Cubic Cell Calculator
Calculate unit cell parameters for cubic crystal structures including simple cubic (SC), body-centered cubic (BCC), face-centered cubic (FCC), and diamond structures.
Type of cubic crystal structure
Edge length of the cubic unit cell
Radius of atoms in the structure (used for packing efficiency)
For density calculation
What are the three cubic crystal structures?
1) Simple Cubic (SC): atoms only at corners, 1 atom/unit cell, coordination number 6. 2) Body-Centered Cubic (BCC): corners + center, 2 atoms/unit cell, CN 8. 3) Face-Centered Cubic (FCC): corners + face centers, 4 atoms/unit cell, CN 12 (closest packing).
How do you calculate atoms per unit cell?
Corner atoms: 8 × 1/8 = 1 atom. Edge atoms: 12 × 1/4 = 3 atoms. Face atoms: 6 × 1/2 = 3 atoms. Body center: 1 × 1 = 1 atom. SC = 1, BCC = 1+1 = 2, FCC = 1+3 = 4, Diamond = 4+4 = 8 (two interpenetrating FCC lattices).
What is packing efficiency?
Packing efficiency = (volume of atoms in unit cell / volume of unit cell) × 100%. SC: 52.4%, BCC: 68.0%, FCC: 74.0% (maximum for equal spheres). Higher packing = denser material. FCC metals (Al, Cu, Ag, Au) are the most densely packed.
How do you calculate density from lattice constant?
Density ρ = (Z × M) / (a³ × N_A), where Z = atoms/unit cell, M = molar mass (g/mol), a = lattice constant (cm), N_A = 6.022 × 10²³. Convert Å to cm: 1 Å = 10⁻⁸ cm. FCC metals typically have high densities due to 4 atoms/cell and close packing.