Four bonding types build fundamentally different 2D unit cells (planar cross-sections of the real 3D structures). Ionic NaCl is a square lattice of alternating cations and anions (CN 4). Covalent honeycomb links every atom to 3 neighbours via directional shared-electron bonds — the loosest packing of the four. Metallic triangular atoms behave as hard discs cemented by a delocalised electron sea, reaching the theoretical maximum circle-packing density in 2D. Molecular crystals stack dimer pairs on a square grid, held together only by weak Van der Waals contacts (dashed lines) far weaker than the covalent bond inside each dimer (solid short line).
a(T) = a₀ · (1 + α·(T − T₀)) linear thermal expansion
φ(T) = φ₀ · (a₀ / a(T))² packing efficiency vs. T (2D area scaling)
CN = nearest neighbours within first coordination shell
- Lattice type — swaps the basis atoms, bond rules, coordination number and packing efficiency for a real 2D unit-cell geometry.
- Temperature — raises the linear expansion coefficient α·ΔT (bigger for weakly-bonded molecular solids, smallest for stiff covalent honeycomb) and the thermal vibration amplitude of every atom.
- Unit cell edges — outlines one repeating a×a cell inside the rendered supercell.
- Click an atom — highlights it and every atom directly bonded to it, reading out its true coordination number.
Real-world relevance: this is why diamond-like covalent solids barely expand when heated (rigid directional bonds, low α) while a molecular crystal expands many times faster and melts at far lower temperature (weak Van der Waals contacts, high α) — the same trade-off engineers account for when picking materials that must hold precise dimensions across a temperature range.