Packing efficiency and coordination number
Solid State · Chemistry
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Prove FCC packing efficiency is 74%. Step 1: 4 atoms/cell; each volume = (4/3)πr³. Step 2: a = 2√2 r → cell volume = a³ = (2√2 r)³ = 16√2 r³. Step 3: Atoms volume = 4 × (4/3)πr³ = (16/3)πr³. Step 4: Efficiency = [(16/3)πr³]/[16√2 r³] × 100 = π/(3√2) × 100 = 74.0%. No packing of equal spheres beats 74% — Kepler's conjecture, proved 1998.