Analytical Chemistry
X-Ray Diffraction (XRD)
Bragg's law nλ = 2d sinθ — periodic crystal lattice diffracts X-rays into sharp peaks; powder, single-crystal, protein
X-ray diffraction (XRD) is the analytical technique in which X-rays of wavelength comparable to interatomic spacing scatter from a periodic crystal lattice and interfere constructively at angles satisfying Bragg's law nλ = 2d sinθ. Max von Laue demonstrated the effect in 1912 (Nobel Prize 1914); William Henry and William Lawrence Bragg formulated the law and pioneered structure determination in 1913 (Nobel Prize 1915). Three modes dominate today: powder XRD identifies phases by their peak fingerprints, single-crystal XRD solves the atomic structures of small molecules and minerals, and macromolecular crystallography delivers protein and nucleic-acid structures at near-atomic resolution.
- Bragg's lawnλ = 2d sinθ
- Cu-Kαλ = 1.5418 Å
- Discoveredvon Laue 1912; Braggs 1913
- Nobel PrizesPhysics 1914, 1915
- Crystal sizeSingle 0.1–0.5 mm; XFEL ≥ few µm
- ModesPowder, single-crystal, MX, SAXS, WAXS
Interactive visualization
Press play, or step through manually. The visualization is yours to drive — try it before reading on.
Watch the 60-second explainer
A condensed visual walkthrough — narrated, captioned, under a minute.
Why XRD matters
- Atomic-resolution structural truth. Single-crystal XRD pinpoints atom positions to ±0.005 Å in small organic and inorganic molecules and to ±0.05 Å in proteins below 2.0 Å resolution. No other method routinely delivers this geometric precision; cryo-EM has caught up for large complexes but XRD remains canonical for <500 kDa systems crystallized in a homogeneous form.
- Phase identification of unknowns. The ICDD Powder Diffraction File (PDF-5+, 2024 release) contains over 1,100,000 reference patterns. A 30-minute powder scan compared against the database identifies mineral mixtures, pharmaceutical polymorphs, corrosion products, and forensic trace evidence within minutes.
- Quantitative phase analysis. Rietveld refinement (Hugo Rietveld, 1969) fits the entire powder diffraction profile and quantifies multi-phase mixtures to ±1 wt%. Cement chemistry uses this routinely to monitor C3S, C2S, C3A, and ferrite-phase ratios in clinker.
- Pharmaceutical polymorph discrimination. Two crystal forms of the same drug (Form A vs Form B) have identical chemistry but distinct dissolution rates and bioavailability. The 1998 Ritonavir polymorph collapse — an unanticipated more-stable Form II appearing mid-production — was diagnosed by powder XRD and informed FDA polymorph guidance ICH Q6A.
- Macromolecular structures power drug design. The Protein Data Bank (PDB) contains over 220,000 entries (April 2026) and roughly 80% are X-ray structures. Imatinib (Gleevec) was designed against the abl-kinase XRD structure; HIV protease inhibitors in the 1990s were direct XRD-driven design.
- Mineralogy and meteoritics. Most mineral identifications rely on powder XRD; the Curiosity rover's CheMin instrument (2012) was a miniaturized XRD/XRF that confirmed clay-mineral phyllosilicates on Mars in Yellowknife Bay sediments — direct evidence of past liquid water.
- Foundation for related techniques. SAXS (small-angle X-ray scattering) extends to nanostructured non-crystalline materials, neutron diffraction sees light atoms (H, Li) that XRD struggles with, and electron diffraction probes µm-scale crystallites. All borrow Bragg's law adapted to their geometry.
Common misconceptions
- XRD always gives the structure. Powder XRD generally identifies phases but cannot solve unknown structures with large unit cells because peaks overlap and information is degenerate. Single-crystal XRD solves structures only when the phase problem is solved (direct methods, MR, or experimental phasing).
- Bragg's law is exact. Bragg's law assumes plane waves and an infinite, perfectly periodic lattice. Real crystals have mosaicity, lattice strain, and finite size that broaden peaks (Scherrer equation). For nanoparticles below ~100 nm, peaks are visibly broadened; for <5 nm crystallites the diffraction pattern becomes ring-like with no sharp peaks.
- Stronger source = better data. X-ray dose damages biological crystals via radiolysis: hydrated electrons break disulfides and decarboxylate aspartate/glutamate residues. Synchrotron data collection is dose-budgeted to the Henderson limit (~3·10⁷ Gy) and beyond that the structure is no longer biologically relevant.
- Hydrogen positions show up directly. X-rays scatter from electrons; H atoms have only one electron and contribute weakly. H positions are usually placed by geometric riding rather than refined directly. Neutron diffraction sees H (and especially D) much more strongly and is the right technique for H-bond geometry studies.
- Anything that diffracts is crystalline. Glasses and amorphous materials produce broad halos at characteristic 2θ from short-range order. Liquids show one or two halos. Crystallinity is operationally defined by sharp Bragg peaks above a diffuse background; semi-crystalline polymers have both.
- The 'molecular structure' from XRD is the gas-phase structure. XRD gives a time- and lattice-averaged structure. Bond lengths are systematically shorter than gas-phase by ~0.01–0.02 Å due to thermal motion projection; molecular packing biases conformational populations toward those that crystallize. Always note 'in the solid state' when reporting bond lengths.
From scattering to structure
X-rays scatter elastically from electrons. The amplitude scattered by an atom at position r in unit cell coordinates is its atomic form factor f(s), where s = (sin θ)/λ is the momentum transfer; f(0) equals the atomic number Z. Summing over all atoms in the unit cell gives the structure factor F(hkl) = Σ f_j exp(2πi(h·x_j + k·y_j + l·z_j)). The diffracted intensity at the (hkl) Bragg peak is I(hkl) = K·|F(hkl)|² where K bundles geometric, polarization, Lorentz, and absorption corrections. Inverting the structure factors with the right phases gives electron density ρ(r) = (1/V) Σ F(hkl) exp(-2πi(h·x + k·y + l·z)), into which atoms are placed and refined iteratively.
A modern single-crystal data collection: the crystal is mounted in a cryoloop, flash-cooled in a 100 K nitrogen stream, centered at the goniometer rotation axis, and rotated through 180–360° while a CCD or CMOS detector records diffraction frames every 0.1–1° of crystal rotation. SHELX (Sheldrick, since 1976), PHENIX, OLEX2, or CrysAlis Pro perform indexing (find unit cell), integration (sum each peak), scaling (correct for absorption and beam decay), and structure solution. For a typical 50-atom small molecule, the entire process takes 6 to 24 hours from mount to publication-ready CIF; for a 30 kDa protein, 1 to 4 weeks.
Powder XRD is conceptually simpler. A flat sample mount is rotated by θ while the detector tracks at 2θ over 10° to 100° in 0.005°–0.02° steps; total scan time 5 minutes to 12 hours depending on resolution and statistics. Peak positions yield the unit cell via least-squares indexing programs (DICVOL, TREOR, McMaille). Rietveld refinement adjusts atomic positions, occupancies, thermal parameters, and instrument parameters to minimize Σ w_i (y_obs - y_calc)². Goodness-of-fit indicators are R_wp and χ² with R_wp ≤ 10% and χ² ≤ 2 typical for a good refinement.
Powder vs single-crystal vs SAXS vs WAXS XRD
| Technique | Sample form | Q-range / 2θ-range | Information | Typical resolution | Use cases |
|---|---|---|---|---|---|
| Powder XRD (Bragg-Brentano) | ~100 mg ground powder | 2θ = 5° to 120° | Phases, lattice params, crystallite size, Rietveld refinement | 2–3 Å spacings | Mineral ID, polymorph screening, cement, catalyst |
| Single-crystal XRD | Crystal 0.1–0.5 mm | 2θ to 50–80° (sin θ/λ to 0.6 Å⁻¹) | Full atomic structure | 0.5–1.5 Å (small mol) | Organics, organometallics, MOFs, minerals |
| Macromolecular X-ray (MX) | Protein crystals 50–500 µm | Resolution 1–4 Å | Protein/nucleic acid 3D structure | 1.5–3.0 Å typical | Drug design, enzymology, structural biology |
| SAXS (small-angle) | Solutions, gels, nano | Q = 0.01–1 nm⁻¹ | Size, shape, radius of gyration, ordering 1–100 nm | Nanometer scale | Polymers, biomolecule envelopes, micelles |
| WAXS (wide-angle) | Polymers, fibers | Q = 1–25 nm⁻¹ | Crystallinity, orientation, lamellar spacing | 0.4–10 nm | Semi-crystalline polymers, fibers, films |
| GIXRD (grazing incidence) | Thin films <500 nm | 0.1–5° incidence | Surface phase, texture | 2–20 nm depth | Semiconductor layers, coatings |
Famous experiments and structural milestones
- Watson-Crick DNA double helix, 1953. Photo 51 (Franklin and Gosling, May 1952) at King's College London, B-form DNA fiber: 34 Å pitch, 10 bp per turn, 3.4 Å rise. Watson and Crick's model in Nature 25 April 1953. Franklin died of ovarian cancer in 1958, four years before the 1962 Nobel to Watson, Crick, and Wilkins.
- Hemoglobin and myoglobin, Perutz and Kendrew 1959–1960. Max Perutz (Cambridge) solved myoglobin first via heavy-atom isomorphous replacement at 6 Å in 1958, refined to 2 Å with Kendrew by 1960. The first protein structure ever determined; the Perutz/Kendrew Nobel followed in 1962. Atomic-resolution hemoglobin came in 1968 — 20 years of effort starting from Bernal's 1934 first protein crystal.
- Lysozyme, David Phillips 1965. The first enzyme structure (Nature, 1965) at 2 Å revealed how a glycoside-hydrolase substrate fits in the active-site cleft. Combined with Arthur Lesk's 1969 catalytic-mechanism work, established the structural basis of enzyme catalysis as an experimental science.
- Curiosity rover CheMin XRD on Mars, 2012–present. The first off-Earth X-ray diffractometer, Curiosity's CheMin uses Co-Kα at 0.6 mm² spot and sample agitation; in October 2012 it identified plagioclase, pyroxene, olivine, and clay minerals in the John Klein and Yellowknife Bay drill samples — direct mineralogical evidence for past habitable conditions in Gale Crater.
- Serial femtosecond crystallography, LCLS 2009–present. An XFEL pulse (~10 fs, 10¹² photons) delivers a single diffraction pattern from a 1–10 µm crystal before the crystal disintegrates from radiation damage. Tens of thousands of patterns are merged. SFX has solved structures of photosystem II, bacteriorhodopsin time-resolved, and several membrane-protein G-protein-coupled receptors that resisted conventional MX.
Frequently asked questions
What does Bragg's law mean physically?
Imagine X-rays incident on a stack of parallel atomic planes spaced d apart. Each plane reflects a small fraction of the beam. Reflections from adjacent planes are in phase, and constructively interfere, when the path-length difference 2d sinθ equals an integer number of wavelengths nλ. For Cu-Kα radiation (λ = 1.5418 Å) reflecting off the (111) plane of silicon (d = 3.135 Å), the n = 1 condition gives sinθ = 1.5418/(2·3.135) = 0.246, so θ ≈ 14.2° (or 2θ ≈ 28.4° as conventionally reported). Each peak in a diffraction pattern corresponds to a Miller-indexed plane (hkl); the positions encode the lattice geometry, and the intensities encode what atoms sit at what positions inside the unit cell.
Why is Cu-Kα the most common XRD source?
Copper Kα radiation (λ = 1.5418 Å for Cu-Kα1, 1.5444 Å for Cu-Kα2, weighted average 1.5418 Å) is produced by bombarding a copper anode with ~40 keV electrons, exciting K-shell vacancies that are filled by L→K transitions. The wavelength sits comfortably in the middle of typical interatomic spacings (1–3 Å), so most peaks fall between 2θ = 10° and 80° where modern detectors are most sensitive. A monochromator or β-filter (Ni foil) suppresses the unwanted Kβ line. For samples containing iron, cobalt, or manganese, Cu-Kα fluoresces them and adds background; alternative anodes (Mo-Kα at 0.7107 Å, Co-Kα at 1.7889 Å, Cr-Kα at 2.2909 Å) are used to avoid this and to give different peak ranges.
How big does a crystal need to be?
Powder XRD needs ~50 to 200 mg of finely ground (5–25 µm grain) sample for a flat-plate transmission or reflection mount. Single-crystal small-molecule XRD typically uses crystals 0.1 to 0.5 mm on a side, mounted on a 100–300 µm loop in a cryoloop and flash-cooled to ~100 K to suppress thermal motion and radiation damage. Macromolecular crystals tend to be slightly smaller (50 µm to 0.5 mm) and far more fragile; the X-FELs at LCLS and SACLA accept crystals as small as a few microns ('serial femtosecond crystallography') by acquiring one diffraction snapshot before the crystal is destroyed by the beam, then merging tens of thousands of snapshots.
What is the difference between powder and single-crystal XRD?
A single crystal preserves both the magnitude and direction of every Bragg reflection: rotating the crystal lets you collect a 3D dataset of structure-factor magnitudes, from which (after solving the phase problem) you can refine atomic positions to ±0.005 Å. Powder XRD averages over all crystallographic orientations because the sample is a random aggregate of microcrystallites, so 3D information is projected onto a 1D scan of intensity versus 2θ. You can identify phases (each compound has a fingerprint catalogued in the ICDD/PDF database), measure lattice parameters and crystallite size, perform Rietveld refinement of structures, and quantify phase mixtures, but you cannot generally solve a previously unknown structure from powder data alone unless the unit cell is small.
What is the phase problem?
X-ray detectors measure intensity, which is the square of the structure-factor magnitude |F(hkl)|; the phase angle of F is lost. To compute the electron density ρ(x,y,z) you need the complex F = |F| exp(iφ), and recovering φ is the phase problem. Solutions: direct methods (Hauptman and Karle, 1985 Nobel) work for small molecules with ≤200 atoms; molecular replacement (a homologous structure as starting model) works for proteins with a known relative; isomorphous replacement (heavy-atom soaks) and anomalous scattering (MAD/SAD) provide experimental phases for novel proteins. For sub-Ångström resolution data of small molecules, intrinsic phasing (charge flipping, dual space) now solves structures fully automatically in seconds.
How did XRD reveal the DNA double helix?
Rosalind Franklin and Raymond Gosling at King's College London produced 'Photo 51' in May 1952 — a fiber diffraction pattern of the B-form of DNA showing a clear X-shaped layer-line pattern. The X spacing implies a helical structure; the layer-line spacing of 3.4 Å gives the rise per base pair, and the meridional reflection at 1/34 Å gives a 34 Å pitch (so 10 base pairs per turn). The missing fourth layer line ruled out a single-strand helix and was consistent with a two-strand antiparallel arrangement. James Watson saw the photo in January 1953 (without Franklin's permission) and combined it with Erwin Chargaff's base-pairing ratios to construct the Watson-Crick model published in Nature on 25 April 1953.