Work out crystal lattice parameter instantly with clear inputs, formula shown and shareable results.
The lattice parameter follows from how the touching atoms are arranged along a cube direction: along the edge for simple cubic (a = 2r), along the body diagonal for body-centred cubic (a = 4r/sqrt3), and along the face diagonal for face-centred cubic (a = 4r/sqrt2). Copper's 128 pm radius therefore gives a 362 pm face-centred cell with the maximum 74% packing.
Lattice parameter
SC: a = 2r; BCC: a = 4r/sqrt(3); FCC: a = 4r/sqrt(2)
Packing efficiency
packing = atoms x (4/3)pi.r^3 / a^3
Because the face diagonal packs four atomic radii into a shorter distance relative to the cell edge, giving 74% occupancy against 68%.
74.05%, achieved by both face-centred cubic and hexagonal close packing. No arrangement of equal spheres beats it.