Crystallography: BCC, FCC, and HCP Structures

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Questions and Answers

What defines the body-centered cubic (BCC) structure?

The BCC structure has a lattice point at each corner and one at the center of the unit cell.

How many metallic elements exhibit the BCC structure?

21 metallic elements have the BCC structure.

What is a characteristic of BCC metals at low temperatures?

BCC metals become brittle at low temperatures.

Describe the face-centered cubic (FCC) structure.

The FCC structure has lattice points at each corner and one at the center of each face. Signup and view all the answers

How many metallic elements have the FCC structure?

17 metallic elements exhibit the FCC structure. Signup and view all the answers

What metals commonly exhibit the hexagonal close packed (HCP) structure?

Metals such as Beryllium, Magnesium, and Titanium commonly have the HCP structure. Signup and view all the answers

What is the coordination number of the BCC crystal structure?

The coordination number of BCC crystals is 8. Signup and view all the answers

What allows FCC metals to retain toughness to absolute zero?

FCC metals have a unique arrangement that allows them to maintain ductility and toughness at low temperatures. Signup and view all the answers

What is the coordination number for atoms in an FCC lattice?

The coordination number for atoms in an FCC lattice is 12. Signup and view all the answers

How does the coordination number in a hexagonal lattice compare to that of the FCC lattice?

The coordination number in a hexagonal lattice is also 12, just like in the FCC lattice. Signup and view all the answers

How many atom points does each corner atom contribute in a unit cell?

Each corner atom contributes 1/8 of an atom to a unit cell. Signup and view all the answers

What is the atomic packing factor (APF) for close-packed structures like FCC and HCP?

The atomic packing factor for FCC and HCP is 0.74, or 74%. Signup and view all the answers

What is the significance of close-packed planes in crystal structures?

Close-packed planes are significant because they allow slip to occur easily in the crystal structure. Signup and view all the answers

Why is aluminium (Al) considered ductile while iron (Fe) and magnesium (Mg) are not?

Aluminium is ductile because it has an FCC structure, while iron has a BCC structure and magnesium has an HCP structure. Signup and view all the answers

What are the lattice points contributed by atoms on faces and edges within a unit cell?

Atoms on faces contribute 1/2 to the unit cell, and atoms on edges contribute 1/4. Signup and view all the answers

Which planes in the FCC lattice are classified as close-packed?

The {111} planes are classified as close-packed in the FCC lattice. Signup and view all the answers

Study Notes

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.

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Description

Explore the fascinating world of crystallography through this quiz focusing on body-centered cubic (BCC), face-centered cubic (FCC), and hexagonal close-packed (HCP) structures. Understand the arrangement of metallic elements and their properties within different crystal lattices. Test your knowledge on lattice constants and atomic radii of various metals.