Crystal Lattice Density Calculator
Calculate theoretical crystal density from unit cell parameters.
Find density for cubic and other crystal systems from lattice constants and molecular weight.
Crystal Lattice Density The theoretical (X-ray) density of a crystal is calculated from its unit cell geometry and composition. ρ = (Z × M) / (Nₐ × V) Where: Z = number of formula units per unit cell M = molar mass of the formula unit (g/mol) Nₐ = Avogadro’s number (6.022 × 10²³ mol⁻¹) V = unit cell volume (cm³)
Cubic Crystal Systems Simple cubic: Z = 1, a = b = c, V = a³ Body-centered cubic (BCC): Z = 2, V = a³ Face-centered cubic (FCC): Z = 4, V = a³ Diamond cubic: Z = 8, V = a³
Other Crystal Systems Tetragonal: V = a² × c Orthorhombic: V = a × b × c Hexagonal: V = a² × c × sin(60°) = a² × c × √3/2
Packing Efficiency Simple cubic: 52.4% — atoms touch along cube edge BCC: 68.0% — atoms touch along body diagonal FCC: 74.0% — highest packing for equal spheres (also HCP) Diamond: 34.0% — very open structure (covalent bonding)
Converting Lattice Constants Lattice constants are given in ångströms (Å) or pm. 1 Å = 10⁻⁸ cm = 100 pm. Use cm³ in the density formula. Typical metal lattice constants: 2.5–6 Å. Typical ionic crystal constants: 4–12 Å.
Common Examples Iron (BCC): a = 2.87 Å, M = 55.85 → ρ = 7.87 g/cm³ Copper (FCC): a = 3.615 Å, M = 63.55 → ρ = 8.92 g/cm³ NaCl (FCC-type): a = 5.64 Å, M = 58.44, Z = 4 → ρ = 2.16 g/cm³ Diamond (diamond cubic): a = 3.567 Å, M = 12.01, Z = 8 → ρ = 3.51 g/cm³
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