Crystal Structure
Crystal structure refers to the ordered, repeating three-dimensional arrangement of atoms, ions, or molecules within a crystalline solid, described mathematically by a lattice (the repeating geometric pattern of points) combined with a basis (the group of atoms attached to each lattice point) — the structure ultimately responsible for many of a material's physical properties.
Curious
Look closely enough at a grain of table salt, and you'd find its sodium and chlorine atoms arranged in a perfectly regular, repeating cubic pattern, extending, with only occasional defects, throughout the entire crystal. This underlying atomic-scale order — invisible to the naked eye but revealed through techniques like X-ray diffraction — is what gives many solids their characteristic flat crystal faces, their tendency to cleave along specific planes, and much of their mechanical, electrical, and optical behaviour.
Not all solids are crystalline in this sense — glass, for instance, is "amorphous," lacking this long-range repeating order despite being solid — but the vast majority of naturally occurring and technologically important solid materials, from table salt to silicon computer chips to diamond, are crystalline, making crystal structure one of condensed matter physics' most foundational concepts.
Exploring
| Symbol | Name | SI Unit |
|---|---|---|
| n | Order of diffraction (integer) | dimensionless |
| λ | Wavelength of incident X-rays | metre (m) |
| d | Spacing between crystal lattice planes | metre (m) |
| θ | Angle of incidence (from the plane) | radian or degree |
Bragg's Law, above, is the key relationship enabling crystal structures to be experimentally determined: X-rays reflecting off successive parallel planes of atoms within a crystal interfere constructively only at specific angles, determined by the spacing between those planes — measuring the angles at which strong reflected X-ray intensity occurs allows the plane spacing, and ultimately the full three-dimensional crystal structure, to be reconstructed.
Deep Dive
William Henry Bragg and his son William Lawrence Bragg developed the theory and experimental technique of X-ray crystallography in 1912–1913, building directly on Max von Laue's 1912 discovery that crystals could diffract X-rays (itself confirming both the wave nature of X-rays and the periodic atomic structure of crystals in a single experiment). The Braggs' simple, elegant law — treating X-ray diffraction as reflection from successive atomic planes, constructively interfering only at specific angles — provided a practical method for determining atomic-scale crystal structures, work that earned the father-son pair the 1915 Nobel Prize in Physics, with William Lawrence Bragg remaining, at 25, the youngest Nobel laureate in history in any field.
The seven crystal systems and Bravais lattices: All possible crystal lattices can be classified into just 14 distinct types (the Bravais lattices), which themselves fall into 7 crystal systems (cubic, tetragonal, orthorhombic, hexagonal, trigonal, monoclinic, and triclinic) based on the symmetry of the unit cell — a remarkably complete mathematical classification worked out by Auguste Bravais in 1850, well before X-ray crystallography existed to experimentally verify it, that remains the standard framework for describing crystal geometry today (see the Codex's forthcoming Bravais Lattices entry for the full classification).
Modern X-ray crystallography, building directly on the Bragg technique, remains one of the most important experimental methods in all of science — used not only for classical inorganic crystal structure determination, but famously also for determining the structures of complex biological macromolecules, including the double-helix structure of DNA (Watson, Crick, Franklin, and Wilkins, 1953) and the structures of thousands of proteins, underpinning much of modern structural biology and drug design.
Concept Relationship Map
Requires: wave-particle duality
Enables: Bravais lattices [PENDING FULL ENTRY], band theory, X-ray diffraction [PENDING FULL ENTRY]
Commonly confused with: treating the unit cell as a uniquely determined physical object rather than a conventional mathematical choice
Sources
- Bragg, W.H., Bragg, W.L. (1913). Proceedings of the Royal Society A, 88(605), 428–438.
- Kittel, C. (2004). Introduction to Solid State Physics, 8th ed. Wiley, Ch. 1–2.