Crystallography

Crystallography is the branch of science that studies the arrangement of atoms in crystalline solids and the principles by which atomic order governs the properties of those materials. Crystals exhibit long-range periodic order, yielding characteristic diffraction patterns when they interact with waves such as X-rays, electrons, or neutrons. The discipline spans chemistry, mineralogy, materials science, physics, and structural biology, and underpins the determination of atomic structures in solid-state systems and related materials.

X-ray crystallography is the principal method for structure determination. It relies on Bragg's law, nλ = 2d sin θ, linking diffraction angles to interplanar spacings. Diffraction data are processed to solve the phase problem and produce electron density maps, from which atomic models are built and refined. Crystals are described by unit cells, lattice parameters, and symmetry through space groups. Other techniques include neutron diffraction—useful for locating light atoms such as hydrogen—and electron diffraction or cryo-electron microscopy for macromolecules and nanoscale materials. Powder diffraction is also common.

Historically, crystallography emerged from studies of symmetry and lattice periodicity and advanced with the Braggs’ X-ray work in the early 20th century, complemented by Laue. The method has become essential in chemistry for solving molecular structures, mineralogy for identifying minerals, and biology for structures of proteins and nucleic acids. Structural data inform drug design, materials engineering, and fundamental science, and are archived in public databases such as the Protein Data Bank and crystallographic repositories.