Visualize simple cubic, body-centered cubic, and face-centered cubic unit cells.
Crystal structure determines the density, hardness, and packing efficiency of metallic and ionic solids, and calculating these properties from a unit cell is a core AP Chemistry Unit 2 and IChO solid-state chemistry skill that rewards spatial reasoning over memorization.
A unit cell is the smallest repeating 3D block that, stacked in all directions, reproduces the entire crystal lattice. Simple cubic (SC) packing places atoms only at the eight corners of a cube, each shared among 8 adjacent cells, giving exactly 1 atom per unit cell and a packing efficiency of just 52% — the least efficient common packing arrangement, with a coordination number of only 6.
Body-centered cubic (BCC) adds one atom at the exact center of the cube in addition to the corner atoms, giving 2 atoms per unit cell (1 from corners + 1 full center atom), 68% packing efficiency, and coordination number 8. Face-centered cubic (FCC) instead places an atom at the center of each of the six faces (each shared between 2 cells) in addition to the corners, giving 4 atoms per unit cell, 74% packing efficiency — the maximum possible for spheres of equal size — and coordination number 12.
Density is calculated directly from unit cell geometry: ρ = (Z × M)/(NA × Vcell), where Z is atoms per unit cell, M is molar mass, NA is Avogadro's number, and Vcell is the unit cell volume calculated from the edge length, which itself relates to atomic radius differently for each packing type (a = 2r for SC, a = 4r/√3 for BCC, a = 2r√2 for FCC). Getting the correct radius-to-edge-length relationship for each structure is the step most often missed.
This simulator renders SC, BCC, and FCC unit cells in interactive 3D, calculates packing efficiency and coordination number automatically, and lets you compute crystal density from atomic radius and molar mass — connecting an abstract geometric model directly to measurable bulk properties.