Cubic Close Packing (CCP/FCC): Structure, Coordination, and Packing Efficiency

What Is Cubic Close Packing?

Cubic Close Packing (CCP), also known as Face-Centred Cubic (FCC), is one of the most efficient ways atoms can be arranged in a crystal. It achieves a packing efficiency of 74%, meaning 74% of the available space is filled with atoms.

CCP is formed by stacking close-packed layers in the sequence ABCABC... — each third layer is offset from both previous layers before the pattern repeats.

Learning Goals: By the end of this guide, you should be able to:

Describe the CCP/FCC unit cell and layer sequence.

Calculate the number of atoms per unit cell.

Determine the coordination number.

Calculate packing efficiency.

Identify elements and compounds with CCP structures.

The Unit Cell

Atom Positions

In an FCC unit cell:

8 corner atoms — each shared among 8 unit cells → contributes $\frac{1}{8}$ each
6 face-centre atoms — each shared between 2 unit cells → contributes $\frac{1}{2}$ each

Atoms per Unit Cell

N = 8 \times \frac{1}{8} + 6 \times \frac{1}{2} = 1 + 3 = 4 \text{ atoms}

Coordination Number

Each atom in CCP touches 12 nearest neighbours:

6 in the same layer
3 in the layer above
3 in the layer below

The coordination number of 12 is the maximum possible for equal-sized spheres.

Packing Efficiency

\text{Packing efficiency} = \frac{\text{Volume of atoms}}{\text{Volume of unit cell}} \times 100\%

For FCC, the face diagonal contains 4 radii: $\sqrt{2}a = 4r$ , so $a = 2\sqrt{2}r$ .

\text{Packing efficiency} = \frac{4 \times \frac{4}{3}\pi r^3}{(2\sqrt{2}r)^3} \times 100\% = \frac{16\pi r^3/3}{16\sqrt{2}r^3} \times 100\% = \frac{\pi}{3\sqrt{2}} \times 100\% \approx 74\%

CCP/FCC Crystal Explorer

Rotate and slice through a face-centred cubic crystal. See the ABCABC layer sequence, count coordination neighbours, and calculate packing efficiency interactively.

Explore CCP in 3D

CCP vs HCP vs BCC

Property	CCP (FCC)	HCP	BCC
Layer sequence	ABCABC	ABABAB	—
Coordination number	12	12	8
Atoms per unit cell	4	6 (hex cell)	2
Packing efficiency	74%	74%	68%
Examples	Cu, Al, Au, Ag	Mg, Zn, Ti	Fe, Na, K, W

Real-World Examples

Copper, Aluminium, Gold, Silver: All adopt CCP — contributing to their ductility and malleability.
NaCl structure: Cl⁻ ions form a CCP arrangement, with Na⁺ in octahedral voids.
Diamond: A modified FCC with a 2-atom basis.

Worked Examples

Example 1: Calculate Density

Given: Copper has FCC structure, $a = 361$ pm, $M = 63.5$ g/mol.

\rho = \frac{Z \times M}{a^3 \times N_A} = \frac{4 \times 63.5}{(3.61 \times 10^{-8})^3 \times 6.022 \times 10^{23}} = 8.92\ g/cm^3

Example 2: Edge Length from Atomic Radius

Given: Gold has $r = 144$ pm.

a = 2\sqrt{2}r = 2\sqrt{2} \times 144 = 407\ pm

Common Mistakes

Confusing CCP with HCP — Both have 74% efficiency and CN = 12, but differ in layer sequence (ABCABC vs ABABAB). CCP has a cubic unit cell; HCP has a hexagonal unit cell.
Miscounting atoms per unit cell — Corner atoms contribute $\frac{1}{8}$ , face atoms $\frac{1}{2}$ . Don't count full atoms at shared positions.
Wrong relationship between $a$ and $r$ — For FCC: $a = 2\sqrt{2}r$ (from the face diagonal). For BCC it's different: $a = \frac{4r}{\sqrt{3}}$ .

Frequently Asked Questions

Why is CCP so common in metals?

CCP maximises packing efficiency and coordination (12 neighbours). This maximises metallic bonding strength, making CCP a very stable arrangement for many metals.

Is CCP the same as FCC?

Yes, they describe the same structure from different perspectives. CCP emphasises the close-packed layer stacking (ABCABC), while FCC describes the cubic unit cell geometry.

Hexagonal Close Packing — The ABABAB alternative with identical packing efficiency.
Octahedral Voids — The holes between atoms in close-packed structures.
Tetrahedral Voids — Smaller holes in close-packed arrangements.