BCC, FCC & HCP: How Atoms Pack in Crystal Structures

The 14 Bravais lattices, and the three that matter for metals

A crystal is an infinite, periodic arrangement of atoms described by a Bravais lattice — a set of points R = n₁a₁ + n₂a₂ + n₃a₃ built from repeating a primitive cell. Auguste Bravais proved in 1848 that only 14 distinct lattice types exist in three dimensions. Of the three cubic ones, simple cubic packs so poorly (APF 52%) that only polonium uses it; the two that actually matter for engineering metals are body-centred cubic and face-centred cubic. Hexagonal close-packed isn't a Bravais lattice at all — it's a hexagonal lattice with a two-atom basis.

Body-centred cubic: 68% packing, 8 neighbours

In BCC, atoms sit at the eight cube corners plus one at the body centre — 2 atoms per unit cell, touching along the body diagonal (4R = a√3):

a = 4R/√3
APF_BCC = π√3/8 ≈ 0.6802 = 68.02%
Coordination number = 8 (+6 next-nearest, only 15% farther)

BCC metals include α-iron (below 912°C), tungsten (the highest melting point of any metal), chromium, molybdenum and vanadium. BCC has no truly close-packed plane, so its dislocations need higher stress to glide — one reason BCC metals like iron are strong but comparatively less ductile at room temperature than FCC metals.

Face-centred cubic: the ductile champion

FCC places atoms at all 8 corners plus the centre of all 6 faces — 4 atoms per cell, touching along the face diagonal (4R = a√2):

a = 2R√2
APF_FCC = π/(3√2) ≈ 0.7405 = 74.05%  (the Kepler-conjecture maximum for spheres)
Coordination number = 12,  stacking sequence ABCABC…

Copper, aluminium, gold, silver, nickel and platinum are all FCC. Its four {111} close-packed planes, each offering three slip directions, give 12 independent slip systems — comfortably above the 5 required by the Von Mises criterion for arbitrary shape change — which is exactly why FCC metals bend, draw and roll so readily.

Hexagonal close-packed: same density, fewer escape routes

HCP reaches the identical 74.05% packing fraction as FCC, but by stacking close-packed planes ABAB — alternating between just two layer positions instead of three. The ideal ratio of cell height to width is (c/a) = √(8/3) ≈ 1.633; magnesium (1.624) sits close to ideal, while zinc (1.856) and titanium (1.587) are visibly distorted. HCP metals — magnesium, titanium, zinc, cobalt — have only 3 basal slip systems at room temperature, short of the 5 needed for unrestricted plastic flow, which is why they're markedly less formable than copper or aluminium unless heated to activate additional pyramidal slip planes.

Why an element picks one structure over another

The choice is ultimately quantum mechanical: whichever arrangement minimises total electronic energy wins. Elements with broad, unfilled d-bands (Cu, Ag, Au, Ni) favour FCC; elements at the ends of the transition-metal series (Group 1, 2, 5, 6) often favour BCC, and iron's BCC phase is further stabilised by ferromagnetic exchange energy below its Curie coupling. The FCC–HCP energy gap is frequently under 10 meV/atom, which is why some metals flip between them with temperature — cobalt transforms HCP→FCC at 417°C, and adding carbon to iron expands the FCC ("austenite") stability range, the whole basis of steel heat treatment.

Frequently asked questions

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