Solid State
Crystal Lattice
Repeating 3D arrangement of atoms — defines crystalline solids
A crystal lattice is the repeating 3D arrangement of atoms, ions, or molecules in a crystalline solid. Defined by unit cell — smallest repeating unit. 14 Bravais lattices possible (combinations of cubic, tetragonal, orthorhombic, monoclinic, triclinic, hexagonal, rhombohedral with primitive, body-centered, face-centered options). Properties: optical, mechanical, electrical all depend on lattice. Examples: NaCl (face-centered cubic), diamond (FCC carbon), graphite (hexagonal layers), metals (close-packed). Crystallography uses X-ray diffraction to determine lattice structure.
- DefinitionRepeating 3D arrangement; defined by unit cell
- Bravais lattices14 unique 3D lattices
- NaClFace-centered cubic (FCC)
- DiamondModified FCC; tetrahedral C
- Metals (most)BCC, FCC, or HCP
- DeterminationX-ray diffraction (Bragg's law)
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Why lattices matter
- Material properties. Strength, conductivity from structure.
- Drug development. Crystal form affects bioavailability.
- Semiconductors. Si lattice enables electronics.
- Mineralogy. Mineral identification.
- Crystallography. Structure determination.
- Pharmacology. Polymorphs of drugs differ.
- Materials engineering. Alloys, composites.
Common misconceptions
- Crystals are perfect. Defects always present.
- Same composition = same structure. Polymorphs (diamond/graphite).
- Lattice is just packing. Symmetry and bonding too.
- Amorphous solids are same as crystalline. Different (no lattice).
- Lattice determined visually. Need diffraction.
- Crystals only at low T. Many at room T (metals, salts).
Frequently asked questions
What's a unit cell?
Smallest repeating unit of crystal lattice. Whole crystal = unit cells stacked in all 3 directions. Defined by lattice parameters: 3 lengths (a, b, c) and 3 angles (α, β, γ). Examples: simple cubic (a=b=c, all 90°), FCC (cubic with atoms at corners + face centers), BCC (cubic with corner + center atoms).
What are the 14 Bravais lattices?
All possible 3D periodic lattices. 7 crystal systems × allowable centerings. Cubic (3): primitive, body-centered (BCC), face-centered (FCC). Tetragonal (2): primitive, body-centered. Orthorhombic (4). Monoclinic (2). Triclinic (1). Hexagonal (1). Rhombohedral (1). Discovered by Auguste Bravais (1850).
What's close packing?
Most efficient way to pack equal spheres. Two main types: HCP (hexagonal close-packed) — ABAB stacking; FCC (face-centered cubic) — ABCABC stacking. Both pack 74% efficiency (74% volume filled). Most metals. Spheres in plane form hexagons; layers stack with each sphere in indentation of layer below.
What's diamond's structure?
Each carbon sp³ hybridized; 4 bonds in tetrahedral arrangement. Modified FCC: 8 atoms per unit cell. Each C bonded to 4 others. 3D network of strong C-C bonds. Properties: hardest natural material, very high melting point, electrical insulator (no free electrons), thermal conductivity excellent (phonon-mediated).
What's graphite's structure?
Layers of carbon hexagons. Each C: sp² hybridized; 3 covalent bonds in plane + delocalized π electron. Layers held by weak van der Waals forces — easily slip past each other (lubricant). Conducts electricity within layers (delocalized π). Stable structure. Diamond and graphite both pure carbon — different lattices give very different properties.
How is structure determined?
X-ray diffraction (XRD). X-rays scatter from electron clouds. Diffraction pattern reveals atomic positions. Bragg's law: nλ = 2d sin(θ). Pattern of bright spots gives unit cell parameters. Modern methods: synchrotron XRD, neutron diffraction, electron diffraction. Resolved many structures (DNA Watson-Crick, drug structures, proteins).
What's an ionic crystal?
Lattice of cations and anions in repeating pattern. NaCl: face-centered cubic; Na⁺ and Cl⁻ alternating. Held by ionic bonds (electrostatic). Each Na⁺ surrounded by 6 Cl⁻ (octahedral); each Cl⁻ by 6 Na⁺. Symmetric arrangement minimizes energy. CsCl is different (simple cubic; 8-coordinate).