Crystallography

Crystallography relies on the diffraction of radiation—X-rays, neutrons, or electrons—by the periodic lattice of a crystal. The resulting diffraction pattern is a Fourier transform of the electron density (for X-rays) or nuclear density (for neutrons), from which the atomic positions can be reconstructed.¹ The phase problem, the loss of phase information in measured intensities, is overcome by methods such as direct methods, Patterson synthesis, or molecular replacement.²

Modern crystallography often uses synchrotron radiation sources, which provide intense, tunable beams, enabling structure determination of tiny crystals and macromolecular complexes. Cryo-electron microscopy has recently complemented crystallography for large assemblies, but crystallography remains the gold standard for atomic-resolution structures of small molecules and many proteins.

The field began in 1912 when Max von Laue, Walter Friedrich, and Paul Knipping demonstrated that X-rays diffract from crystals, proving their wave nature and periodic atomic arrangement.³ William Henry Bragg and William Lawrence Bragg then derived the Bragg equation, nλ = 2d sinθ, and solved the first crystal structures, including sodium chloride and diamond.⁴

Dorothy Crowfoot Hodgkin used crystallography to determine the structures of penicillin, vitamin B12, and insulin, earning the 1964 Nobel Prize in Chemistry.⁵ The development of direct methods by Herbert Hauptman and Jerome Karle in the 1950s automated structure solution, earning them the 1985 Nobel Prize in Chemistry.⁶

Crystallography is essential in materials science for understanding the properties of metals, alloys, ceramics, and semiconductors. It enables the design of new materials with tailored properties, such as high-temperature superconductors and metal-organic frameworks (MOFs).⁷ In geology, it identifies minerals and reveals their formation conditions.

In structural biology, crystallography has determined the structures of thousands of proteins, nucleic acids, and their complexes, including the DNA double helix (though that was solved by fiber diffraction) and the ribosome, for which Venkatraman Ramakrishnan, Thomas Steitz, and Ada Yonath shared the 2009 Nobel Prize in Chemistry.⁸ The technique is also used in drug discovery, enabling structure-based design of pharmaceuticals.

Beyond X-rays, neutron crystallography can locate hydrogen atoms, crucial for understanding enzyme mechanisms, and electron crystallography is used for two-dimensional crystals and thin films. The International Year of Crystallography in 2014 celebrated the field's contributions, and the UNESCO-recognized Crystallography in Latin America initiative has helped develop the field in developing countries.

An obscure but notable fact: the first crystal structure solved by X-ray diffraction was not a mineral but the salt sodium chloride, by the Braggs in 1913. Also, the term "crystallography" originally referred to the study of crystal shapes, a purely geometric discipline, before the advent of diffraction methods. The mathematical framework of space groups, developed by Fedorov and Schoenflies in the 19th century, was later confirmed by X-ray diffraction.

Quasicrystals, discovered by Dan Shechtman in 1982, exhibit diffraction patterns with fivefold symmetry, once considered impossible for crystals; Shechtman won the 2011 Nobel Prize in Chemistry for this discovery.⁹ The International Union of Crystallography (IUCr) defines a crystal as any solid with a discrete diffraction diagram, thus including quasicrystals.

Another edge case is the use of crystallography in art history: analysis of pigments in ancient paintings can reveal their provenance and authenticity. Also, the structure of ice has been studied crystallographically, revealing over 20 different crystalline phases depending on pressure and temperature, with implications for planetary science.

Diffraction

The bending and spreading of waves when they encounter an obstacle or aperture, producing interference patterns that reveal structural information.

Phase problem

The difficulty in determining the phases of diffracted waves, which are lost in intensity measurements, requiring computational or experimental methods to recover.

Space group

The set of symmetry operations that describe the arrangement of atoms in a crystal, combining translations, rotations, and reflections.

Quasicrystal

A solid with a non-periodic, but ordered, atomic structure that exhibits diffraction patterns with forbidden symmetries like fivefold.