the body-centered cubic structure
Picture a cube with an atom at each of its eight corners and one lone atom sitting right in the middle of the box. It is a roomier arrangement than the tightest cannonball pile — the atoms are not quite as densely packed. This is the body-centered cubic structure.
Counting atoms: 8 corners times 1/8 plus 1 centre equals 2 atoms per cell. Here the atoms touch along the body diagonal (corner to opposite corner through the centre), so 4R = a times sqrt(3), giving a = 4R/sqrt(3). Each atom has 8 nearest neighbours (coordination number 8) and the packing factor is 0.68 (68 percent) — looser than FCC's 74 percent. Alpha-iron (ferrite) at room temperature, chromium, tungsten, and molybdenum are BCC.
BCC metals are generally strong, but many can turn brittle when cold: the ductile-to-brittle transition of BCC steels is why some steels crack in freezing conditions, a factor in the Titanic's hull and the World War II Liberty-ship fractures. Iron's ability to switch between BCC (ferrite) and FCC (austenite) on heating is the foundation of all steel heat treatment.
Alpha-iron (ferrite) is BCC. Atoms touch along the body diagonal, so 4R = a times sqrt(3). With only 2 atoms per cell it packs to just 0.68 — looser than FCC — which is one reason iron can dissolve more carbon when it flips to FCC austenite on heating.
BCC: 2 atoms per cell, coordination number 8, 68 percent packed.
Despite the atom in the centre, BCC is not close-packed — 0.68 versus 0.74. Its slip geometry gives BCC metals a temperature-dependent brittleness that FCC metals lack.