X-ray crystallography does not photograph atoms. It measures how X-rays diffract when they pass through a regularly ordered crystal, then uses those measurements and a mathematical model to reconstruct electron density and infer the positions of atoms.
How does a crystal turn X-rays into a diffraction pattern?
Repeating order makes the waves interfere
A crystal contains scattering centres arranged in a repeating pattern. When X-rays encounter that ordered arrangement, waves scattered from different parts of the crystal overlap. Depending on their directions, they reinforce one another or cancel. The resulting diffraction pattern records reflections—often seen as spots—with intensities that depend on the crystal structure and the scattering geometry. The International Union of Crystallography (IUCr) explains the basic relationship in its X-ray diffraction educational pamphlet.
Bragg’s law describes the geometry of strong reflections
Strong reflections occur when scattered waves reinforce one another. For planes in a crystal, the condition is expressed by Bragg’s law:
2d sin θ = nλ
- d is the spacing between lattice planes.
- θ is the angle between the incident X-ray wave and those planes.
- λ is the X-ray wavelength.
- n is an integer.
At a matching angle and wavelength, waves scattered by successive planes travel distances that allow them to arrive in step, producing a reflection. Bragg’s law specifies where reflections can occur; it does not, by itself, reveal the complete molecular structure.
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What does a crystallography experiment measure?
In a single-crystal experiment, the crystal is exposed to X-rays and diffraction data are collected across accessible directions. The measurements are reflection intensities. They are evidence about the structure—not a ready-made image of the molecule. The IUCr describes the collection of diffraction data and reflections in its educational explanation of X-ray diffraction.
Each reflection corresponds to a particular direction in reciprocal space, a way of representing the repeating geometry of the crystal. Taken together, the measured reflections provide constraints on the arrangement of scattering matter. Turning those measurements into a map of electron density requires an additional piece of information that the detector does not directly supply: phase.
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Why is phase information needed to reconstruct electron density?
A reflection is described by a structure factor, which has both an amplitude and a phase. The measured intensity is related to the amplitude, but routine diffraction measurements do not directly provide the phase. Yet Fourier reconstruction—the mathematical step used to calculate electron density from diffraction data—requires both amplitude and phase.
This missing information is known as the phase problem. Crystallographers use structure-solution methods to estimate or recover phases, then combine them with measured amplitudes to calculate an electron-density map. As the IUCr explains in its discussion of X-ray crystallography, the map is reconstructed from diffraction data; it is not an image captured directly by the experiment.
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How does electron density become a molecular structure?
Interpret the density
Once a useful electron-density map has been calculated, crystallographers interpret its features and propose positions for atoms. The map constrains where atoms can plausibly be placed, but constructing a molecular structure involves interpretation rather than simply tracing a photograph.
Refine the model against the measurements
The proposed atomic model is used to calculate structure factors. Crystallographers compare those calculated values with the observed diffraction data and adjust the model iteratively. This refinement seeks a model consistent with the measurements and the density. Atomic motion and other features affect the density, so it does not necessarily appear as a set of sharp, fixed points.
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The final structure is therefore an evidence-constrained model of the crystal: it is inferred from measured diffraction, reconstructed density, and refinement. It should not be described as a direct photograph of atoms.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.What does resolution tell you about a crystallographic structure?
Crystallographic resolution is tied to the smallest spacing between lattice planes represented by the measured intensities. In practical terms, higher resolution means the data extend to finer spacings, which can make it easier to distinguish neighbouring features in an electron-density map. The IUCr defines resolution in relation to the minimum plane spacing and the measured diffraction data in its crystallographic glossary entry.
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Quick Recap
The path from diffraction to a molecular model
- Order: A crystal’s repeating arrangement causes scattered X-ray waves to interfere.
- Measure: The experiment records reflection intensities at accessible diffraction directions.
- Solve phases: Because intensities do not directly provide phase, structure-solution methods estimate or recover it.
- Reconstruct: Amplitudes and phases are used in a Fourier calculation to produce an electron-density map.
- Model and refine: Atoms are placed into the interpreted density, and the model is iteratively checked against the observed data.
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