Crystallography: BCC, FCC, and HCP Structures

Crystallography

• Crystallography is the study of the arrangement of atoms in solids.
• The majority of stable elements are metallic.
• Of the metallic elements, the majority (68) have one of three common structures: body-centered cubic (BCC), face-centered cubic (FCC), and hexagonal close-packed (HCP).

Structures of Common Materials

• BCC, FCC, and HCP are simple crystal structures.

Lattice Constant and Atomic Radius

• A table lists the lattice constant (a and c) and atomic radius for various metals in BCC, FCC and HCP structures.

The Body-centered Cubic (BCC) Structure

• BCC has a non-primitive cubic unit cell with one lattice point at each corner and one at the center of the unit cell.
• 21 metallic elements have this structure (mostly rare earths).
• BCC metals are ductile when hot, allowing them to be rolled or shaped by deformation processing.
• BCC metals are tough and resist crack propagation.
• BCC metals become brittle at low temperatures.
• Strength of BCC metals depends on temperature.
• BCC metals can be hardened with interstitial solutes.

The Face-centered Cubic (FCC) Structure

• FCC is a non-primitive cubic unit cell with one lattice point at each corner and one at the center of each face.
• 17 metallic elements have this structure.
• FCC metals are very ductile when pure and can be rolled or shaped by deformation processing.
• FCC metals are tough and resist crack propagation.
• FCC metals retain their ductility and toughness to absolute zero.

Hexagonal Close Packed (HCP) Structure

• HCP structure refers to layers of spheres packed so that spheres in alternating layers overlie one another.
• HCP is a slip system, which is a close-packed structure.
• HCP is very common for elemental metals like Beryllium, Cadmium, Magnesium, Titanium, Zinc, Zirconium.
• HCP structure is elastic.

Coordination Number

• Coordination number (CN) is the number of nearest neighbors of a central atom or ion.
• The CN of a BCC crystal is 8.
• The body-centered atom is in contact with all the eight corner atoms.
• The CN in FCC is 12.
• In the FCC lattice, each atom is in contact with 12 neighboring atoms.
• The center atom of the top face in the hexagonal lattice is in touch with six corner atoms, three atoms of the mid-layer and other three atoms of the mid-layer of the unit cell above it.

The Number of Lattice Points Per Cell

• Atoms inside the cell share 1 atom.
• Atoms on faces are shared with 1/2 atom.
• Atoms on edges are share with 1/4 atom.
• Atoms in corners are shared with 1/8 atom.
• The total number of lattice points per cell is given by: N = Ni + (Nf/2) + (Nc/8). N₁ being the number of interior points, Nf being the number of faces and Nc being the number of corners.

Atomic Packing Factor (APF)

• APF, or packing efficiency, measures the fraction of the unit cell volume occupied by atoms.
• APF for a simple cubic structure is approximately 0.52.
• APF for BCC is about 0.68.
• APF for FCC is about 0.74.
• APF for HCP is about 0.74.

Structure-Property Correlation

• The crystal structure of a metal affects its mechanical properties, such as ductility and strength.
• The slip system of a metal plays a role in its ductility.