How this calculator works
Treat equal atoms as touching hard spheres. Nearest neighbours touch along a cube edge in SC, a body diagonal in BCC and a face diagonal in FCC. Shared corner and face sites contribute fractional ownership to a conventional unit cell. Real atomic radii depend on bonding, so the hard-sphere relationship is a model rather than a universal measured radius.
Formula
SC: a = 2r, Z = 1. BCC: a = 4r/sqrt(3), Z = 2. FCC: a = 2sqrt(2)r, Z = 4. Packing = Z(4pi r^3/3)/a^3.
Worked example
SC with r = 0.1 nm has a = 0.2 nm and volume 0.008 nm3. BCC with r = sqrt(3)/4 nm has a = 1 nm and two atoms per cell.
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Frequently asked questions
Are these primitive cells?
SC is primitive; the conventional BCC and FCC cubes contain two and four atoms respectively.
Which length units should I enter?
Enter both radius and lattice parameter in nanometres. One nanometre is ten angstroms.
Does this apply to diamond?
Diamond has an additional basis and different nearest-neighbour geometry. Use the appropriate crystal structure relation.