The Building Block of Crystals
Every crystalline material is built from a single repeating motif — the unit cell. Like a three-dimensional tile, the unit cell tessellates space perfectly, generating the macroscopic crystal through translation alone. The geometry of this fundamental block determines everything from how X-rays scatter to how electrons conduct through the material.
Crystal Systems and Lattice Types
The seven crystal systems classify unit cells by their symmetry: cubic (a=b=c, all angles 90°), tetragonal (a=b≠c), orthorhombic (a≠b≠c, all 90°), hexagonal, trigonal, monoclinic, and triclinic. Within each system, centering operations produce 14 Bravais lattices — the complete set of distinct periodic point arrangements in three dimensions.
Packing and Coordination
The atomic packing fraction quantifies how efficiently atoms fill space. Simple cubic achieves only 52%, leaving large voids. Body-centered cubic reaches 68% with 8 nearest neighbors. Face-centered cubic and hexagonal close-packed both achieve the theoretical maximum of 74% for equal spheres, with 12 nearest neighbors — explaining why most metals adopt these structures.
From Unit Cell to Material Properties
The unit cell is not merely a geometric curiosity — it directly governs material behavior. Slip planes for plastic deformation follow close-packed directions. Electronic band structure emerges from the periodic potential. Optical anisotropy in minerals reflects unit cell symmetry. Understanding the unit cell is the gateway to predicting and engineering material properties.