Crystallography

Crystallography is the study of how atoms, ions or molecules arrange themselves in ordered, repeating patterns to form solid materials. At its heart lies the concept of the unit cell: the smallest three‐dimensional block whose translation in space generates the entire crystal lattice. The symmetry elements of that lattice—rotational axes, mirror planes, inversion centres and translational repeats—are captured by the 230 space groups that classify every possible crystal structure. X-ray, neutron and electron diffraction provide the experimental means to measure interatomic spacings and intensities of scattered waves, which are then inverted by phase‐retrieval algorithms to yield electron‐density maps. From these maps one derives precise atomic coordinates, bond lengths and angles, and hence insights into chemical bonding, physical properties and material functionality. Crystallography underpins fields as diverse as mineralogy, materials science, chemistry and structural biology. It reveals how subtle structural distortions control superconductivity in ceramics, how framework flexibility governs gas adsorption in metal–organic frameworks, and how protein conformations determine biochemical activity. Advances in ultrabright X-ray free-electron lasers and coherent diffraction imaging have extended the technique to femtosecond time‐resolved studies, capturing transient states of matter before radiation damage sets in. Modern crystallography thus bridges scales from sub-ångström atomic resolution to the mesoscale, offering a comprehensive picture of structure–property relationships in crystalline materials.

Research from Nature Portfolio

Innovations in defining atomic and molecular boundaries have recently emerged from the comparison of experimental thermodynamic data with electron-density contours. By demonstrating that an iso‐density surface contoured at 0.0016 atomic units aligns closely with measured phase‐change effective surfaces, researchers have established a universal metric for atomic and ionic radii that unites quantum-chemical computations and macroscopic observables. In parallel, a new artificial-intelligence-enabled pipeline for real-time X-ray ptychographic imaging has been developed. By streaming coherent diffraction data at kilohertz rates into deep-learning models at the experiment’s edge, this workflow achieves rapid phase retrieval with orders of magnitude less data and lower dose than conventional methods. The integration of high-performance computing with neural-network priors allows immediate feedback on nanoscale structure, paving the way for dynamic in situ studies of functional materials and live biological specimens.

Research from all publishers

Diffraction before destruction of single proteins has been realised using ultrafast X-ray pulses from free-electron lasers. In a landmark experiment, diffraction patterns were recorded from individual GroEL chaperonin molecules on the femtosecond timescale, confirming that snapshots can be obtained before the onset of sample damage. These measurements enable orientation determination of single macromolecules in the absence of crystals, opening new avenues for time-resolved studies of conformational changes in solution. Meanwhile, three-dimensional ptycho-tomographic imaging has been accelerated through deep-learning strategies that reduce the necessary angular projections by an order of magnitude. By training neural networks on conventional tomography reconstructions and then applying them to limited-angle data, researchers have achieved nanometre-scale volumetric reconstructions over tens of micrometres in seconds rather than hours. Such approaches promise rapid, high-resolution views of strain fields, defects and compositional heterogeneities in materials science and biology.

Crystallography publication trend

The graph below shows the total number of articles in crystallography across all publications each year (not limited to Nature Index journals).

Technical terms

Unit cell: The fundamental repeating block of a crystal lattice, defined by three vectors that generate the entire structure through translation.

Space group: A mathematical classification of crystal symmetry that combines point operations (rotations, reflections, inversions) with translational symmetry.

Bragg’s law: The relationship nλ = 2d sin θ linking X-ray wavelength λ, diffraction angle θ and interplanar spacing d for constructive interference.

Electron-density map: A three-dimensional distribution of electron probability reconstructed from diffraction intensities and phase information.

Ptychography: A coherent diffraction imaging technique in which overlapping illuminated regions yield redundant data for robust phase retrieval and high-resolution reconstruction.

Iso-density surface: A surface of constant electron density used to demarcate atomic or molecular boundaries in computational chemistry and crystallography.

References

1. Introduction to Crystallography.
2. Electron iso-density surfaces provide a thermodynamically consistent representation of atomic and molecular surfaces. Nature Communications (2024).
3. Deep learning at the edge enables real-time streaming ptychographic imaging. Nature Communications (2023).
4. Observation of a single protein by ultrafast X-ray diffraction. Light: Science & Applications (2024).
5. Three-dimensional nanoscale reduced-angle ptycho-tomographic imaging with deep learning (RAPID). eLight (2023).