Metal Crystal Structures: BCC, FCC and HCP Explained

Walk into a greengrocer’s and look at the oranges on display. Nobody stacks them in neat square columns, one directly on top of the next. Instead each orange in a new layer settles into the dip between three oranges below it. The grocer is not thinking about geometry; gravity does the work, and the result happens to be the densest way to stack equal spheres.

Metal atoms face a very similar problem. In metallic bonding the positive ions sit in a sea of delocalised electrons, and that bond has no preferred direction. Each ion simply “wants” as many close neighbours as it can get, because more neighbours means more attraction to the shared electrons. So metal atoms behave a lot like hard spheres packed as tightly as possible, and the vast majority of metals end up in one of just three arrangements:

• body-centred cubic (BCC)
• face-centred cubic (FCC), also called cubic close-packed
• hexagonal close-packed (HCP)

This post builds each one from the ground up, explains why two of them are equally dense, and shows how the choice of structure leaves fingerprints on a metal’s behaviour.

Building close-packed layers

Start with one flat layer of spheres. The tightest way to arrange them is a hexagonal pattern: every sphere touches six others in the same plane, like coins pushed together on a table. Call this layer A.

Now add a second layer. Each sphere of the new layer drops into a hollow in layer A. There are two sets of hollows, but only half of them can be used at once, because neighbouring spheres in the new layer would otherwise overlap. Whichever set you pick, call the second layer B.

The third layer is where the story splits. Its spheres sit in hollows of layer B, and again there are two choices:

1. Put them directly above the spheres of layer A. The pattern repeats ABABAB…. That is hexagonal close packing.
2. Put them above the hollows of layer A that layer B did not use. This gives a new position, C, and the pattern runs ABCABCABC…. That is cubic close packing, which is the same thing as face-centred cubic.

Both stackings give each sphere exactly 12 nearest neighbours: six in its own layer, three in the layer above and three in the layer below. Both fill 74 % of space with spheres. Nothing more efficient is possible for identical spheres, a result (the Kepler conjecture) that took mathematicians almost four centuries to prove rigorously.

Face-centred cubic (FCC)

It is not obvious that ABC stacking has anything cubic about it. The cube only appears when you tilt your head: the close-packed layers lie perpendicular to the body diagonal of a cube.

In the conventional FCC unit cell there is an atom at each of the eight corners and one in the centre of each of the six faces. Along a face diagonal, the corner atoms and the face-centre atom touch. The face diagonal is a√2 and spans four radii, so

a√2 = 4r, which rearranges to a = 2√2 r.

Counting atoms, each corner is shared by eight cells and each face by two:

8 × ⅛ + 6 × ½ = 1 + 3 = 4 atoms per cell.

Coordination number: 12. Packing efficiency: 74 %.

Familiar FCC metals at room temperature include copper, aluminium, silver, gold, nickel and lead.

Hexagonal close-packed (HCP)

HCP keeps the ABAB stacking. Its conventional cell is a hexagonal prism: atoms on the 12 corners, one in the centre of each hexagonal face, and three tucked inside the middle layer. Each corner is shared by six prisms and each face by two, giving

12 × ⅙ + 2 × ½ + 3 = 2 + 1 + 3 = 6 atoms per prism.

(The smallest repeating cell is one-third of this prism and holds 2 atoms. Both descriptions are correct; they just carve the same crystal into different blocks.)

For perfect spheres the ratio of the prism’s height to its edge, c/a, would be about 1.633. Real HCP metals come close to this or depart from it; zinc, for example, is noticeably stretched along the c axis. The departure tells you the atoms are not quite behaving as hard spheres.

Coordination number: 12. Packing efficiency: 74 %.

HCP metals at room temperature include magnesium, zinc, titanium and cobalt.

Body-centred cubic (BCC)

BCC is the odd one out because it is not close-packed. It has an atom at each corner of a cube and one in the very centre. The corner atoms do not touch each other; instead, each corner atom touches the central atom along the body diagonal. The body diagonal of a cube is a√3 and spans four radii:

a√3 = 4r, so a = 4r/√3.

Atoms per cell: 8 × ⅛ + 1 = 2.

Each atom touches 8 nearest neighbours (the central atom touches all eight corners). There are also six second-nearest neighbours, at a distance a, only about 15 % farther away. That is why BCC is less loosely packed than its coordination number suggests.

Packing efficiency works out at π√3 ⁄ 8, or 68 %.

Well-known BCC metals at room temperature include iron (in its α form), chromium, tungsten, sodium and potassium. The soft, low-density alkali metals are a reminder that BCC is common among metals with only one or two valence electrons per atom, where the bonding is relatively weak.

The three side by side

	BCC	FCC (ccp)	HCP
Close-packed?	No	Yes (ABC…)	Yes (AB…)
Nearest neighbours	8	12	12
Atoms per conventional cell	2	4	6 (prism)
Atoms touch along	Body diagonal	Face diagonal	Within each layer and between layers
Edge vs radius	a = 4r/√3	a = 2√2 r	a = 2r (within a layer)
Packing efficiency	68 %	74 %	74 %
Examples	α-Fe, Cr, W, Na, K	Cu, Al, Ag, Au, Ni, Pb	Mg, Zn, Ti, Co

Why structure changes behaviour

Ductility and slip

A metal bends by slip: whole planes of atoms slide over one another. Close-packed planes are the smoothest to slide on, like sheets of paper compared with egg boxes.

FCC metals contain close-packed planes in four different orientations, each with three sliding directions. With so many ways to slip, a grain can deform whichever way it is pushed. That is why gold can be beaten into leaf thin enough to let light through, and why copper and aluminium draw easily into wire.

HCP metals have only one set of close-packed planes (the basal planes). At room temperature they have fewer easy slip options, so magnesium and zinc tend to be less ductile and are often shaped warm.

BCC metals have no truly close-packed plane, so slip is harder to start and depends strongly on temperature. Many BCC steels change from ductile to brittle when they get very cold, which is a genuine engineering hazard in cold-climate structures and ships.

Density and packing

Packing efficiency is only one factor in density. Tungsten is BCC, less efficiently packed than FCC copper, yet it is more than twice as dense, because each tungsten atom is so much heavier. Structure fixes how much space is filled; atomic mass sets how heavy each filled piece is. The companion post on unit cells shows how to combine both into a density calculation.

Holes and alloys

Even the closest packing leaves 26 % empty space. In FCC and HCP that space forms small tetrahedral holes and larger octahedral holes. Small atoms such as carbon, nitrogen or hydrogen can sit in these gaps to form interstitial alloys. Steel is the classic case: carbon fits more comfortably into the octahedral holes of FCC iron than into the smaller gaps of BCC iron, which is why the high-temperature form of iron dissolves far more carbon. See alloys and bonding for more.

Polymorphism: when one metal uses more than one structure

The best packing at one temperature is not always the best at another. Iron is BCC (α-iron) at room temperature, switches to FCC (γ-iron) above 912 °C, and returns to a BCC form just below its melting point. Titanium is HCP at room temperature and becomes BCC above about 882 °C. These phase transitions are the basis of heat treatment: quenching steel from the FCC region traps carbon in a strained structure and makes the metal much harder.

The small energy differences between structures come from details of the electronic structure, especially how d electrons fill bands. That is why neighbouring transition metals in the same period can prefer different structures, and why simple rules for predicting which metal adopts which arrangement do not really work.

An analogy to hold on to

Think of a crowded party. In an FCC or HCP room, everyone is shoulder to shoulder with 12 people and there is no way to squeeze tighter. In a BCC room, each person has 8 close friends, with 6 more acquaintances just a little farther off: slightly more elbow room, and a looser crowd overall. Whether the rows of the crowd repeat every two (HCP) or every three (FCC) doesn’t change how crowded it feels locally, but it does change how easily whole rows of people can shuffle past one another.

Common mistakes

• “BCC atoms touch along the cube edge.” They don’t. In BCC, atoms touch along the body diagonal, so a = 4r/√3, not 2r. Using the edge gives a radius that is far too large.
• “FCC and HCP have different packing efficiencies.” Both are 74 %. They differ in stacking sequence, not in how tightly each atom is surrounded.
• “Close-packed means no gaps.” Spheres can never fill space completely; about a quarter is always empty, and those holes matter for alloys.
• “Denser packing means a denser metal.” Atomic mass usually matters more. Compare BCC tungsten with FCC aluminium.
• “A metal has one crystal structure.” Several important metals, including iron and titanium, change structure with temperature.
• “Cubic close-packed and FCC are different things.” They are two names for the same arrangement, described from different viewpoints.

Key takeaways

• Non-directional metallic bonding favours many neighbours, so most metals adopt BCC, FCC or HCP.
• FCC (ABC stacking) and HCP (AB stacking) are both close-packed: coordination number 12 and 74 % of space filled.
• BCC is not close-packed: coordination number 8 and 68 % packing, with atoms touching along the body diagonal (a = 4r/√3).
• In FCC atoms touch along the face diagonal (a = 2√2 r); the cell holds 4 atoms, BCC holds 2.
• FCC metals are usually the most ductile; HCP metals have fewer slip options; BCC metals can turn brittle when cold.
• Iron and titanium change structure on heating, which underpins the heat treatment of steels and titanium alloys.