texture. When intensities matter, preferred orientation of the crystallites (texture) has to be modelled, for example with a spherical-harmonic term in a Rietveld refinement (Cline et al. 2015).

For a methods figure or graphical abstract, show the X-ray source, the sample and the detector with the incident and diffracted beams at angle θ, and next to it the pattern with labelled peaks. In LabCanvas the figure editor’s Library has the diffractometer as an editable object, including a cutaway of the beam path from tube to sample to detector, and an editable XRD data plot. You can label peaks with their hkl indices, mark the 2θ scale, add a reference pattern for comparison and export the figure at journal resolution. To estimate crystallite size from a peak width, use the Scherrer calculator linked below.