The Face-Centered Cubic (FCC) structure is one of the most common crystal structures in metals. FCC metals are highly ductile and closely packed, which makes them ideal for forming and machining operations.

Understanding FCC is crucial for engineers because it explains ductility, slip systems, and mechanical behavior of metals.

Definition

Face-Centered Cubic (FCC) Structure

FCC is a cubic crystal structure where atoms are located at each corner and at the center of each face of the cube.

Structure of FCC

• Corner atoms: 8 (each shared by 8 unit cells → contributes 1 atom total)

• Face atoms: 6 (each shared by 2 unit cells → contributes 3 atoms total)

Total atoms per unit cell = 4

• Lattice parameter (a) = edge length of the cube

• Relationship between atomic radius (r) and lattice parameter:

$$a = 2\sqrt{2} r$$

Coordination Number

Coordination number = Number of nearest neighbor atoms surrounding a central atom.

• In FCC → 12

• Each atom is surrounded by 12 nearest neighbors, making FCC metals more ductile.

Atomic Packing Factor (APF)

APF = Fraction of volume occupied by atoms in the unit cell.

For FCC:

APF = \frac{\text{Volume of atoms in cell}}{\text{Volume of unit cell}} = 0.74 \text{ (74%)}

FCC metals are densely packed, which contributes to high ductility and malleability.

Examples of FCC Metals

Common FCC metals include:

• Aluminium (Al)

• Copper (Cu)

• Nickel (Ni)

• Gold (Au)

• Silver (Ag)

Characteristics of FCC Metals

• High ductility and malleability

• High packing efficiency (74%)

• Good electrical and thermal conductivity

• Slip systems → 12 (more slip planes → easier deformation)

• Generally moderate to high strength

Importance in Engineering

• Aluminium and Copper → electrical wiring and heat exchangers

• Nickel, Gold, Silver → chemical-resistant components and electronics

• FCC metals are easier to form, roll, and draw compared to BCC metals.

FCC structure explains why these metals are preferred for ductile and formable engineering applications.

Exam-Focused Points

• FCC has 8 corner atoms + 6 face atoms → total 4 atoms/unit cell.

• Coordination number = 12

• Atomic Packing Factor = 74%

• Lattice parameter: a = 2√2 r

• Common FCC metals: Al, Cu, Ni, Au, Ag

• Properties: highly ductile, closely packed, good conductivity

Common Exam Traps

• Confusing FCC and BCC in terms of atoms per unit cell and packing efficiency.

• Forgetting coordination number = 12 for FCC.

• Using wrong formula for lattice parameter.

• Assuming FCC metals are brittle (they are ductile).

Example Competitive Exam Questions

How many atoms are present in an FCC unit cell?
Answer — 4 atoms.

What is the coordination number of FCC?
Answer — 12.

Packing efficiency of FCC structure?
Answer — 74%.

Relation between atomic radius (r) and lattice parameter (a) in FCC?
Answer — a = 2√2 r

Give an example of FCC metal.
Answer — Aluminium, Copper, Nickel.

Quick Revision

• FCC = 8 corner atoms + 6 face atoms → 4 atoms/unit cell

• Coordination number = 12

• Atomic Packing Factor = 74%

• Lattice parameter: a = 2√2 r

• Common FCC metals: Al, Cu, Ni, Au, Ag

• Properties: highly ductile, closely packed, easy to form